GATE 2023 IN Q.16: solution and answer

GATE 2023 · INQ.16 · 1 mark · MCQ

The table shows the present state Q(t), next state Q(t+1), and the control input in a flip-flop. Identify the flip-flop.

| Q (t) | Q (t+1) | Input |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |

GATE 2023 IN question 16: A table with three columns headed Q (t), Q (t+1) and Input, and four rows: (Q(t), Q(t+1), Input) = (0, 0, 0), (0, 1, 1)… — Figure from the GATE 2023 IN paper. It is part of the question.

(A)
T flip-flop
(B)
D flip-flop
(C)
SR flip-flop
(D)
JK flip-flop

Answer and solution

ANSWER

The table matches $Q (t + 1) = Input \oplus Q (t)$ : the state holds when the input is 0 and toggles when it is 1. That is a T flip-flop, option (A).

Official answer: ASource: Official answer key, GATE 2023 IN (IIT Kanpur)

The table has only one control-input column, so the device is a single-input flip-flop: T or D. SR and JK flip-flops each have two control inputs ( $S, R$ or $J, K$ ), so a one-column table cannot describe them. This rules out (C) and (D).
Read the rows where the input is $0$ : the state holds, $0 \to 0$ and $1 \to 1$ .
Read the rows where the input is $1$ : the state flips, $0 \to 1$ and $1 \to 0$ .
Holding on $0$ and toggling on $1$ is the defining behaviour of the T flip-flop. Its characteristic equation is $Q (t + 1) = T \oplus Q (t)$ .
Check every row against $Q (t + 1) = Input \oplus Q (t)$ : row 1, $0 \oplus 0 = 0$ ; row 2, $1 \oplus 0 = 1$ ; row 3, $1 \oplus 1 = 0$ ; row 4, $0 \oplus 1 = 1$ . All four rows match.
Rule out D, whose characteristic equation is $Q (t + 1) = D$ . In row 3 the input is $1$ but $Q (t + 1) = 0$ , and in row 4 the input is $0$ but $Q (t + 1) = 1$ . So the next state does not simply copy the input, and the device cannot be a D flip-flop.
The flip-flop is a T flip-flop, option (A).

KEY IDEA

Look for the pattern that links the input to the change of state. A T flip-flop holds when $T = 0$ and toggles when $T = 1$ , so $Q (t + 1) = T \oplus Q (t)$ . A D flip-flop copies its input, so $Q (t + 1) = D$ .

WATCH OUT FOR

Picking D because the input equals $Q (t + 1)$ in the first two rows. Rows 3 and 4 break that pattern. The input actually equals $Q (t) \oplus Q (t + 1)$ , which means it tells the flip-flop whether to change state. That is the T flip-flop's excitation rule.

From the GATE 2023 IN paper. Every question of this paper · Download the full paper · All 30 Sequential questions, with notes

GATE 2023 IN Q.16: solution and answer

Answer and solution

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