DESIGN PROBLEM

Absolute value of the difference. The operands and $B)$ are $4-$bit unsigned numbers. The operation is $x=|A-B|.$

This circuit can be built out of two $5-$bit adders, $5$ NOT gates, and $5$ XOR gates as depicted in the figure.

$,$ The output of the top $5-$bit adder is $R=A-B,$ where $R=r_4{r}_3{r}_2{r}_1{r}_0.$

a For this adder: cin $=1,$ cout is unused.

$,$ The output of the bottom $5-$bit adder is $x=|R|=|A-B|.$

For this adder: cin$=r_4,$ cout is unused.

Given the result $x=x_4{x}_3{x}_2{x}_1{x}_0,$ it can be demonstrated that $x_4=0.$ Thus, it is very common to only use $x_3{x}_2{x}_1{x}_0$ as the $4-$bit unsigned result of $x=|A-B|.$

The figure below depicts the internal architecture of the $4-$bit adder and the $5-$bit adder. The full adder $($FA$)$ circuit is also shown.