Design a $4-$bit adder$-$subtractor using the minimum number of full adders and any additional necessary logic gates. The circuit has a mode input $M$ that controls its operation. Specifically, when $M=0,$ the circuit becomes a $4-$bit adder and when $M=1,$ the circuit becomes a $4-$bit subtractor. Specifically, consider A$,$ B are two $4-$bits binary numbers, then:

When $M=0,$ we perform $A+B,$ and we assume that both numbers are unsigned numbers. So$,$ the maximum sum value will be $15($since we are assuming A and $B$ are $4-$bit numbers$).$

When $M=1,$ we perform $A-B$ as follows:

$A+(B{)}_2$ 'Eomplement

That is$,$ we find first the $2\text{'}$s complement of B then adds it to A$.$ Hence, here the answer of the operation A$-$B is expressed in $2\text{'}$s complement representation.

German$-$Jordanian University

School of Electrical Engineering and Information Technology Department of Computer Engineering

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German Jordanian University

Note: in the lab use the IC number $74$LS$83$ to implement the $4-$bit adder$-$subtractor. The $74$LS$83$ is a high$-$speed $4-$Bit binary Full Adder with internal carry lookahead. It accepts two $4-$bit binary words $($A$1-$ A$4,$ B$1-$ B$4)$ and a Carry Input $($C$0).$ It generates the binary Sum outputs ${\displaystyle \underset{?}{\overset{?}{}}}1-{\displaystyle \underset{?}{\overset{?}{}}}4)$ and the Carry Output $($C$4)$ from the most significant bit.

CONNFCTION MIAGRAM IIP $($TOP VIFIN$)$