GATE CSE 1987

The Boolean expression A \oplus B \oplus A is equivalent to

The below figure shows four D-type flip-flops connected as a shift register using a XOR gate. The initial state and three subsequent states for three clock pulses are also given.


\begin{array}{|c|c|c|c|c|} \hline \text{State} & Q_{A} & Q_{B} & Q_{C} & Q_{D} \\\hline \text{Initial} & 1 & 1 & 1 & 1 \\\hline \text{After the first clock} & 0 & 1 & 1 & 1 \\\hline \text{After the second clock} & 0 & 0 & 1 & 1 \\\hline \text{After the third clock} & 0 & 0 & 0 & 1 \\\hline \end{array}

The state Q_{A} Q_{B} Q_{C} Q_{D} after the fourth clock pulse is

Fig. below shows the circuit diagram of a wien bridge oscillator using an op-amp.

The frequency of oscillation is given by f= 1/2 \pi CR. To have the system oscillate the ratio R_{2}/R_{1} should be

A Boolean function f is to be realized only by NOR gates. Its K-map is given below:

The realization is

The refreshing rate of dynamic RAMs is in the range of