pyqm-week1/notebooks/pyqm-1.3-binary-operations.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "2d2c4c5d",
   "metadata": {
    "cell_id": "00000-31dea6ce-9329-4002-9119-14cd7e5b8162",
    "deepnote_cell_type": "markdown",
    "id": "ZBt4X2XzK2DF"
   },
   "source": [
    "<center>\n",
    "    \n",
    "# Python For Quantum Mechanics\n",
    "# Week 1: Binary Operations\n",
    "    \n",
    "</center>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "1e89ed96",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/jpeg": 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\n",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"700\"\n",
       "            height=\"400\"\n",
       "            src=\"https://www.youtube.com/embed/dMw8E-8cQpc\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x10dc8cf40>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import YouTubeVideo\n",
    "YouTubeVideo('dMw8E-8cQpc',width=700, height=400)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ec7d0fbd",
   "metadata": {},
   "source": [
    "## Overview of Binary\n",
    "Why does 9 come berfore 10? It might seem like a silly question but the answer is that that is how humans have decided to write numbers. That is that after ten numbers (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) we increase the ten's digit by one. What if instead we chose to do so after just two numbers; that is we start with 0 and then go to 1 but then take 10, and then 11. After that we will have 100 and then 101 and so on. This is known as binary and it is how computers ultimately work with data.\n",
    "\n",
    "| Number in base 10 (decimal) | Number in base 2 (binary) |\n",
    "| :-: | :-: |\n",
    "| 0 | 0 |\n",
    "| 1 | 1 |\n",
    "| 2 | 10 |\n",
    "| 3 | 11 |\n",
    "| 4 | 100 |\n",
    "| 5 | 101 |\n",
    "| 6 | 110 |\n",
    "| 7 | 111 |\n",
    "| 8 | 1000 |\n",
    "| 9 | 1001 |\n",
    "| 10 | 1010 |\n",
    "| 11 | 1011 |\n",
    "| 12 | 1100 |\n",
    "| 13 | 1101 |\n",
    "| 14 | 1110 |\n",
    "| 15 | 1111 |\n",
    "\n",
    "Base 10 (or decimal) is what we are most used to and that can be thought of in the following way\n",
    "$$\\begin{equation}\n",
    "\\begin{split}\n",
    "1503 &= 1\\times 1000 + 5\\times 100 + 0\\times 10 + 3\\times 1 \\\\\n",
    "&= 1\\times 10^3 + 5\\times 10^2 + 0\\times 10^1 + 3\\times 10^0 \\\\\n",
    "\\end{split}\n",
    "\\end{equation}$$\n",
    "so we can read off the digits 1503. Binary numbers can be thought of in a similar way\n",
    "$$ 1010_{\\text(binary)} = 1\\times 2^3 + 0\\times 2^2 + 1\\times 2^1 + 0\\times 2^0 = 10_\\text{(decimal)}$$\n",
    "An alternate method is diagramed below where multiple divisions are performed and the remainders are recorded.\n",
    "<img src=\"images/binary.png\" alt=\"two dice\" width=\"400\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "519dfde3",
   "metadata": {
    "cell_id": "00002-abcb1236-0cfa-4956-803f-72b1e1abf4a2",
    "deepnote_cell_type": "markdown",
    "id": "ivxpNC_ie465"
   },
   "source": [
    "We can cast numbers into binary using the `bin()` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f7ead03d",
   "metadata": {
    "cell_id": "00003-180091b3-b4e2-4466-8617-3f13c82c1283",
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "deepnote_cell_type": "code",
    "executionInfo": {
     "elapsed": 371,
     "status": "ok",
     "timestamp": 1624445371441,
     "user": {
      "displayName": "Sean Courtney",
      "photoUrl": "",
      "userId": "17219612104113445790"
     },
     "user_tz": -60
    },
    "id": "OyzNFaZ4e2gl",
    "outputId": "fb425149-6eb3-43b1-bdf0-20851156d23e"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0b10010010\n"
     ]
    }
   ],
   "source": [
    "print(bin(146))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "823eea12",
   "metadata": {
    "cell_id": "00004-06288b89-004b-4454-8260-de5821473a69",
    "deepnote_cell_type": "markdown",
    "id": "dmi_85rNfaM4"
   },
   "source": [
    "Here the `0b` tells us we are in binary."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c27ebeb8",
   "metadata": {
    "cell_id": "00005-0afc3e67-866f-46b0-9e78-271c8668bd9d",
    "deepnote_cell_type": "markdown",
    "id": "9e97e34d"
   },
   "source": [
    "## Bitwise Operators\n",
    "\n",
    "There is multiple bitwise operators we can use in Python, namely the AND `&`, OR `|`, NOT `~`, and XOR `^`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2f2525a0",
   "metadata": {
    "cell_id": "00006-2e8efd59-21c5-4326-9a4c-fbefd03e5994",
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "deepnote_cell_type": "code",
    "executionInfo": {
     "elapsed": 5,
     "status": "ok",
     "timestamp": 1624439984778,
     "user": {
      "displayName": "Sean Courtney",
      "photoUrl": "",
      "userId": "17219612104113445790"
     },
     "user_tz": -60
    },
    "id": "6bfe7008",
    "outputId": "395955a8-8c77-4ae6-f9aa-569df3682e8d"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a & b =  0\n",
      "a | b =  15\n",
      "~ b =  -6\n",
      "a ^ b =  15\n"
     ]
    }
   ],
   "source": [
    "a = 10 # 1010\n",
    "b = 5 #  0101\n",
    "\n",
    "print(\"a & b = \", a & b) #Returns 1 if both bits are 1, otherwise returns 0\n",
    "\n",
    "\n",
    "print(\"a | b = \", a | b) #Returns 1 if either bits are 1, otherwise returns 0\n",
    "\n",
    "\n",
    "print(\"~ b = \", ~b) #Returns the compliment of the number: -(0101 + 0001) = - 6\n",
    "\n",
    "print(\"a ^ b = \", a ^ b) #Returns 1 if one bit is 1 and the other is 0, otherwise returns 0"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "033312fd",
   "metadata": {
    "cell_id": "00007-d122362b-4d6a-4558-9ad8-e76aa52d8f88",
    "deepnote_cell_type": "markdown",
    "id": "8dd50afd"
   },
   "source": [
    "## Shift Operators\n",
    "\n",
    "There is also the right `>>` and left `<<` shift operators. The shift operators have the effect of multiplying or dividing the number by 2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6024eede",
   "metadata": {
    "cell_id": "00008-10e53afd-3cb2-4dbd-9df5-56c108720719",
    "deepnote_cell_type": "code",
    "id": "50e3ac41",
    "outputId": "986ba4a8-7188-4fce-c426-f9e1f4c71438"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a >> 1 =  5\n",
      "a >> 2 =  2\n",
      "a << 1 =  20\n",
      "a << 2 =  40\n"
     ]
    }
   ],
   "source": [
    "a = 10 # 1010\n",
    "\n",
    "print(\"a >> 1 = \",a >> 1) # 1010 >> 1 = 0101 = 5\n",
    "print(\"a >> 2 = \",a >> 2) # 1010 >> 2 = 0010 = 2\n",
    "\n",
    "print(\"a << 1 = \",a << 1) # 1010 << 1 = 10100 = 20 \n",
    "print(\"a << 2 = \",a << 2) # 1010 << 2 = 101000 = 40 "
   ]
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [],
   "name": "PyQM_1.4_Binary_Operations.ipynb",
   "provenance": []
  },
  "deepnote": {},
  "deepnote_execution_queue": [],
  "deepnote_notebook_id": "d692ff9e-31fe-48f5-be2f-cd81f3adbd70",
  "kernelspec": {
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