{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1. Bits, Data Types, and Operations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For today's class, we will work in small groups (two or three). One of you, open a blank notebook, and the others should close their laptops. We will trade-off typing as we go."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.1 Representing Signed Integers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Three representations of signed integers:\n",
    "\n",
    "<img src=\"Figure2-1.png\" width=\"500\"/>\n",
    "\n",
    "Q1: What is unusual about two of the columns? There is a number there that you don't usually see."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.2 Signed Magnitude"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Q2: What is 11111 + 01111 ?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.3 One's Complement"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Q3: What is 10000 + 01111 ?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.4 Two's Complement"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Q4: Work out by hand: What is 10001 + 01111 ?\n",
    "\n",
    "Q5: Work out by hand: What is the two's complement for -13?\n",
    "\n",
    "Q6: Work out by hand: What is the two's complement for -57 ?\n",
    "\n",
    "Q7: Using the LC-3, compute the following:\n",
    "\n",
    "* a: 8 + -7\n",
    "* b: 5 + 5\n",
    "* c: -5 + -5\n",
    "* d: -15 + 15\n",
    "* e: -8 + 1\n",
    "* f: -15 + -1\n",
    "* g: -16 + -1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.5 Binary to Decimal Conversion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "NOTE: All binary will be in two's complement.\n",
    "\n",
    "Q8: Work out by hand: convert 01000 to decimal\n",
    "\n",
    "Q9: Work out by hand: convert 11000 to decimal\n",
    "\n",
    "Q10: Work out by hand: convert 11111 to decimal\n",
    "\n",
    "Q11: Work out by hand: convert 111111111 to decimal\n",
    "\n",
    "Q12: Work out by hand: convert 000001000 to decimal"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.6 Decimal to Binary Conversion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Q13: Convert decimal 105 to binary\n",
    "\n",
    "Q14: Convert decimal -105 to binary\n",
    "\n",
    "Q15: convert decimal 99 to binary\n",
    "\n",
    "Q16: convert decimal -14 to binary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.7 Additional Additions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Explore the patterns of adding any two numbers to itself. Try positive and negative numbers. \n",
    "\n",
    "Q17: Do you see a pattern? Describe it."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. Logical Operations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Two new instructions:\n",
    "\n",
    "Bitwise AND and NOT (16 bits each):\n",
    "\n",
    "```\n",
    "AND: 0101 DST SRC 1 VVVVV\n",
    "NOT: 1001 DST SRC 111111\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "where:\n",
    "\n",
    "* DST - destination register, in three bits\n",
    "* SRC - source register, in three bits\n",
    "* VVVVV - value to AND with source register contents\n",
    "\n",
    "Q18: Write out the truth tables for AND and NOT.\n",
    "\n",
    "Q19: Write out the truth tables for OR and XOR\n",
    "\n",
    "Q20: Try out the AND and NOT instructions on the LC-3. Do they work as described?"
   ]
  }
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