bit manipulation

Binary numbers:

$${\left(a_k{a}_{k-1}\dots a_1{a}_0\right)}_2=a_k\cdot 2^k+a_{k-1}\cdot 2^{k-1}+\cdots +a_1\cdot 2^1+a_0\cdot 2^0$$

$\&$  : AND operator.

• 1 if both are 1. 0 otherwise.

$|$  : inclusive OR operator.

• 1 if one or both of the two bits = 1. 0 otherwise.

$\wedge$  : exclusive OR (XOR) operator.

• 1 if only one of the bits = 1. 0 otherwise.
• called exclusive because it excludes the case where both bits are 1.

$\sim$  : complement (NOT) operator

• flips each bit of a number