Chapter 2.2, Problem 2.20PP

Program Plan Intro

“T2U” function:

• The function “T2U” means conversion of “Two’s complement to unsigned” with “w” length bits.
• From the above equation, first convert the two’s complement to binary and then convert the binary to unsigned.
• The equation “2.5” is

${\text{T2U}}_{\text{w}}\left(\text{x}\right)\text{=}\left\{\begin{array}{l}\text{x}\text{+}{\text{2}}^{\text{w}}\text{,}\text{x}\text{<}\text{0}\\ \text{x}\text{,}\text{x}\ge \text{0}\end{array}\right\}$

• From the above equation,
  • When “x < 0” that is “x” is negative, then “${\text{T2U}}_{\text{w}}\left(\text{x}\right)\text{=}\text{x}\text{+}{\text{2}}^{\text{w}}$”.
  • When “x ≥ 0” that is “x” is nonnegative, then “${\text{T2U}}_{\text{w}}\left(\text{x}\right)\text{=}\text{x}$”.

Example:

The example of “T2U_w” is shown below:

Consider value of “x” is “-6” and bit length “w” is “4”.

Here, the value of “x” is negative that is “x < 0”. So, ${\text{T2U}}_{\text{w}}\left(\text{x}\right)\text{=}\text{x}\text{+}{\text{2}}^{\text{w}}$

$\begin{array}{l}{\text{T2U}}_4\left(\text{-6}\right)\text{=}\text{-6}\text{+}{\text{2}}^{\text{4}}\\ \text{=}\text{-6}\text{+}\text{16}\\ \text{=}\text{10}\end{array}$

Therefore, ${\text{T2U}}_{\text{4}}\left(\text{-6}\right)\text{=}\text{10}$