A digital circuit which compares two numbers $${A_3}{A_2}{A_1}{A_0},\,\,{B_3}{B_2}{B_1}{B_0}$$ is shown in Fig. To get output $$Y=0,$$ choose one pair of correct input numbers

For the circuit shown in Fig. the Boolean expression for the output $$Y$$ in terms of inputs $$P,$$ $$Q,$$ $$R$$ and $$S$$ is

For a flip-flop formed from two $$NAND$$ gates as shown in figure. The unusable state corresponds to

The logic function $$f = \overline {\left( {x.\overline y } \right) + \left( {\overline x .y} \right)} $$ is the same as