bitwise magic

[prosviriakova]

Binary Representation of Powers of 2:

Numbers that are powers of 2 have exactly one bit set to 1 in their binary representation.

Examples:

• 1 (2^0): 0001
• 2 (2^1): 0010
• 4 (2^2): 0100
• 8 (2^3): 1000

Subtracting 1 from a Power of 2:

When you subtract 1 from a power of 2, all bits after the single 1 bit are flipped.

Examples:

• 2 (0010) - 1 = 1 (0001)
• 4 (0100) - 1 = 3 (0011)
• 8 (1000) - 1 = 7 (0111)

Bitwise AND Operation:

The bitwise AND operation compares each bit of n and n-1:

If n is a power of 2:

The result of n & (n - 1) is 0 because there are no overlapping 1 bits.

Examples:

• 4 (0100) & 3 (0011) = 0000
• 8 (1000) & 7 (0111) = 0000

If n is not a power of 2:

The result of n & (n - 1) is not 0 because there are overlapping 1 bits.

Examples:

• 6 (0110) & 5 (0101) = 0100
• 10 (1010) & 9 (1001) = 1000