https://github.com/tentaclepurple/42_ready_set_boole

Boolean algrebra training
https://github.com/tentaclepurple/42_ready_set_boole

mathematics python

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Boolean algrebra training

• Host: GitHub
• URL: https://github.com/tentaclepurple/42_ready_set_boole
• Owner: tentaclepurple
• Created: 2025-01-15T14:15:35.000Z (26 days ago)
• Default Branch: main
• Last Pushed: 2025-01-26T01:07:22.000Z (16 days ago)
• Last Synced: 2025-01-26T02:26:16.795Z (16 days ago)
• Topics: mathematics, python
• Language: Python
• Homepage:
• Size: 32.2 KB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
## Logic Gates and Bitwise Operators

Operator     Symbol   Description                              Example (`5 & 3`)           

-----------------------------------------------------------------------------------------

AND           `&`     1 if both bits are 1                     `0101 & 0011 → 0001 (1)`    

OR            `|`     1 if at least one bit is 1               `0101 | 0011 → 0111 (7)`    

XOR           `^`     1 if bits are different                  `0101 ^ 0011 → 0110 (6)`    

NOT           `~`     Flips all bits (one's complement)        `~0101 → -0110 (-6)`      

Left Shift    `<<`    Shifts bits left, filling with 0         `0101 << 1 → 1010 (10)`   

Right Shift   `>>`    Shifts bits right, dropping right bits   `0101 >> 1 → 0010 (2)`   

## Adder

a + b

5 (0101) + 3 (0011)

- First Iteration

Calculate no_carry:

a ^ b = 0101 ^ 0011 = 0110 (this is like adding without carries).

Calculate carry: (a & b) << 1:

0101 & 0011 = 0001

0001 << 1 = 0010

Update:

a = 0110 (no_carry)

b = 0010 (carry) 

- Second Iteration (b != 0)

a ^ b = 0110 ^ 0010 = 0100

(a & b) << 1 

0110 & 0010 = 0010

0010 << 1 = 0100

Update:

a = 0100

b = 0100 

- Third Iteration (b != 0)

a ^ b = 0100 ^ 0100 = 0

(a & b) << 1 

0100 & 0100 = 0100

0100 << 1 = 1000

Update:

a = 0000

b = 1000 

- Fourth Iteration (b != 0)

a ^ b = 0000 ^ 1000 = 1000

(a & b) << 1 

0000 & 1000 = 0000

0010 << 1 = 0000

Update:

a = 1000

b = 0 

- Result

1000 = 8

## Multiplier

Init:

a = 5 (101)

b = 3 (011)

result = 0

First iteration:

- b & 1 = 011 & 001 = 1 (last bit is 1)

- result = 0 + 101 = 101

- a = 101 << 1 = 1010

- b = 011 >> 1 = 001

Second iteration:

- b & 1 = 001 & 001 = 1 (last bit is1)

- result = 101 + 1010 = 1111

- a = 1010 << 1 = 10100

- b = 001 >> 1 = 000

Third iteration:

- b is 0, finish

- result = 1111 (15)