P3 4/21 Binary Overview

• Learning Objectives
  • DAT-1.A: Representing Data with Bits
    • Basic Information
    • Examples
  • DAT-1.B: The Consequences of Using Bits to Represent Data
    • Basic Information
    • Examples
  • DAT-1.C: Binary Math
    • Basic Information
    • Examples
• Hacks & Grading (Due SUNDAY NIGHT 4/23)

Learning Objectives

DAT-1.A: Representing Data with Bits

Basic Information

• Bit is short for __ digit, and represents a value of either 0 or 1.
  • A byte is 8 bits.
• Sequences of bits are used to represent different things.
  • Representing data with sequences of bits is called ___.

Examples

• Boolean variables (true or false) are the easiest way to visualize binary.
  • 0 = False
  • 1 = True

import random

def example(runs):
    # Repeat code for the amount of runs given
    while runs > 0:
        # Assigns variable boolean to either True or False based on random binary number 0 or 1.
        boolean = False if random.randint(0, 1) == 0 else True 

        # If the number was 1 (True), it prints "awesome."
        if boolean:
            print("binary is awesome")
            
        # If the number was 2 (False), it prints "cool."
        else:
            print("binary is cool")
            
        runs -= 1
     
# Change the parameter to how many times to run the function.   
example(10)

DAT-1.B: The Consequences of Using Bits to Represent Data

Basic Information

• Integers are represented by a fixed number of bits, this limits the range of integer values. This limitation can result in __ or other errors.
• Other programming languages allow for abstraction only limited by the computers memory.
• Fixed number of bits are used to represent real numbers/limits

Examples

import math

def exponent(base, power):
    # Print the operation performed, turning the parameters into strings to properly concatenate with the symbols "^" and "=".
    print(str(base) + "^" + str(power) + " = " + str(math.pow(base, power)))

# How can function become a problem? (Hint: what happens if you set both base and power equal to high numbers?)
exponent(5, 2)

DAT-1.C: Binary Math

Basic Information

• Binary is Base 2, meaning it can only represent values between 0 and 1.
• Decimal is Base 10, meaning it can represent from 0 to 9.
• Conversion between sequences of binary to decimal depend on how many binary numbers there are, their values and their positions.

Examples

• Using 6 bits, we can represent 64 numbers, from 0 to 63, as 2^6 = 64.
• The numbers in a sequence of binary go from right to left, increasing by powers of two from 0 to the total amount of bits. The whole number represented is the sum of these bits. For example:
  1. 111111
  2. 2^5 + 2^4 + 2^3 + 2^2 + 2^1 + 2^0
  3. 32 + 16 + 8 + 4 + 2 + 1
  4. 63
• Fill in the blanks (convert to decimal)
  1. 001010 = _
  2. 11100010 = _
  3. 10 = _

Hacks & Grading (Due SUNDAY NIGHT 4/23)

• Complete all of the popcorn hacks (Fill in the blanks + run code cells and interact) [0.2 or nothing]
• Create a program to conduct basic mathematical operations with binary sequences (addition, subtraction, multiplication, division) [0.7 or nothing]
  • For bonus, program must be able to conduct mathematical operations on binary sequences of varying bits (for example: 101 + 1001 would return decimal 14.) [0.1 or nothing]