{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "0af62e9f",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Big Number Conversion"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d780ee8",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    },
    "tags": [
     "remove-cell"
    ]
   },
   "source": [
    "**CS1302 Introduction to Computer Programming**\n",
    "___"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "5c484b36",
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import floor, log2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "45363c7e",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Conversion to Decimal"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2d0b6cc0",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "In this notebook, we will use iterations to convert numbers with arbitrary size."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dda6a986",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Binary-to-Decimal"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f5d167f3",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "In a previous lab, we considered converting a byte string to decimal. What about converting a binary string of arbitrary length to decimal?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "18784aaa",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "````{prf:definition} Binary numbers\n",
    "\n",
    "Given a binary string of an arbitrarily length $k$,\n",
    "\n",
    "$$ \n",
    "b_{k-1}\\circ \\dots \\circ b_1\\circ b_0,\n",
    "$$\n",
    "the decimal number is given by the formula\n",
    "\n",
    "$$\n",
    "2^0 \\cdot b_0 + 2^1 \\cdot b_1 + \\dots + 2^{k-1} \\cdot b_{k-1}.\n",
    "$$ (b2d:1)\n",
    "\n",
    "````"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1a4eaba1",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "In mathematics, we use the summation notation to write the above formula {eq}`b2d:1`:\n",
    "\n",
    "$$ \n",
    "\\sum_{i=0}^{k-1} 2^i \\cdot b_{i}.\n",
    "$$ (b2d:2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "524a2f4a",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "In a program, the formula can be implemented as a for loop:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "27dabb4b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def binary_to_decimal_v1(binary_str):\n",
    "    k = len(binary_str)\n",
    "    decimal = 0  # initialization\n",
    "    for i in range(k):\n",
    "        decimal += 2 ** i * int(binary_str[(k - 1) - i])  # iteration\n",
    "    return decimal"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c631fe61",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Note that $b_i$ is given by `binary_str[(k-1)-i]` for different index `i` as shown below:\n",
    "\n",
    "$$\n",
    "\\begin{array}{c|c:c:c:c|}\\texttt{binary_str} & b_{k-1} & b_{k-2} & \\dots & b_0\\\\ \\text{indexing} & [0] & [1] & \\dots & [k-1] \\end{array}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "60fccfa3",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "The following is another way to write the for loop."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "b83dc8f1",
   "metadata": {},
   "outputs": [],
   "source": [
    "def binary_to_decimal_v2(binary_str):\n",
    "    decimal = 0  # initialization\n",
    "    for bit in binary_str:\n",
    "        decimal = decimal * 2 + int(bit)  # iteration\n",
    "    return decimal"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0b0c44c6",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The algorithm implements the same formula factorized as follows:\n",
    "\n",
    "$$\n",
    "\\begin{aligned} \\sum_{i=0}^{k-1} 2^i \\cdot b_{i} \n",
    "&=  \\left(\\sum_{i=1}^{k-1} 2^i \\cdot b_{i}\\right) + b_0\\\\\n",
    "&=  \\left(\\sum_{i=1}^{k-1} 2^{i-1} \\cdot b_{i}\\right)\\times 2 + b_0 \\\\\n",
    "&=  \\left(\\sum_{j=0}^{k-2} 2^{j} \\cdot b_{j+1}\\right)\\times 2 + b_0 && \\text{with $j=i-1$} \\\\\n",
    "&= \\underbrace{(\\dots (\\underbrace{(\\underbrace{\\overbrace{0}^{\\text{initialization}\\kern-2em}\\times 2 + b_{k-1}}_{\\text{first iteration} }) \\times 2 + b_{k-2}}_{\\text{second iteration} }) \\dots )\\times 2 + b_0}_{\\text{last iteration} }.\\end{aligned}\n",
    "$$ (b2d:3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f15d242",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "**Exercise** Write your own converter `binary_to_decimal` below. Make it as efficient as possible."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b73572eb",
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "f1e194aff055633aead3f89c8047a17a",
     "grade": false,
     "grade_id": "binary_to_decimal",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    },
    "slideshow": {
     "slide_type": "-"
    },
    "tags": [
     "remove-output"
    ]
   },
   "outputs": [],
   "source": [
    "def binary_to_decimal(binary_str):\n",
    "    # YOUR CODE HERE\n",
    "    raise NotImplementedError()\n",
    "    return decimal"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "29e03709",
   "metadata": {},
   "source": [
    "````{hint}\n",
    "\n",
    "You can choose one of the two implementations above but take the time to type in the code instead of copy-and-paste.\n",
    "\n",
    "````"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "6c916325",
   "metadata": {
    "code_folding": [
     0
    ],
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "91fc75df3ab7d19f958f9c774d809914",
     "grade": true,
     "grade_id": "test-binary_to_decimal",
     "locked": true,
     "points": 1,
     "schema_version": 3,
     "solution": false,
     "task": false
    },
    "slideshow": {
     "slide_type": "-"
    },
    "tags": [
     "hide-input",
     "remove-output"
    ]
   },
   "outputs": [
    {
     "ename": "NotImplementedError",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNotImplementedError\u001b[0m                       Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-5-b6ba04170964>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     11\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     12\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 13\u001b[0;31m \u001b[0mtest_binary_to_decimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"0\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     14\u001b[0m \u001b[0mtest_binary_to_decimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m255\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"11111111\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     15\u001b[0m \u001b[0mtest_binary_to_decimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m52154\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"1100101110111010\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-5-b6ba04170964>\u001b[0m in \u001b[0;36mtest_binary_to_decimal\u001b[0;34m(decimal, binary_str)\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mtest_binary_to_decimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdecimal\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbinary_str\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 6\u001b[0;31m     \u001b[0mdecimal_\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mbinary_to_decimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbinary_str\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      7\u001b[0m     \u001b[0mcorrect\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdecimal_\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mint\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mdecimal_\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mdecimal\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      8\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mcorrect\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-4-7c9ca5fd1066>\u001b[0m in \u001b[0;36mbinary_to_decimal\u001b[0;34m(binary_str)\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mbinary_to_decimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbinary_str\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m     \u001b[0;31m# YOUR CODE HERE\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m     \u001b[0;32mraise\u001b[0m \u001b[0mNotImplementedError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      4\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mdecimal\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNotImplementedError\u001b[0m: "
     ]
    }
   ],
   "source": [
    "# tests\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "def test_binary_to_decimal(decimal, binary_str):\n",
    "    decimal_ = binary_to_decimal(binary_str)\n",
    "    correct = isinstance(decimal_, int) and decimal_ == decimal\n",
    "    if not correct:\n",
    "        print(f\"{binary_str} should give {decimal} not {decimal_}.\")\n",
    "    assert correct\n",
    "\n",
    "\n",
    "test_binary_to_decimal(0, \"0\")\n",
    "test_binary_to_decimal(255, \"11111111\")\n",
    "test_binary_to_decimal(52154, \"1100101110111010\")\n",
    "test_binary_to_decimal(3430, \"110101100110\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "30af2bd1",
   "metadata": {
    "code_folding": [
     0
    ],
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "4021762033790ce89b1b10c76cbe7dae",
     "grade": true,
     "grade_id": "hidden_test-binary_to_decimal",
     "locked": true,
     "points": 1,
     "schema_version": 3,
     "solution": false,
     "task": false
    },
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [],
   "source": [
    "# hidden tests"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "1ca89ec3",
   "metadata": {
    "code_folding": [
     0
    ],
    "slideshow": {
     "slide_type": "-"
    },
    "tags": [
     "remove-output"
    ]
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "aefb1e67616b4fc485e083336432f8d0",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(Text(value='1011', description='binary_str'), Output()), _dom_classes=('widget-interact'…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# binary-to-decimal converter\n",
    "from ipywidgets import interact\n",
    "\n",
    "bits = [\"0\", \"1\"]\n",
    "\n",
    "\n",
    "@interact(binary_str=\"1011\")\n",
    "def convert_byte_to_decimal(binary_str):\n",
    "    for bit in binary_str:\n",
    "        if bit not in bits:\n",
    "            print(\"Not a binary string.\")\n",
    "            break\n",
    "    else:\n",
    "        print(\"decimal:\", binary_to_decimal(binary_str))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f384b93e",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Undecimal-to-Decimal"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ffd423fb",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "A base-11 number system is called an [undecimal system](https://en.wikipedia.org/wiki/Undecimal). The digits range from 0 to 10 with 10 denoted as X:\n",
    "\n",
    "$$\n",
    "0, 1, 2, 3, 4, 5, 6, 7, 8, 9, X.\n",
    "$$\n",
    "\n",
    "The [International Standard Book Number (ISBN)](https://en.wikipedia.org/wiki/International_Standard_Book_Number) uses an undecimal digit."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "11c7c742",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "**Exercise** In the following code, assign to `decimal` the integer represented by an undecimal string of arbitrary length."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fd85e0dc",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "````{hint}\n",
    "\n",
    "Write a conditional to \n",
    "1. check if a digit is (capital) `'X'`, and if so, \n",
    "2. convert the digit to the integer value 10.\n",
    "\n",
    "````"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "2f67b38f",
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "55bbfbe8143ad30f684efd927989183e",
     "grade": false,
     "grade_id": "undecimal_to_decimal",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    },
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": [
     "remove-output"
    ]
   },
   "outputs": [],
   "source": [
    "def undecimal_to_decimal(undecimal_str):\n",
    "    # YOUR CODE HERE\n",
    "    raise NotImplementedError()\n",
    "    return decimal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "acf91182",
   "metadata": {
    "code_folding": [
     0
    ],
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "af19b56f1f1c98807e67e6ab8829606a",
     "grade": true,
     "grade_id": "test-undecimal_to_decimal",
     "locked": true,
     "points": 1,
     "schema_version": 3,
     "solution": false,
     "task": false
    },
    "slideshow": {
     "slide_type": "-"
    },
    "tags": [
     "hide-input",
     "remove-output"
    ]
   },
   "outputs": [
    {
     "ename": "NotImplementedError",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNotImplementedError\u001b[0m                       Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-9-e00222cfe0b9>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      8\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      9\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 10\u001b[0;31m \u001b[0mtest_undecimal_to_decimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m27558279079916281\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"6662X0X584839464\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     11\u001b[0m \u001b[0mtest_undecimal_to_decimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m23022771839270\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"73769X2556695\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     12\u001b[0m \u001b[0mtest_undecimal_to_decimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m161804347284488\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"476129248X2067\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-9-e00222cfe0b9>\u001b[0m in \u001b[0;36mtest_undecimal_to_decimal\u001b[0;34m(decimal, undecimal_str)\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;31m# tests\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mtest_undecimal_to_decimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdecimal\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mundecimal_str\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m     \u001b[0mdecimal_\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mundecimal_to_decimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mundecimal_str\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      4\u001b[0m     \u001b[0mcorrect\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdecimal_\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mint\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mdecimal_\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mdecimal\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mcorrect\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-8-a21c011ebdff>\u001b[0m in \u001b[0;36mundecimal_to_decimal\u001b[0;34m(undecimal_str)\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mundecimal_to_decimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mundecimal_str\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m     \u001b[0;31m# YOUR CODE HERE\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m     \u001b[0;32mraise\u001b[0m \u001b[0mNotImplementedError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      4\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mdecimal\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNotImplementedError\u001b[0m: "
     ]
    }
   ],
   "source": [
    "# tests\n",
    "def test_undecimal_to_decimal(decimal, undecimal_str):\n",
    "    decimal_ = undecimal_to_decimal(undecimal_str)\n",
    "    correct = isinstance(decimal_, int) and decimal_ == decimal\n",
    "    if not correct:\n",
    "        print(f\"{undecimal_str} should give {decimal} not {decimal_}.\")\n",
    "    assert correct\n",
    "\n",
    "\n",
    "test_undecimal_to_decimal(27558279079916281, \"6662X0X584839464\")\n",
    "test_undecimal_to_decimal(23022771839270, \"73769X2556695\")\n",
    "test_undecimal_to_decimal(161804347284488, \"476129248X2067\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "85c7da77",
   "metadata": {
    "code_folding": [
     0
    ],
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "da072224351c55417d95cad1736e15af",
     "grade": true,
     "grade_id": "hidden_test-undecimal_to_decimal",
     "locked": true,
     "points": 1,
     "schema_version": 3,
     "solution": false,
     "task": false
    },
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [],
   "source": [
    "# hidden tests"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "d5100bb0",
   "metadata": {
    "code_folding": [
     0
    ],
    "slideshow": {
     "slide_type": "-"
    },
    "tags": [
     "remove-output"
    ]
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "1aa044f59e65418d940fa9245d6367c8",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(Text(value='X', description='undecimal_str'), Output()), _dom_classes=('widget-interact'…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# undecimal-to-decimal calculator\n",
    "from ipywidgets import interact\n",
    "\n",
    "undecimal_digits = [str(i) for i in range(10)] + [\"X\"]\n",
    "\n",
    "\n",
    "@interact(undecimal_str=\"X\")\n",
    "def convert_undecimal_to_decimal(undecimal_str):\n",
    "    for digit in undecimal_str:\n",
    "        if digit not in undecimal_digits:\n",
    "            print(\"Not an undecimal string.\")\n",
    "            break\n",
    "    else:\n",
    "        print(\"decimal:\", undecimal_to_decimal(undecimal_str))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ec27f1aa",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Conversion from Decimal"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "326acb91",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Consider the reverse process that converts a non-negative decimal number of arbitrary size to a string representation in another number system."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c1a6e00",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Decimal-to-Binary"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6bc3bb2f",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "The following code converts a decimal number to a binary string."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0326411c",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "```Python\n",
    "def decimal_to_binary(decimal):\n",
    "    binary_str = str(decimal % 2)\n",
    "    while decimal // 2:\n",
    "        decimal //= 2\n",
    "        binary_str = str(decimal % 2) + binary_str\n",
    "    return binary_str\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46f51715",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "To understand the while loop, consider the same formula {eq}`b2d:3`, where the braces indicate the value of `decimal` at different times:\n",
    "\n",
    "$$\n",
    "\\begin{aligned} \\sum_{i=0}^{k-1} 2^i \\cdot b_{i} &=  \\left(\\sum_{i=0}^{k-2} 2^{i-2} \\cdot b_{i-1}\\right)\\times 2 + b_0 \\\\\n",
    "&= \\underbrace{(\\underbrace{ \\dots (\\underbrace{(0\\times 2 + b_{k-1}) \\times 2 + b_{k-2}}_{\\text{right before the last iteration} }  )\\times 2 \\dots + b_1}_{\\text{right before the second iteration} })\\times 2 + b_0}_{\\text{right before the first iteration} }.\\end{aligned}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "82b5a053",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- $b_0$ is the remainder `decimal % 2` right before the first iteration,\n",
    "- $b_1$ is the remainder `decimal // 2 % 2` right before the second iteration, and\n",
    "- $b_{k-1}$ is the remainder `decimal // 2 % 2` right before the last iteration."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "26c9e05e",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We can also write a for loop instead of a while loop:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "0e1702f9",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "def decimal_to_binary(decimal):\n",
    "    binary_str = \"\"\n",
    "    num_bits = 1 + (decimal and floor(log2(decimal)))\n",
    "    for i in range(num_bits):\n",
    "        binary_str = str(decimal % 2) + binary_str\n",
    "        decimal //= 2\n",
    "    return binary_str"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "f4082f66",
   "metadata": {
    "code_folding": [
     0
    ],
    "slideshow": {
     "slide_type": "-"
    },
    "tags": [
     "remove-output"
    ]
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "399f895b70ee46948318a49d7f3e8ea7",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(Text(value='11', description='decimal'), Output()), _dom_classes=('widget-interact',))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# decimal-to-binary calculator\n",
    "@interact(decimal=\"11\")\n",
    "def convert_decimal_to_binary(decimal):\n",
    "    if not decimal.isdigit():\n",
    "        print(\"Not a non-negative integer.\")\n",
    "    else:\n",
    "        print(\"binary:\", decimal_to_binary(int(decimal)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "06aaa601",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "**Exercise** Explain what the expression `1 + (decimal and floor(log2(decimal)))` calculates. In particular, explain the purpose of the logical `and` operation in the expression?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "03df0d05",
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "12d1969b35591f01fcf2478d720b06aa",
