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 binary 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 abstraction.

Practice Questions:

How many bits are in 3 bytes?

24

What digital information can be represented by bits?

0 and 1

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

Digital since the data is only limited to 0 and 1.

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)

binary is awesome
binary is cool
binary is awesome
binary is cool
binary is cool
binary is cool
binary is awesome
binary is cool
binary is cool
binary is cool

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 overflow 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:

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

1 , 2 , 4 , 8 , 16 => 31

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?

2^(56-16)

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)

+- , 1 , 2 , 4 , 8 => 8

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)

5^2 = 25.0

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 each 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:

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

0 to 4

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

Hexadecimal is base 16. Each digit can represent 0 to 15.

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?

base 10 number 23: 9 + 9 + 5 => 599

base 30 number 23: N

base 50 number 23: N

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 = 10
2. 11100010 = 226
3. 10 = 2
Fill in the blanks (convert to binary)
1. 12 = 1100
2. 35 = 100011
3. 256 = 10000000

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]

req = input("Select an arithmetic operation (add, subtract, multiply, divide)")        # 

def operations(x, y):               # all operations defined in one function
    if req.lower() == 'add':        # .lower in case the user enters capitalized letters
        return bin(x + y)[2:]
    elif req.lower() == 'subtract':
        return bin(x - y)[2:] 
    elif req.lower() == 'multiply':
        return bin(x * y)[2:] 
    elif req.lower() == 'divide':
        return bin(x // y)[2:]      # '//' should be used instead of '/' for binary operations

if req.lower() in ['add', 'subtract', 'multiply', 'divide']:
    x = input("First binary number?")
    print("x =" , x)
    y = input("Second binary number?")
    print("y =" , y)
    x_int = int(x, 2)
    y_int = int(y, 2)
    result = operations(x_int, y_int)
    print("Result:", result)
else:                                # only accepts add, subtract, multiply, and divide
    print("Please select a valid operation. Operation'" , req , "' is not available.")

-"1001"-=>-"1110"" aria-hidden="true">Call 1: "Add" => "1001" => "1110"

req = input("Select an arithmetic operation (add, subtract, multiply, divide)")

def operations(x, y):
    if req.lower() == 'add':
        return bin(x + y)[2:]
    elif req.lower() == 'subtract':
        return bin(x - y)[2:] 
    elif req.lower() == 'multiply':
        return bin(x * y)[2:] 
    elif req.lower() == 'divide':
        return bin(x // y)[2:]

if req.lower() in ['add', 'subtract', 'multiply', 'divide']:
    x = input("First binary number?")
    print("x =" , x)
    y = input("Second binary number?")
    print("y =" , y)
    x_int = int(x, 2)
    y_int = int(y, 2)
    result = operations(x_int, y_int)
    print("Result:", result)
else:
    print("Please select a valid operation. Operation'" , req , "' is not available.")

x = 1001
y = 1110
Result: 10111

Code 2: Unvalid Operation "Remainder"

req = input("Select an arithmetic operation (add, subtract, multiply, divide)")

def operations(x, y):
    if req.lower() == 'add':
        return bin(x + y)[2:]
    elif req.lower() == 'subtract':
        return bin(x - y)[2:] 
    elif req.lower() == 'multiply':
        return bin(x * y)[2:] 
    elif req.lower() == 'divide':
        return bin(x // y)[2:]

if req.lower() in ['add', 'subtract', 'multiply', 'divide']:
    x = input("First binary number?")
    print("x =" , x)
    y = input("Second binary number?")
    print("y =" , y)
    x_int = int(x, 2)
    y_int = int(y, 2)
    result = operations(x_int, y_int)
    print("Result:", result)
else:
    print("Please select a valid operation. Operation'" , req , "' is not available.")

Please select a valid operation. Operation' Remainder ' is not available.