Inputs Xi and Yi of each full adder in an arithmetic circuit have digital logics pecified...

Inputs Xi and Yi of each full adder in an arithmetic circuit have digital logics pecified by the Boolean functions

where S is a selection variable, Cin is the input carry, and Ai and Bi are in put data for stage i.

(a) Draw the logic diagram for the 4-bit circuit, using full adders and multiplexers.

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(b) Determine the arithmetic operation performed for each of the four combinations of S and Cin: 00, 01, 10, and 11.