Chapter 2.3, Problem 2.28PP

Program Plan Intro

Unsigned negation:

The unsigned negation is represented by “${\text{-}}_{\text{w}}^{\text{u}}$”

For any number “x” such that $\text{0 }\le \text{ x <}{\text{2}}^{\text{w}}$, its “w-bit” unsigned negation is denoted by below formula 

${\text{-}}_{\text{w}}^{\text{u}}\text{x = }\left\{\begin{array}{l}\text{x, x = 0}\\ {\text{2}}^{\text{w}}\text{ - x, x > 0}\end{array}\right\}$

From the above equation,

• When “x” is “0”, then its unsigned negation value is “0”.
• When “x > 0”, then its unsigned negation value is “2^w – x”.

Example:

The example for unsigned negation is shown below:

Here assume bit length, “w” is “4”.

Case 1: consider the value of “x” is “0”, then ${\text{-}}_4^{\text{u}}\text{0 = 0}$.

Case 2: consider the value of “x” is “6” that is “x > 0”. So, compute the unsigned negation by using ${\text{-}}_{\text{w}}^{\text{u}}{\text{x = 2}}^{\text{w}}\text{ - x}$

$\begin{array}{l}{\text{-}}_4^{\text{u}}\text{6 }{\text{= 2}}^4\text{ - 6}\\ \text{ = 16 - 6}\\ \text{ = 10}\end{array}$

Therefore, ${\text{-}}_4^{\text{u}}\text{6 = 10}$

Table for corresponding hexadecimal and binary value:

Hex digit	0	1	2	3	4	5	6	7
Decimal value	0	1	2	3	4	5	6	7
Hex digit	8	9	A	B	C	D	E	F
Decimal value	8	9	10	11	12	13	14	15