Question

Given the following State Diagram, write the equations for the D-Flipflop A,
D-Flipflop B, and Output. Please enter the equations in the space provided.

11/0 АВ 00 XҮ/Z 01/1 11/0 00/1 01/1, 10/0 00/0, 01/0, 10/0 10 01 00/0 11/1 11/1 10/1 01/1, 10/1 11 00/0 A B

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Answer #1

Truth table for the given diagram:

Next Present Outputs Inputs state state А В Z XY АВ 1 00 1 1 00 0 1 0 01 00 0 10 1 1 00 0 0 1 11 00 0 1 1 00 01 0 1 1 01 01 1 0 0 10 01 1 1 1 11 01 1 00 1 1 10 0 0 01 10 0 0 0 10 10 1 0 10 11 10 1 0 11 00 1 0 10 11 01 0 0 0 11 10 0 1 0 11 11

For Melay machines, next state output is the input for the D-flipflop.

Input equation for the D-flipflop A, by solving directly or by K-map:

0,2,6,7,8,11,12,13) A ABY ABX + ABX+ AXY ABXY

Similarly,

Input equation for the D-flipflop B, by solving directly or by K-map:

(0,12,4,5,7,8,15) B AXABY + BXY BY

The output of the given diagram:

(0,3,4,5,7,8,9,12) Z = XY+ ABX + ABY + AXY

Therefore, the final result:

A = ABY AB.X+ ABX AXY+ ABXY B AX ABY+BXY BY Z = XY ABX + ABY + AXY

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