Binary and Bitwise Ops

The Idea

Bitwise operators work lane by lane, with no carries between lanes. & keeps a 1 only where both sides have one, | where either does, ^ where they differ.

~ flips every lane. Shifts slide the whole row: << doubles, >> halves.

Real-World Example

File permissions are nine bits wide: read, write and execute for owner, group and others. chmod 644 is literally a number, and the kernel answers "may this process write?" with a single AND against a mask — no lookup, no branch.

The Code

a, b = 12, 10           # 0b1100 and 0b1010
print(bin(a), bin(b))   # 0b1100 0b1010
print(a & b)            # 8  -> 1 only where both are 1
print(a | b)            # 14 -> 1 where either is 1
print(a ^ b)            # 6  -> 1 only where they differ
print(~a)               # -13 -> flips every bit, sign included
print(a << 1)           # 24 -> shifting left doubles
print(a >> 2)           # 3  -> shifting right halves, twice

x = 5          # 0b101
y = 3          # 0b011
print(x & y, x | y, x ^ y)