Draw the Truth Table of a JK Flip-Flop

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Nov 4, 2026

A JK flip-flop is described by its characteristic (truth) table, which specifies the next state $Q_{n+1}$ from the present state $Q_n$ and inputs $J$ and $K$ . The table is typically drawn for the combinations of $J,K$ and the two possible present values of $Q_n$ (i.e., $Q_n=0$ or $Q_n=1$ ). For a JK flip-flop: $J=0,K=0$ holds $Q$ ; $J=1,K=0$ sets $Q$ ; $J=0,K=1$ resets $Q$ ; and $J=1,K=1$ toggles $Q$ .

To verify/derive the toggling row, use the fact that when $J=K=1$ the flip-flop acts like a controlled inverter: if $Q_n=0$ then $Q_{n+1}=1$ , and if $Q_n=1$ then $Q_{n+1}=0$ .

Mermaid depiction of the “case” logic:

Step-by-step: draw the JK flip-flop truth (characteristic) table

1
Step 1
Write $Q_{n+1}$ as a function of present state $Q_n$ and inputs $J,K$ .
2
Step 2
Use columns: $J$ , $K$ , $Q_n$ , and $Q_{n+1}$ .
3
Step 3
When $J=0$ and $K=0$ , the flip-flop is in the hold mode: $Q_{n+1}=Q_n$ .
4
Step 4
When $J=1$ and $K=0$ , the flip-flop is in the set mode: $Q_{n+1}=1$ (independent of $Q_n$ ).
5
Step 5
When $J=0$ and $K=1$ , the flip-flop is in the reset mode: $Q_{n+1}=0$ (independent of $Q_n$ ).
6
Step 6
When $J=1$ and $K=1$ , the flip-flop toggles: if $Q_n=0$ then $Q_{n+1}=1$ , and if $Q_n=1$ then $Q_{n+1}=0$ .
7
Step 7
You’ll end with 8 rows total (all combinations of $J,K$ with $Q_n\in\{0,1\}$ ).
8
Step 8
Present the completed characteristic table as the “truth table” of the JK flip-flop’s state transition.

JK flip-flop truth/characteristic table

$J$	$K$	$Q_n$	$Q_{n+1}$	Mode
0	0	0	0	Hold
0	0	1	1	Hold
1	0	0	1	Set
1	0	1	1	Set
0	1	0	0	Reset
0	1	1	0	Reset
1	1	0	1	Toggle
1	1	1	0	Toggle

Hold and Set and Reset and Toggle are the four essential behaviors.

Mermaid view of toggle:

Pro Tip: quick mental rule for the 11 row

For $J=1$ and $K=1$ , do not “set” or “reset”—instead invert the present state: $Q_{n+1} = \overline{Q_n}$ (toggle).

Common mistake: mixing up toggling vs set/reset

A frequent error is writing $Q_{n+1}=1$ for $J=K=1$ . That is only the set case ( $J=1,K=0$ ). The $J=K=1$ case must depend on $Q_n$ and produce inversion.

(Optional) Next-state Boolean form

Many textbooks also express the next-state equation of a JK flip-flop as:

Q_{n+1} = J\\overline{Q_n} + \\overline{K}Q_n

This equation is consistent with the characteristic table:

if $J=0,K=0$ , then $Q_{n+1}=Q_n$ (hold)
if $J=1,K=0$ , then $Q_{n+1}=1$ (set)
if $J=0,K=1$ , then $Q_{n+1}=0$ (reset)
if $J=1,K=1$ , then $Q_{n+1}=\\overline{Q_n}$ (toggle)

Key terms: Next state and Characteristic table and Present state.

Knowledge Check

Question 1 of 4

Q1Single choice

In a JK flip-flop, what is $Q_{n+1}$ when $J=0$ and $K=0$ ?

$Q_{n+1}=Q_n$

$Q_{n+1}=1$

$Q_{n+1}=0$

$Q_{n+1}=\overline{Q_n}$

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