For a JK Flip‐flop A. When J = 0, K = 1, Q n+1 = 0 B. When J = 1, K = 1, Q n+1 = 1 C. When J = 1, K = 1, Q n+1 =\(\rm \overline{Q_n}\) D. When J = 1, K = 0, Q n+1 = 1 E. When J = 1, K = 0, Q n+1 = 0 Choose the correct answer from the options given below:
A, C and D only
Understanding JK Flip‐flop Behavior
A JK flip‐flop is a fundamental building block in sequential logic circuits. It is an improvement over the SR flip‐flop, addressing the indeterminate state issue that occurs when both S and R inputs are high simultaneously. The JK flip‐flop has two inputs, J and K, a clock input, and two outputs, Q and $\overline{Q}$. The next state of the JK flip‐flop, denoted as $Q_{n+1}$, depends on the current state $Q_n$ and the inputs J and K when the clock signal transitions.
JK Flip‐flop Truth Table
The behavior of a JK flip‐flop can be summarized by its truth table, which shows the next state ($Q_{n+1}$) for all possible combinations of current state ($Q_n$) and inputs (J, K).
| J | K | Qn | Qn+1 | Mode |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | No Change |
| 0 | 0 | 1 | 1 | No Change |
| 0 | 1 | 0 | 0 | Reset |
| 0 | 1 | 1 | 0 | Reset |
| 1 | 0 | 0 | 1 | Set |
| 1 | 0 | 1 | 1 | Set |
| 1 | 1 | 0 | 1 | Toggle |
| 1 | 1 | 1 | 0 | Toggle |
Analyzing the Given Statements
Let's evaluate each statement based on the JK flip‐flop truth table:
- Statement A: When J = 0, K = 1, Qn+1 = 0.
According to the truth table, when J=0 and K=1, the JK flip‐flop is in the Reset mode. In this mode, the next state $Q_{n+1}$ is always 0, regardless of the current state $Q_n$. This statement is True. - Statement B: When J = 1, K = 1, Qn+1 = 1.
According to the truth table, when J=1 and K=1, the JK flip‐flop is in the Toggle mode. In this mode, the next state $Q_{n+1}$ is the inverse of the current state ($Q_{n+1} = \overline{Q_n}$). $Q_{n+1}$ is 1 only if $Q_n$ was 0. It is not always 1. This statement is False. - Statement C: When J = 1, K = 1, Qn+1 = $\overline{Q_n}$.
According to the truth table, when J=1 and K=1, the JK flip‐flop is in the Toggle mode, and the next state $Q_{n+1}$ is indeed the complement of the current state $Q_n$. This statement is True. - Statement D: When J = 1, K = 0, Qn+1 = 1.
According to the truth table, when J=1 and K=0, the JK flip‐flop is in the Set mode. In this mode, the next state $Q_{n+1}$ is always 1, regardless of the current state $Q_n$. This statement is True. - Statement E: When J = 1, K = 0, Qn+1 = 0.
According to the truth table, when J=1 and K=0, the JK flip‐flop is in the Set mode, and the next state $Q_{n+1}$ is always 1. It is never 0 in this mode. This statement is False.
Based on the analysis, the true statements are A, C, and D.
Conclusion
The statements that correctly describe the behavior of a JK flip‐flop are A, C, and D.
Revision Table: JK Flip‐flop Operations
| J Input | K Input | Operation Mode | Next State (Qn+1) |
|---|---|---|---|
| 0 | 0 | No Change | Qn |
| 0 | 1 | Reset | 0 |
| 1 | 0 | Set | 1 |
| 1 | 1 | Toggle | $\overline{Q_n}$ |
Additional Information: Types of Flip‐flops
Flip‐flops are sequential logic devices capable of storing one bit of information. They are edge‐triggered or level‐triggered, depending on when they respond to inputs relative to the clock signal. Besides the JK flip‐flop, other common types include:
- SR Flip‐flop: Has S (Set) and R (Reset) inputs. It has an indeterminate state when both S and R are high.
- D Flip‐flop: Has a single D (Data) input. The next state $Q_{n+1}$ is always equal to the D input at the clock edge ($Q_{n+1} = D$). It acts as a delay element.
- T Flip‐flop: Has a single T (Toggle) input. If T=0, the state remains unchanged. If T=1, the state toggles ($Q_{n+1} = \overline{Q_n}$).
The JK flip‐flop is considered versatile as it can perform the functions of SR, D, and T flip‐flops by appropriate input connections.
Important Questions from Flip-Flop
What type of Flip Flop is used in Counters?
What is the characteristic of a master-slave flip-flop?
The basic building block of sequential logic circuit is-
A single flip-flop is a modulo __________ counter.
In a JK flip flop, if J = K, then resulting flip flop is ______.