     "grade": true,
     "grade_id": "number-of-bits",
     "locked": false,
     "points": 1,
     "schema_version": 3,
     "solution": true,
     "task": false
    },
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "YOUR ANSWER HERE"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2b1a4ee6",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Decimal-to-Undecimal"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c995cf3f",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "**Exercise** Assign to `undecimal_str` the undecimal string that represents a non-negative integer `decimal` of any size."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "3841bde8",
   "metadata": {
    "code_folding": [
     0
    ],
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "701b02e9f4258346bf3709536abd9661",
     "grade": false,
     "grade_id": "decimal_to_undecimal",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    },
    "slideshow": {
     "slide_type": "-"
    },
    "tags": [
     "remove-output"
    ]
   },
   "outputs": [],
   "source": [
    "def decimal_to_undecimal(decimal):\n",
    "    # YOUR CODE HERE\n",
    "    raise NotImplementedError()\n",
    "    return undecimal_str"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "53fc90c1",
   "metadata": {
    "code_folding": [
     0
    ],
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "af7198d1334cca1f1b3e7cbef25622e4",
     "grade": true,
     "grade_id": "test-decimal_to_undecimal",
     "locked": true,
     "points": 1,
     "schema_version": 3,
     "solution": false,
     "task": false
    },
    "slideshow": {
     "slide_type": "-"
    },
    "tags": [
     "hide-input",
     "remove-output"
    ]
   },
   "outputs": [
    {
     "ename": "NotImplementedError",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNotImplementedError\u001b[0m                       Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-15-4abedf727c79>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     10\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     11\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 12\u001b[0;31m \u001b[0mtest_decimal_to_undecimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"X\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m10\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     13\u001b[0m \u001b[0mtest_decimal_to_undecimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"0\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     14\u001b[0m \u001b[0mtest_decimal_to_undecimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"1752572309X478\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m57983478668530\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-15-4abedf727c79>\u001b[0m in \u001b[0;36mtest_decimal_to_undecimal\u001b[0;34m(undecimal, decimal)\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;31m# tests\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mtest_decimal_to_undecimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mundecimal\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdecimal\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m     \u001b[0mundecimal_\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdecimal_to_undecimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdecimal\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      4\u001b[0m     \u001b[0mcorrect\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mundecimal\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstr\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mundecimal\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mundecimal_\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mcorrect\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-14-244977b69def>\u001b[0m in \u001b[0;36mdecimal_to_undecimal\u001b[0;34m(decimal)\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mdecimal_to_undecimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdecimal\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m     \u001b[0;31m# YOUR CODE HERE\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m     \u001b[0;32mraise\u001b[0m \u001b[0mNotImplementedError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      4\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mundecimal_str\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNotImplementedError\u001b[0m: "
     ]
    }
   ],
   "source": [
    "# tests\n",
    "def test_decimal_to_undecimal(undecimal, decimal):\n",
    "    undecimal_ = decimal_to_undecimal(decimal)\n",
    "    correct = isinstance(undecimal, str) and undecimal == undecimal_\n",
    "    if not correct:\n",
    "        print(\n",
    "            f\"{decimal} should be represented as the undecimal string {undecimal}, not {undecimal_}.\"\n",
    "        )\n",
    "    assert correct\n",
    "\n",
    "\n",
    "test_decimal_to_undecimal(\"X\", 10)\n",
    "test_decimal_to_undecimal(\"0\", 0)\n",
    "test_decimal_to_undecimal(\"1752572309X478\", 57983478668530)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "b7069a4b",
   "metadata": {
    "code_folding": [
     0
    ],
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "e824531a2ae5e3112d2cb45ea8a244d2",
     "grade": true,
     "grade_id": "hidden_test-decimal_to_undecimal",
     "locked": true,
     "points": 1,
     "schema_version": 3,
     "solution": false,
     "task": false
    },
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [],
   "source": [
    "# hidden tests"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "1563a08f",
   "metadata": {
    "code_folding": [
     0
    ],
    "slideshow": {
     "slide_type": "-"
    },
    "tags": [
     "remove-output"
    ]
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "5f6eb9522adb4072b1c1229120003264",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(Text(value='10', description='decimal'), Output()), _dom_classes=('widget-interact',))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# undecimal-to-decimal calculator\n",
    "from ipywidgets import interact\n",
    "\n",
    "\n",
    "@interact(decimal=\"10\")\n",
    "def convert_decimal_to_undecimal(decimal):\n",
    "    if not decimal.isdigit():\n",
    "        print(\"Not a non-negative integer.\")\n",
    "    else:\n",
    "        print(\"undecimal:\", decimal_to_undecimal(int(decimal)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "108d8227",
   "metadata": {},
   "source": [
    "## Timer (Optional)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f28483d6",
   "metadata": {},
   "source": [
    "### Benchmark"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "65f01203",
   "metadata": {},
   "source": [
    "Recall the two versions of binary-to-decimal converters defined at the beginning of the lab:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "1907679b",
   "metadata": {},
   "outputs": [],
   "source": [
    "binary_to_decimal_v1??"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "2f817883",
   "metadata": {},
   "outputs": [],
   "source": [
    "binary_to_decimal_v2??"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b6e0dc3e",
   "metadata": {},
   "source": [
