In a JK flipflop, J and K inputs are set to logic 1, the output Q(0) will be _______ when Q(-1) is _________.
1, 0
JK Flip-Flop Fundamentals
A JK flip-flop is a fundamental sequential circuit component used in digital electronics for memory and control applications. It has two data inputs, J (for 'Set') and K (for 'Reset'), and two outputs, Q and its complement $\bar{Q}$. The behavior of a JK flip-flop is synchronized by a clock signal, meaning its output changes only at the rising or falling edge of the clock pulse.
One of the key advantages of the JK flip-flop over an SR flip-flop is its ability to handle the "undefined" state. In an SR flip-flop, when both S and R inputs are logic 1, the output becomes unpredictable. The JK flip-flop resolves this by entering a "toggle" state under similar conditions.
JK Flip-Flop Truth Table
To fully understand the operation of a JK flip-flop, it is essential to refer to its characteristic truth table. This table defines the next state ($Q(t+1)$ or $Q(0)$ in the question's context) based on the current inputs J and K, and the present state ($Q(t)$ or $Q(-1)$ in the question's context).
| J | K | $Q(t)$ (Previous Output) |
$Q(t+1)$ (Next Output) |
Mode of Operation |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | No Change (Hold) |
| 0 | 0 | 1 | 1 | No Change (Hold) |
| 0 | 1 | 0 | 0 | Reset ($Q(t+1) = 0$) |
| 0 | 1 | 1 | 0 | Reset ($Q(t+1) = 0$) |
| 1 | 0 | 0 | 1 | Set ($Q(t+1) = 1$) |
| 1 | 0 | 1 | 1 | Set ($Q(t+1) = 1$) |
| 1 | 1 | 0 | 1 | Toggle ($Q(t+1) = \overline{Q(t)}$) |
| 1 | 1 | 1 | 0 | Toggle ($Q(t+1) = \overline{Q(t)}$) |
JK Flip-Flop Logic 1 Inputs (Toggle Mode)
The question specifically states that both J and K inputs are set to logic 1. Referring to the JK flip-flop truth table, when $J=1$ and $K=1$, the flip-flop enters its "toggle" mode. In this mode, the next output state, $Q(0)$ (or $Q(t+1)$), will be the complement (opposite) of the previous output state, $Q(-1)$ (or $Q(t)$).
Mathematically, this can be expressed as: $Q(t+1) = \overline{Q(t)}$ when $J=1$ and $K=1$.
Determining the Output Q(0) based on Q(-1)
We are asked to find $Q(0)$ when $Q(-1)$ is given, under the condition that J and K are both logic 1. Let's analyze the behavior in toggle mode:
- If the previous output $Q(-1)$ was 0:
- According to the toggle mode operation, the current output $Q(0)$ will be the complement of $Q(-1)$.
- So, $Q(0) = \overline{0} = 1$.
- If the previous output $Q(-1)$ was 1:
- According to the toggle mode operation, the current output $Q(0)$ will be the complement of $Q(-1)$.
- So, $Q(0) = \overline{1} = 0$.
The question asks for the pair $Q(0)$, $Q(-1)$. We need to find the option that correctly represents this relationship under the $J=1, K=1$ condition:
- Option 1: (0, 0) $\implies$ If $Q(-1)=0$, $Q(0)$ should be 1 (toggle), not 0. Incorrect.
- Option 2: (1, 1) $\implies$ If $Q(-1)=1$, $Q(0)$ should be 0 (toggle), not 1. Incorrect.
- Option 3: (undefined, 1) $\implies$ The state is not undefined for a JK flip-flop. If $Q(-1)=1$, $Q(0)$ would be 0. Incorrect.
- Option 4: (1, 0) $\implies$ This means $Q(0)=1$ when $Q(-1)=0$. This perfectly aligns with the toggle behavior of a JK flip-flop when both J and K inputs are set to logic 1. If the previous state was 0, it toggles to 1.
Therefore, in a JK flip-flop, when J and K inputs are set to logic 1, the output $Q(0)$ will be 1 when $Q(-1)$ is 0.
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.
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:
