- Consider the following circuit with four inputs 20,21,22,23 and four outputs yo, Y1, 42, 43: - - y2 y1 (a) Does this logic circuit implement the operation of taking a number represented in width-4 sign- magnitude representation and producing the width-4 sign-magnitude representation of (-1) times this number? If yes, explain why using the definition of sign-magnitude representation and consider all possible inputs. If no, provide specific example input values, trace the circuit to compute its output for this example, and use the definition to calculate the two numbers being represented and explain why these numbers support your conclusion. (b) Does this logic circuit implement the operation of taking a number represented in width-4 2s complement representation and producing the width-4 2s complement representation of (-1) times this number? If yes, explain why using the definition of 2s complement representation and consider all possible inputs. If no, provide specific example input values, trace the circuit to compute its output for this example, and use the definition to calculate the two numbers being represented and explain why these numbers support your conclusion. (c) Recall the definition of binary fixed-width addition (adding one bit at time, using the usual column-by-column and carry arithmetic, and ignoring the carry from the leftmost column) from 3- warmup and from class. We call the first summand 23X2X120, we call the second summand YzY2Yyo, and we call the result Z3222120. Give an example of input bits Xo, X1, X2, X3 to the circuit pictured above such that in the fixed-width sum with first summand X3X2X1Xand second summand Y3y2yyo, all of the statements below are true. i. When interpreting each of the summands and the result in binary fixed-width 4, the result represents the actual value of the sum of the summands. ii. When interpreting each of the summands and the sum in sign-magnitude width 4, the result represents the actual value of the sum of the summands. iii. When interpreting each of the summands and the sum in 2s complement width 4, the result represents the actual value of the sum of the summands