    "**How to compare their speed?**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aea6bd1a",
   "metadata": {},
   "source": [
    "We can use the [time](https://docs.python.org/3/library/time.html) module."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "749ae181",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "time.struct_time(tm_year=2021, tm_mon=11, tm_mday=19, tm_hour=12, tm_min=9, tm_sec=26, tm_wday=4, tm_yday=323, tm_isdst=0)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import time\n",
    "\n",
    "time.localtime()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "85279fca",
   "metadata": {},
   "source": [
    "We can also [format](https://docs.python.org/3/library/time.html#time.strftime) the current [local time](https://docs.python.org/3/library/time.html#time.localtime) to a more easily readable string:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "325a2c68",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Fri, 19 Nov 2021 12:09:26'"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "time.strftime(\"%a, %d %b %Y %H:%M:%S\", time.localtime())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d58e4312",
   "metadata": {},
   "source": [
    "**How to implement a timer?**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b868994c",
   "metadata": {},
   "source": [
    "The idea is to record the start time and end time, and then compute their difference:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "ebb9c4b5",
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "unsupported operand type(s) for -: 'time.struct_time' and 'time.struct_time'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-22-d4f1c4d1fdf3>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      2\u001b[0m  \u001b[0;31m# code to be timed\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0mend\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtime\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlocaltime\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m \u001b[0mend\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mstart\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m: unsupported operand type(s) for -: 'time.struct_time' and 'time.struct_time'"
     ]
    }
   ],
   "source": [
    "start = time.localtime()\n",
    "...  # code to be timed\n",
    "end = time.localtime()\n",
    "end - start"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d7aa1def",
   "metadata": {},
   "source": [
    "Unfortunately, the above code fails because `-` is note defined for the time object `time.struct_time`."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "83c76a51",
   "metadata": {},
   "source": [
    "**How to compute the difference in time?**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e743b614",
   "metadata": {},
   "source": [
    "Instead of implementing `-` for `time.struct_time`, a simpler solution is to use [`time.time()`](https://docs.python.org/3/library/time.html#time.time), which returns the current time as a floating point number."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "d705ca8c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1637294966.3099682"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "time.time()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "83d2b6db",
   "metadata": {},
   "source": [
    "This is the number of *seconds* elapsed after certain [epoch](https://docs.python.org/3/library/time.html#epoch) (a point in time). For linux/unix, the `time` module uses the [unix epoch](https://en.wikipedia.org/wiki/Unix_time), which is January 1, 1970, 00:00:00 ([UTC](https://en.wikipedia.org/wiki/Coordinated_Universal_Time)):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "50924df4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Thu, 01 Jan 1970 00:00:00 +0000 '"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "time.strftime(\n",
    "    \"%a, %d %b %Y %H:%M:%S +0000 \", time.gmtime(0)\n",
    ")  # Convert zero seconds to UTC time"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0731553c",
   "metadata": {},
   "source": [
    "The following code implements the timer:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "3a1f3d3d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def time_b2d(binary_to_decimal, binary_str):\n",
    "    \"\"\"Return the time in secs for running binary_to_decimal on binary_str.\"\"\"\n",
    "    start = time.time()\n",
    "    decimal = binary_to_decimal(binary_str)\n",
    "    end = time.time()\n",
    "    return end - start"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "43b9d5ef",
   "metadata": {},
   "source": [
    "In the following, `t1` and `t2` keeps the time it takes for `binary_to_decimal_v1` and `binary_to_decimal_v2` to run on the same input byte `binary_str`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "d1897ec0",
   "metadata": {
    "tags": [
     "remove-output"
    ]
   },
   "outputs": [
    {
     "ename": "StdinNotImplementedError",
     "evalue": "raw_input was called, but this frontend does not support input requests.",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mStdinNotImplementedError\u001b[0m                  Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-26-9b2e83455a58>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0;32mif\u001b[0m \u001b[0minput\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Ready? [Y/n]\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlower\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0;34m\"n\"\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m     \u001b[0mbinary_str\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m\"1\"\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0;36m8\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m     \u001b[0mt1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtime_b2d\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbinary_to_decimal_v1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbinary_str\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m     \u001b[0mt2\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtime_b2d\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbinary_to_decimal_v2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbinary_str\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m     \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34mf\"t1 = {t1:.3g}s\\nt2 = {t2:.3g}s\\nt1/t2 = {t1/t2:.3g}\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/my-conda-envs/jb/lib/python3.8/site-packages/ipykernel/kernelbase.py\u001b[0m in \u001b[0;36mraw_input\u001b[0;34m(self, prompt)\u001b[0m\n\u001b[1;32m    843\u001b[0m         \"\"\"\n\u001b[1;32m    844\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_allow_stdin\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 845\u001b[0;31m             raise StdinNotImplementedError(\n\u001b[0m\u001b[1;32m    846\u001b[0m                 \u001b[0;34m\"raw_input was called, but this frontend does not support input requests.\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    847\u001b[0m             )\n",
      "\u001b[0;31mStdinNotImplementedError\u001b[0m: raw_input was called, but this frontend does not support input requests."
     ]
    }
   ],
   "source": [
    "if input(\"Ready? [Y/n]\").lower() != \"n\":\n",
    "    binary_str = \"1\" * 8\n",
    "    t1 = time_b2d(binary_to_decimal_v1, binary_str)\n",
    "    t2 = time_b2d(binary_to_decimal_v2, binary_str)\n",
    "    print(f\"t1 = {t1:.3g}s\\nt2 = {t2:.3g}s\\nt1/t2 = {t1/t2:.3g}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fd8b0dfd",
   "metadata": {},
   "source": [
    "**Exercise** (Optional) Observe the difference in speeds for longer `binary_str`, e.g., with `binary_str = '1' * 100000`. Is the ratio `t1/t2` of the running times roughly the same regardless of the input length?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bb0c3e2a",
   "metadata": {},
   "source": [
    "There can be variations in the running time due to many factors. To measure the typical performance, we should run the code multiple times and report the total or average running time. The following is the modified timer:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "99d7ddf5",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def time_b2d(binary_to_decimal, binary_str, n_iters):\n",
    "    \"\"\"Return the time in secs for running binary_to_decimal on binary_str.\"\"\"\n",
    "    start = time.time()\n",
    "    for i in range(n_iters):\n",
    "        decimal = binary_to_decimal(binary_str)\n",
    "    end = time.time()\n",
    "    return end - start"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "815d5721",
   "metadata": {},
   "source": [
    "To compare:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "b75ac294",
   "metadata": {
    "tags": [
     "remove-output"
    ]
   },
   "outputs": [
    {
     "ename": "StdinNotImplementedError",
     "evalue": "raw_input was called, but this frontend does not support input requests.",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mStdinNotImplementedError\u001b[0m                  Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-28-1121c87c56be>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0;32mif\u001b[0m \u001b[0minput\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Ready? [Y/n]\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlower\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0;34m\"n\"\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m     \u001b[0mbinary_str\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m\"1\"\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0;36m8\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m     \u001b[0mn_iters\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m100\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m     \u001b[0mt1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtime_b2d\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbinary_to_decimal_v1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbinary_str\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mn_iters\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m     \u001b[0mt2\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtime_b2d\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbinary_to_decimal_v2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbinary_str\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mn_iters\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/my-conda-envs/jb/lib/python3.8/site-packages/ipykernel/kernelbase.py\u001b[0m in \u001b[0;36mraw_input\u001b[0;34m(self, prompt)\u001b[0m\n\u001b[1;32m    843\u001b[0m         \"\"\"\n\u001b[1;32m    844\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_allow_stdin\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 845\u001b[0;31m             raise StdinNotImplementedError(\n\u001b[0m\u001b[1;32m    846\u001b[0m                 \u001b[0;34m\"raw_input was called, but this frontend does not support input requests.\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    847\u001b[0m             )\n",
      "\u001b[0;31mStdinNotImplementedError\u001b[0m: raw_input was called, but this frontend does not support input requests."
