### GATE 1993 ECE Video Solutions on Digital Circuits (Digital Electronics)

1. For the logic circuit shown in figure, the output Y is equal to 2. The truth table for the output Y in terms of three inputs A, B and C are given. Draw a logic circuit realization using only NOR gates. 3. 2’s complement representation of a 16 bit number (one sign bit and 15 magnitude bits) is FFFF. Its magnitude in decimal representation is
a. 0
b. 1
c. 32,767
d. 65,535

4. Boolean expression for the output of XNOR logic gate with inputs A and B is
a. AB’ + A’B
b. (AB)’ + AB
c. (A’ + B)(A + B’)
d. (A’ + B’)(A + B)

5. A pulse train with a frequency of 1 MHz is counted using a modulo 1024 ripple counter built with JK flip-flops. For proper operation of the counter, the maximum permissible propagation delay per flip flop stage is ____ nsec.

6. In a microprocessor, wait states are used to
a. Make the processor wait during a DMA operation
b. Make the processor wait during an interrupt processing
c. Make the processor wait during a power shutdown
d. Interface slow peripherals to the processor
Solution:

7. Signals A, B, C, D and D’ are available. Using a single 8 to 1 multiplexer and no other gate, implement the Boolean function F(A, B,C, D) = BC + ABD’ + A’C’D

8. A clocked sequential circuit has three states, A, B and C and one input X. As long as the input X is ‘0’, the circuit alternates between the states A and B. if the input X becomes ‘1’(either in state A or in state B), the circuit goes to state C and remains in state C as long as X continues to be 1. The circuit returns to state A if the input becomes ‘0’ once again and from then on repeats its behavior. Assume that the state assignments are A = 00, B = 01 and C = 10.
a. Draw the state diagram of the circuit.
b. Give the state table of the circuit.
c. Draw the circuit using D flip flops.

9. A microprocessor has five address lines [A4 – A0] and eight data lines [D7 – D0]. An input device A, an output device B, a ROM and a RAM are memory mapped to the microprocessor at the addresses as shown in figure. Devices A and B have four addressable registers each/ RAM has 8 bytes and ROM has 16 bytes. a. Indicate the address lines to be connected to each device and memory.
b. Obtain the minimum sum of product expression for the chip select (CS) function of each device/memory.