Design an $8-$bit Adder$/$Subtractor with overflow detection using Full Adders. Assume the FA block is already available, so no need for a truth table and a k$-$map.

Use the following $8-$bit inputs $A=a_7{a}_6{a}_5{a}_4{a}_3{a}_2{a}_1{a}_0,B=b_7{b}_6{b}_5{b}_4{b}_3{b}_2{b}_1{b}_0,$ where A and B are the numbers to be added or subtracted, and a one bit input M to indicate the mode $($adder or subtractor$).$ In the case of subtraction, use A as the minuend and B is the subtrahend.

Use the following $8-$bit output $S=S_7{S}_6{S}_5{S}_4{S}_3{S}_2{S}_1{S}_0$ to indicate the sum result, and the one$-$bit output C for the final carry out, and the one$-$bit output V for overflow. $(74=21$ points$)$

In each of the following cases, determine the values of $S,C,$ and V :

a$)M=0,A=01110111,B=01100110$

b$)M=0,A=10001000,B=10011001$

c$)M=1,A=11001100,B=10001000$

d$)M=1,A=01010101,B=10101010$

e$)M=1,A=00000000,B=00010001$

f$)M=0,A=00111001,B=11010001$

g$)M=1,A=00111001,B=11010001$