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Design the sequential circuit specified by the following state diagram using T flip-flop.

 

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Using the state diagram, we can easily get the state table.

         Present State     Input         Next State          Flip Flop Input
$A$                         $B$             $X$ $A_{Next}$                  $B_{Next}$ $T_{A}$                   $T_{B}$
0                         0               0   0                           0 0                        0
0                         0      1   0                           1 0                        1
0                         1      0  1                            0 1                        1
0                         1      1  0                            1 0                        0
1                         0      0  1                            0 0                        0
1                         0      1  1                            1 0                        1
1                         1      0  1                            1 0                        0
1                         1      1  0                            0 1                        1

$K-Map$ for $T_{A}:$

$T_{A} = A'BX' + ABX$

 

$K-Map$ for $T_{B}:$

$T_{B} = A'BX' + B'X + AX$


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