Bit Manipulation Basics

What is Bit Manipulation?

Operating on individual bits inside binary numbers.

You’ve already seen XOR. Here are the other common operations.

AND

Both bits must be 1 to get 1.

Only 1 AND 1 gives 1. Everything else is 0.

Example:

$1011 \land 1100 = 1000$

Compare each column. Both 1? Keep it. Otherwise, 0.

OR

Either bit being 1 gives 1.

Only 0 OR 0 gives 0. Everything else is 1.

Example:

$1011 \lor 1100 = 1111$

NOT

Flip every bit.

$\lnot 1011 = 0100$

1 becomes 0. 0 becomes 1.

Left Shift

Move all bits to the left. Fill the right with 0.

$1011 \ll 1 = 10110$

$1011 \ll 2 = 101100$

Each left shift multiplies by 2.

Right Shift

Move all bits to the right. Bits on the right fall off.

$1011 \gg 1 = 101$

$1011 \gg 2 = 10$

Each right shift divides by 2 (drops remainder).

Quick Reference