Conversion between signed and unsigned integer

Conversion from two’s complement to unsigned

Assume an integer, $x$ , which is encoded in two’s complement form in a $w$ -bit word $x$ , such that $TM i n_{w} \leq x \leq TM a x_{w}$ , then the unsigned integer represented by the bit vector $x$ will be given by:

T 2 U_{w} (x) = {x + 2^{w}, x, x < 0 x \geq 0

For an unsigned integer $u$ such that $0 \leq u \leq U M a x_{w}$ represented by $u$ , the corresponding two’s complement integer is given by:

U 2 T_{w} (u) = {u, u - 2^{w}, u \leq TM a x_{w} u > TM a x_{w}