     ]
    }
   ],
   "source": [
    "if input(\"Ready? [Y/n]\").lower() != \"n\":\n",
    "    binary_str = \"1\" * 8\n",
    "    n_iters = 100\n",
    "    t1 = time_b2d(binary_to_decimal_v1, binary_str, n_iters)\n",
    "    t2 = time_b2d(binary_to_decimal_v2, binary_str, n_iters)\n",
    "    print(f\"t1 = {t1:.3g}s\\nt2 = {t2:.3g}s\\nt1/t2 = {t1/t2:.3g}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5219d2fa",
   "metadata": {},
   "source": [
    "**Exercise** (Optional) Increase the number of iterations until you get can a variation in `t1/t2` less than 0.2 in two consecutive runs most of the time."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d456ba46",
   "metadata": {},
   "source": [
    "Indeed, IPython has a [built-in magic](https://ipython.readthedocs.io/en/stable/interactive/magics.html#magic-timeit) to time an execution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "0cfb423c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.52 µs ± 15.2 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "binary_to_decimal_v1(\"1\" * 8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "151c20ce",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "966 ns ± 4.76 ns per loop (mean ± std. dev. of 7 runs, 1000000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "binary_to_decimal_v2(\"1\" * 8)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e2f7e106",
   "metadata": {},
   "source": [
    "Note that the numbers of loops are decided automatically."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b11e6749",
   "metadata": {},
   "source": [
    "### Alarm clock"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "33e3d512",
   "metadata": {},
   "source": [
    "**How to set an alarm in python to go off after certain time?**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "53b5775b",
   "metadata": {},
   "source": [
    "We can write a loop like the following:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "4b38fba5",
   "metadata": {
    "tags": [
     "remove-output"
    ]
   },
   "outputs": [
    {
     "ename": "StdinNotImplementedError",
     "evalue": "raw_input was called, but this frontend does not support input requests.",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mStdinNotImplementedError\u001b[0m                  Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-31-708e92f85bf2>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mduration\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0minput\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"How many seconds to wait?\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0mstart\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtime\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtime\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0;32mwhile\u001b[0m \u001b[0mtime\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtime\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mstart\u001b[0m \u001b[0;34m<=\u001b[0m \u001b[0mduration\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m     \u001b[0;32mpass\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Time's up!\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/my-conda-envs/jb/lib/python3.8/site-packages/ipykernel/kernelbase.py\u001b[0m in \u001b[0;36mraw_input\u001b[0;34m(self, prompt)\u001b[0m\n\u001b[1;32m    843\u001b[0m         \"\"\"\n\u001b[1;32m    844\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_allow_stdin\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 845\u001b[0;31m             raise StdinNotImplementedError(\n\u001b[0m\u001b[1;32m    846\u001b[0m                 \u001b[0;34m\"raw_input was called, but this frontend does not support input requests.\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    847\u001b[0m             )\n",
      "\u001b[0;31mStdinNotImplementedError\u001b[0m: raw_input was called, but this frontend does not support input requests."
     ]
    }
   ],
   "source": [
    "duration = int(input(\"How many seconds to wait?\"))\n",
    "start = time.time()\n",
    "while time.time() - start <= duration:\n",
    "    pass\n",
    "print(\"Time's up!\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e5c83721",
   "metadata": {},
   "source": [
    "A simpler way is to use `time.sleep`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "2432c9fb",
   "metadata": {
    "tags": [
     "remove-output"
    ]
   },
   "outputs": [
    {
     "ename": "StdinNotImplementedError",
     "evalue": "raw_input was called, but this frontend does not support input requests.",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mStdinNotImplementedError\u001b[0m                  Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-32-9a88e5a3675f>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mtime\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msleep\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0minput\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"How many seconds to wait?\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0mget_ipython\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun_line_magic\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'pinfo'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'time.sleep'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/my-conda-envs/jb/lib/python3.8/site-packages/ipykernel/kernelbase.py\u001b[0m in \u001b[0;36mraw_input\u001b[0;34m(self, prompt)\u001b[0m\n\u001b[1;32m    843\u001b[0m         \"\"\"\n\u001b[1;32m    844\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_allow_stdin\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 845\u001b[0;31m             raise StdinNotImplementedError(\n\u001b[0m\u001b[1;32m    846\u001b[0m                 \u001b[0;34m\"raw_input was called, but this frontend does not support input requests.\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    847\u001b[0m             )\n",
      "\u001b[0;31mStdinNotImplementedError\u001b[0m: raw_input was called, but this frontend does not support input requests."
     ]
    }
   ],
   "source": [
    "time.sleep(int(input(\"How many seconds to wait?\")))\n",
    "time.sleep?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e2e1a27c",
   "metadata": {},
   "source": [
    "**How to play a sound when time is up?**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "670f644c",
   "metadata": {},
   "source": [
    "To play a beep sound in jupyter notebook, we can use the `jupyter_beeper` module:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "ad5025d6",
   "metadata": {
    "tags": [
     "remove-output"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/html": [],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import jupyter_beeper\n",
    "\n",
    "beeper = jupyter_beeper.Beeper()\n",
    "\n",
    "\n",
    "def alarm(seconds):\n",
    "    time.sleep(seconds)\n",
    "    beeper.beep()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "59cee997",
   "metadata": {},
   "source": [
    "To set the alarm to 3 seconds after now:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "5d92aa23",
   "metadata": {
    "tags": [
     "remove-output"
    ]
   },
   "outputs": [
    {
     "ename": "StdinNotImplementedError",
     "evalue": "raw_input was called, but this frontend does not support input requests.",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mStdinNotImplementedError\u001b[0m                  Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-34-fcec62133e63>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0malarm\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0minput\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"How many seconds to wait?\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m~/my-conda-envs/jb/lib/python3.8/site-packages/ipykernel/kernelbase.py\u001b[0m in \u001b[0;36mraw_input\u001b[0;34m(self, prompt)\u001b[0m\n\u001b[1;32m    843\u001b[0m         \"\"\"\n\u001b[1;32m    844\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_allow_stdin\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 845\u001b[0;31m             raise StdinNotImplementedError(\n\u001b[0m\u001b[1;32m    846\u001b[0m                 \u001b[0;34m\"raw_input was called, but this frontend does not support input requests.\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    847\u001b[0m             )\n",
      "\u001b[0;31mStdinNotImplementedError\u001b[0m: raw_input was called, but this frontend does not support input requests."
