Two T flip-flops are connected as shown. Initially A = B = 1. Input x takes values 1,0,1 in the next three clock cycles. Find the decimal value of binary $(ABy)_2$ after the third cycle, with A the MSB and y the LSB.
From the diagram, $T_A=\overline{xB}$, $T_B=x$, and $y=A+B$. A T flip-flop updates by $Q^+=Q\oplus T$. Start at AB = 11. For x = 1, $T_A=0,T_B=1$, giving 10. For x = 0, $T_A=1,T_B=0$, giving 00. For x = 1 again, both toggle, giving 11. Then y = 1, so $(ABy)_2=111_2=7$.
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