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Chapter 14: Bitwise operators

Examples

Bitwise operators

Bitwise operators perform operations on bit values of data. These operators convert operands to
signed 32-bit integers in two's complement.

Conversion to 32-bit integers

Numbers with more than 32 bits discard their most significant bits. For example, the following
integer with more than 32 bits is converted to a 32-bit integer:

Before: 10100110111110100000000010000011110001000001
After: 10100000000010000011110001000001

Two's Complement

In normal binary we find the binary value by adding the 1's based on their position as powers of 2 -
The rightmost bit being 2^0 to the leftmost bit being 2^n-1 where n is the number of bits. For
example, using 4 bits:

// Normal Binary
// 8 4 2 1
0 1 1 0 => 0 + 4 + 2 + 0 => 6

Two complement's format means that the number's negative counterpart (6 vs -6) is all the bits for
a number inverted, plus one. The inverted bits of 6 would be:

// Normal binary
0 1 1 0
// One's complement (all bits inverted)
1 0 0 1 => -8 + 0 + 0 + 1 => -7
// Two's complement (add 1 to one's complement)
1 0 1 0 => -8 + 0 + 2 + 0 => -6

Note: Adding more 1's to the left of a binary number does not change its value in two's
compliment. The value 1010 and 1111111111010 are both -6.

Bitwise AND

The bitwise AND operation a & b returns the binary value with a 1 where both binary operands
have 1's in a specific position, and 0 in all other positions. For example:

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