ctci/05. Bit manipulation

Chapter 5. Bit manipulation

5.1. Two's complement and negative numbers

Positive numbers are represented as themselves, negative numbers as the two's complement of its absolute value, with a 1 in its sign bit, indicating it's negative.

The two's complement of an N-bit number (N: # bits used for the number, excluding the sign bit), is the complement of the number with respect to 2^N.

The binary representation of -K as a N-bit number is concat(1, 2^N-1 - K).

5.2. Arithmetic vs. Logical right shift

Arithmetic right shift: division by two. Logical right shift: 'shifting the bits'.

5.2.1. Logical shift

Indicated with a >>> operator, all bits are shifted, sign bit too.

• -75: 10110101
• 90: 01011010

5.2.2. Arithmetic shift

The sign bit is kept, and all bits (sign bit too) are shifted.

• -75: 10110101
• -38: 11011010

5.3. Common bit tasks: getting and setting