A logic designer who had not taken this course designed a

Chapter 15, Problem 15.33

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A logic designer who had not taken this course designed a sequential circuit with an input W using three T flip-flops, A, B, and C. The input equations for these flip-flops are

                                    \(\begin{aligned}& T_A=W^{\prime} A^{\prime} B+W^{\prime} B C^{\prime}+A^{\prime} BC^{\prime}+A B^{\prime} C+W B^{\prime} C+W A C \\& T_B=W^{\prime} A^{\prime}C+W^{\prime} A^{\prime} B+A^{\prime} B C+A B^{\prime} C^{\prime}+W B^{\prime}C^{\prime}+W A C^{\prime} \\& T_C=W^{\prime} A C+W^{\prime} B^{\prime}C^{\prime}+W B C+W A^{\prime} C^{\prime}\end{aligned}\)

and the output equation is \(Z=W^{\prime} B C^{\prime}\). Find an equivalent sequential circuit which uses fewer states. Realize it, trying to minimize the amount of logic required.

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