     ]
    }
   ],
   "source": [
    "alarm(int(input(\"How many seconds to wait?\")))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7a0b3fd4",
   "metadata": {},
   "source": [
    "Notice that the alarm is blocking the execution. To avoid that, we need to run it as a [thread](https://docs.python.org/3/library/threading.html):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "0c0386ad",
   "metadata": {},
   "outputs": [],
   "source": [
    "import threading\n",
    "\n",
    "\n",
    "def background_alarm(seconds):\n",
    "    threading.Thread(target=alarm, args=(seconds,)).start()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d48ee605",
   "metadata": {},
   "source": [
    "To set two alarms simultaneously:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "ebc3186b",
   "metadata": {
    "tags": [
     "remove-output"
    ]
   },
   "outputs": [
    {
     "ename": "StdinNotImplementedError",
     "evalue": "raw_input was called, but this frontend does not support input requests.",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mStdinNotImplementedError\u001b[0m                  Traceback (most recent call last)",
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          "\u001b[0;32m~/my-conda-envs/jb/lib/python3.8/site-packages/ipywidgets/widgets/interaction.py\u001b[0m in \u001b[0;36mupdate\u001b[0;34m(self, *args)\u001b[0m\n\u001b[1;32m    254\u001b[0m                     \u001b[0mvalue\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mwidget\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_interact_value\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    255\u001b[0m                     \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mwidget\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_kwarg\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mvalue\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 256\u001b[0;31m                 \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mresult\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    257\u001b[0m                 \u001b[0mshow_inline_matplotlib_plots\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    258\u001b[0m                 \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mauto_display\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mresult\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
          "\u001b[0;32m<ipython-input-7-81c96c71ef4e>\u001b[0m in \u001b[0;36mconvert_byte_to_decimal\u001b[0;34m(binary_str)\u001b[0m\n\u001b[1;32m     12\u001b[0m             \u001b[0;32mbreak\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     13\u001b[0m     \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 14\u001b[0;31m         \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"decimal:\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbinary_to_decimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbinary_str\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
          "\u001b[0;32m<ipython-input-4-7c9ca5fd1066>\u001b[0m in \u001b[0;36mbinary_to_decimal\u001b[0;34m(binary_str)\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mbinary_to_decimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbinary_str\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m     \u001b[0;31m# YOUR CODE HERE\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m     \u001b[0;32mraise\u001b[0m \u001b[0mNotImplementedError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      4\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mdecimal\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
          "\u001b[0;31mNotImplementedError\u001b[0m: "
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          "\u001b[0;31mNotImplementedError\u001b[0m                       Traceback (most recent call last)",
          "\u001b[0;32m~/my-conda-envs/jb/lib/python3.8/site-packages/ipywidgets/widgets/interaction.py\u001b[0m in \u001b[0;36mupdate\u001b[0;34m(self, *args)\u001b[0m\n\u001b[1;32m    254\u001b[0m                     \u001b[0mvalue\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mwidget\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_interact_value\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    255\u001b[0m                     \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mwidget\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_kwarg\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mvalue\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 256\u001b[0;31m                 \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mresult\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    257\u001b[0m                 \u001b[0mshow_inline_matplotlib_plots\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    258\u001b[0m                 \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mauto_display\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mresult\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
          "\u001b[0;32m<ipython-input-11-8b8d3053af48>\u001b[0m in \u001b[0;36mconvert_undecimal_to_decimal\u001b[0;34m(undecimal_str)\u001b[0m\n\u001b[1;32m     12\u001b[0m             \u001b[0;32mbreak\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     13\u001b[0m     \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 14\u001b[0;31m         \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"decimal:\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mundecimal_to_decimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mundecimal_str\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
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          "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
          "\u001b[0;31mNotImplementedError\u001b[0m                       Traceback (most recent call last)",
          "\u001b[0;32m~/my-conda-envs/jb/lib/python3.8/site-packages/ipywidgets/widgets/interaction.py\u001b[0m in \u001b[0;36mupdate\u001b[0;34m(self, *args)\u001b[0m\n\u001b[1;32m    254\u001b[0m                     \u001b[0mvalue\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mwidget\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_interact_value\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    255\u001b[0m                     \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mwidget\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_kwarg\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mvalue\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 256\u001b[0;31m                 \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mresult\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    257\u001b[0m                 \u001b[0mshow_inline_matplotlib_plots\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    258\u001b[0m                 \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mauto_display\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mresult\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
          "\u001b[0;32m<ipython-input-17-3672dc29221b>\u001b[0m in \u001b[0;36mconvert_decimal_to_undecimal\u001b[0;34m(decimal)\u001b[0m\n\u001b[1;32m      8\u001b[0m         \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Not a non-negative integer.\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      9\u001b[0m     \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 10\u001b[0;31m         \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"undecimal:\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdecimal_to_undecimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdecimal\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
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