Counters Questions and Answers

31.

Match the List – I and List – II :

List – I (Type of counters)	List – II (No. of flip flops required)
a. Mod-6	i. 3
b. Mod-11	ii. 4
c. Mod-31	iii. 5

Codes : a b c

A.iii ii i
B.i ii iii
C.ii iii i
D.iii i ii

Exam Year(s)

UGC NET - 2013,

Answer: B

The number of flip flops needed is the smallest n with 2^n at least the modulus. Mod-6 needs 3 (since 2^3 = 8), mod-11 needs 4 (since 2^4 = 16) and mod-31 needs 5 (since 2^5 = 32). So the match is i, ii, iii, which is the second option. The other codes reverse the numbers of flip flops.

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32.

How many flip-flops are required to build a digital counter to count from 0 to 1024 ?

A.11
B.6
C.10
D.24

Exam Year(s)

UGC NET - 2013,

Answer: A

A counter that counts from 0 to 1024 passes through 1025 different states. With n flip-flops there are \(2^{n}\) states, so we need

\[ 2^{n} \ge 1025 \]

Since \(2^{10} = 1024\) is one short and \(2^{11} = 2048\) is enough, n = 11 and the answer is option (A).

Ten flip-flops (option C) can reach only 1023, so they cannot show 1024. Six flip-flops (option B) count only to 63, and 24 (option D) is far more than needed.

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33.

In the circuit shown below, the output Y1 and Y2 for the given initial condition Y1 = Y2 = 1 and after four input pulses will be

Two JK flip-flops sharing one clock input: Q of the first drives J2 and is the output Y1, Q-bar of the first drives K2, Q of the second is the output Y2 and feeds K1, and Q-bar of the second feeds J1.

A.Y1 = 1, Y2 = 1
B.Y1 = 1, Y2 = 0
C.Y1 = 0, Y2 = 1
D.Y1 = 0, Y2 = 0

Exam Year(s)

UGC NET - 2014,

Answer: A

After four pulses the outputs are Y1 = 1 and Y2 = 1. Read the wiring: flip-flop 1 has \(J_{1} = \overline{Q_{2}}\) and \(K_{1} = Q_{2}\); flip-flop 2 has \(J_{2} = Q_{1}\) and \(K_{2} = \overline{Q_{1}}\). Both share the clock, and each JK flip-flop sets when J = 1, K = 0, resets when J = 0, K = 1.

Starting from (Y1, Y2) = (1, 1):

\[ \text{pulse 1: } (0,1) \]

\[ \text{pulse 2: } (0,0) \]

\[ \text{pulse 3: } (1,0) \]

\[ \text{pulse 4: } (1,1) \]

The counter is a four-state ring, so after four pulses it is back at the start. The other options are states reached after one to three pulses.

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