Masks and Power of Two

The Idea

A mask is a number whose 1s mark the lanes you care about. 1 << i builds the mask for a single position.

From there: OR sets a bit, AND with the inverted mask clears it, XOR flips it, and shifting right then ANDing 1 reads it. n & (n - 1) == 0 says n has at most one bit set.

Real-World Example

Feature flags ship as one integer. "Dark mode on, beta search off" is a single OR and a single AND — one field in the database instead of forty boolean columns, and the check costs one instruction on the request path.

The Code

def get_bit(x, i):   return (x >> i) & 1
def set_bit(x, i):   return x | (1 << i)
def clear_bit(x, i): return x & ~(1 << i)
def flip_bit(x, i):  return x ^ (1 << i)

x = 0b1011                   # 11
print(get_bit(x, 2))         # 0
print(bin(set_bit(x, 2)))    # 0b1111
print(bin(clear_bit(x, 0)))  # 0b1010
print(bin(flip_bit(x, 3)))   # 0b11

def is_power_of_two(n):
    return n > 0 and n & (n - 1) == 0   # exactly one bit set

print(is_power_of_two(16), is_power_of_two(12))   # True False

x = 0b1010
x = x | (1 << 0)
x = x & ~(1 << 3)
print(bin(x))