Select the circuit which will produce the given output $$Q$$ for the input signals $${X_1}$$ and $${X_2}$$ given in the figure.

The shift register shown in Fig. is initially loaded with the bit pattern $$1010.$$ Subsequently the shift register is clocked, and with each clock pulse the pattern gets shifted by one bit position to the right. With each shift, the bit at the serial input is pushed to the left most position $$(MSB).$$ After how many clock pulses will the content of the shift register become $$1010$$ again?

A dual-slope analog-to-digital converter uses an $$N$$-bit counter. When the input signal $${V_a}$$ is being integrated, the counter is allowed to count up to a value:

The counter shown in Fig. is initially in state $${Q_2} = 0,\,{Q_1} = 1,\,{Q_0} = 0.$$ With reference to the $$CLK$$ input, draw waveforms for $${Q_2},{Q_1},{Q_0}$$ and $$P$$ for the next three $$CLK$$ cycles.