How to contact us

Join the "coding" channel on slack! That is the only place where we will be answering questions or sending announcements about lessons. If you have a question please contact us there.

How to join

  • Click on "add channels" below the list of channels
  • Click on "browse channels"
  • Search for "coding"
  • Click the green "Join" button on the right

Learning Objectives

CollegeBoard Requirements for Binary

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 ___.

Practice Questions:

  1. How many bits are in 3 bytes?

  2. What digital information can be represented by bits?

  3. Are bits an analog or digital form of storing data? What is the difference between the two?

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

Practice Questions:

  1. What is the largest number can be represented by 5 bits?

  2. One programing language can only use 16 bits to represent non-negative numbers, while a second language uses 56 bits to represent numbers. How many times as many unique numbers can be represented by the second language?

  3. 5 bits are used to represent both positive and negative numbers, what is the largest number that can be represented by these bits? (hint: different thatn question 1)

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

Practice Questions:

  1. What values can each digit of a Base 5 system represent?

  2. What base is Hexadecimal? What range of values can each digit of Hexadecimal represent?

  3. When using a base above 10, letters can be used to represent numbers past 9. These letters start from A and continue onwards. For example, the decimal number 10 is represented by the letter A in Hexadecimal. What letter would be used to represent the Base 10 number 23 in a Base 30 system? What about in a Base 50 system?

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 = _

  • Fill in the blanks (convert to binary)

    1. 12 = _
    2. 35 = _
    3. 256 = _

Hacks & Grading (Due SUNDAY NIGHT 4/23)

  • Complete all of the popcorn hacks (Fill in the blanks + run code cells and interact + Answer ALL questions) [0.3 or nothing]
  • Create a program to conduct basic mathematical operations with binary sequences (addition, subtraction, multiplication, division) [0.6 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]