Whether bit i is set. Independent yes/no facts map naturally to bit positions.

A bit is a labeled switch. The integer is merely the board holding those switches. Say what each position means before performing clever arithmetic.

What the function promises: Return mask membership, insertion, removal, and toggle results for a nonnegative mask and index.

def has_bit(mask, index): return bool(mask & (1 << index))
def add_bit(mask, index): return mask | (1 << index)
def remove_bit(mask, index): return mask & ~(1 << index)
def toggle_bit(mask, index): return mask ^ (1 << index)

mask = add_bit(0, 2)
assert has_bit(mask, 2) and not has_bit(mask, 1)
assert remove_bit(mask, 2) == 0
assert toggle_bit(toggle_bit(0, 4), 4) == 0

Work and storage: Each operation is O(1) in the fixed-machine-word model; arbitrary-precision Python cost grows with bit length.

When to recognize it: Independent yes/no facts map naturally to bit positions.

Check before applying it: Compact storage does not reduce the 2^n number of possible masks, and signed-width assumptions vary by language.

Use int.bit_count(), or repeatedly clear the lowest set bit with x &= x−1.