$15$

$[$NL$53-67]$

A sequential circuit has one flip$-$flop; two inputs $\backslash ($ A $\backslash )$ and $\backslash ($ B $\backslash )$ and one output $\backslash ($ S $\backslash ).$ It consists of a full adder circuit connected to a JK flip$-$flop as shown. Fill in the truth table for this sequential circuit.

$\backslash$begin$\{$tabular$\}\{|$ccc$|$c$|$c$|\}$

$\backslash$hline$\backslash ($ A $\backslash )$ & $\backslash ($ B $\backslash )$ & $\backslash ($ Q$\_\{$t$\}\backslash )$ & $\backslash ($ Q$\_\{$t$+1\}\backslash )$ & $\backslash ($ S $\backslash )\backslash \backslash$

$\backslash$hline $\backslash$hline $0$ & $0$ & $0$ & & $\backslash \backslash$

$\backslash$hline $0$ & $0$ & $1$ & & $\backslash \backslash$

$\backslash$hline $0$ & $1$ & $0$ & & $\backslash \backslash$

$\backslash$hline $0$ & $1$ & $1$ & & $\backslash \backslash$

$\backslash$hline $1$ & $0$ & $0$ & & $\backslash \backslash$

$\backslash$hline $1$ & $0$ & $1$ & & $\backslash \backslash$

$\backslash$hline $1$ & $1$ & $0$ & & $\backslash \backslash$

$\backslash$hline $1$ & $1$ & $1$ & & $\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$