In the iterative circuit below the input X is a 2s

Chapter 16, Problem 16.18

(choose chapter or problem)

In the iterative circuit below the input X is a 2’s complement number and the output Y is the 2’s complement of X. ( \(x_0\) and \(y_0\) are the least significant bits.)

(a) Construct a transition table for typical cell. (Note that \(a_0\) is 0.)

(b) Derive expressions for \(a_{i +1}\) and \(y_i\).

(c) Construct a sequential circuit that will compute the 2’s complement of its input. (Use D flip-flops. Assume the flip-flops are reset at the beginning of an input sequence.)

                                                 

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