# GATE CSE 1987

 Question 1
The Boolean expression $A \oplus B \oplus A$ is equivalent to
 A $AB + \bar {A}\bar B$ B $\bar{A}B+A\bar{B}$ C B D $\bar{A}$
Digital Logic   Boolean Algebra
Question 1 Explanation:
 Question 2
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
 A 0000 B 1111 C 1001 D 1000
Digital Logic   Sequential Circuit
Question 2 Explanation:

 Question 3
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 0.5 B 29 C 2 D Any value
Digital Logic   Combinational Circuit
Question 3 Explanation:
 Question 4
A Boolean function f is to be realized only by NOR gates. Its K-map is given below: The realization is A A B B C C D D
Digital Logic   Boolean Algebra
Question 4 Explanation:
 Question 5
The refreshing rate of dynamic RAMs is in the range of
 A 2 microseconds B 2 milliseconds. C 50 milli seconds D 500 milliseconds
Computer Organization   Memory Chip Design
Question 5 Explanation:

There are 5 questions to complete.