P3-M 4/21 Binary Overview + Hacks
A series of binary lessons focused on math and conversions.
- How to contact us
- Learning Objectives
- Hacks & Grading (Due SUNDAY NIGHT 4/23)
- Math Program with Binary Hack
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
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?
- In 3 bytes there are 24 bits.
- What digital information can be represented by bits?
- data, numbers, etc can use bits to represent them
- Are bits an analog or digital form of storing data? What is the difference between the two?
- Bits are a digital form of storing data. Definition: "The difference between analog and digital technologies is that in analog technology, information is translated into electric pulses of varying amplitude. In digital technology, translation of information is into binary format (zero or one) where each bit is representative of two distinct amplitudes." #### 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 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?
- The largest number that can be represented by 5 bits is 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?
- 65,536 in a 16 bit and 2^56 in 56 bits.
- 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 than question 1)
- The first bit will be used to represent positive or negative, so it would be like a four bit number. The largest number is 15. #### 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(156, 257)
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:
- What values can each digit of a Base 5 system represent?
- Base 5 represents 5 digits in total
- What base is Hexadecimal? What range of values can each digit of Hexadecimal represent?
- Hexadecimal is base 16.
- 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?
- W in base 10, 23, 23 #### 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:
- 111111
- 2^5 + 2^4 + 2^3 + 2^2 + 2^1 + 2^0
- 32 + 16 + 8 + 4 + 2 + 1
- 63
-
Fill in the blanks (convert to decimal)
- 001010 = 2^1 + 2^3 = 10
- 11100010 = 2^1+2^6+2^7+2^8 = 226
- 10 = 2
-
Fill in the blanks (convert to binary)
- 12 = 1100
- 35 = 100011
- 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]
import math
x = int(input("Input your first number"))
y = int(input("Input your second number"))
smad = input("Input S for subtraction, M for multiplication, A for addition, or D for division")
def binary(n):
for i in range(5, -1, -1):
v = n >> i
if (v & 1):
print("1", end="")
else:
print("0", end="")
if smad == "S":
answer = (x - y)
print(x,"minus", y, "=", answer)
print(binary(answer))
elif smad == "M":
answer = (x * y)
print(x,"times", y, "=", answer)
print(binary(answer))
elif smad == "A":
answer = (x + y)
print(x,"plus", y, "=", answer)
print(binary(answer))
elif smad == "D":
answer = (x / y)
print(x,"divided by", y, "=", answer)
print(binary(answer))
else:
print("Please input letters S, M, A, or D")