# (Solved): Design an 8-bit Adder/Subtractor with overflow detection using Full Adders. Assume the FA block is ...

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 $$\mathrm{A}=a_{7} a_{6} a_{5} a_{4} a_{3} a_{2} a_{1} a_{0}, \mathrm{~B}=b_{7} b_{6} b_{5} b_{4} b_{3} b_{2} b_{1} b_{0}$$, where $$\mathrm{A}$$ 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 $$\mathrm{A}$$ as the minuend and $$\mathrm{B}$$ is the subtrahend. Use the following 8-bit output $$\mathrm{S}=S_{7} S_{6} S_{5} S_{4} S_{3} S_{2} S_{1} S_{0}$$ to indicate the sum result, and the one-bit output $$\mathrm{C}$$ for the final carry out, and the one-bit output $$\mathrm{V}$$ for overflow. (30 points) In each of the following cases, determine the values of $$\mathrm{S}, \mathrm{C}$$, and $$\mathrm{V}$$ : a) $$\mathrm{M}=0, \mathrm{~A}=01110111, \mathrm{~B}=01100110$$ b) $$\mathrm{M}=0, \mathrm{~A}=10001000, \mathrm{~B}=10011001$$ c) $$\mathrm{M}=1, \mathrm{~A}=11001100, \mathrm{~B}=10001000$$ d) $$\mathrm{M}=1, \mathrm{~A}=01010101, \mathrm{~B}=10101010$$ e) $$\mathrm{M}=1, \mathrm{~A}=00000000, \mathrm{~B}=00010001$$

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