Characteristic table

Also called: flip-flop characteristic table, flip-flop table

A table that gives a latch's or flip-flop's next state Q⁺ for every combination of its inputs and its present state Q.

A characteristic table answers the question: what happens next? For each combination of a storage element's inputs and its present output Q, it lists the next output Q⁺ (also written Q(t+1)): the value after the next clock edge, or after the inputs act for a latch.

Q is now.
Q⁺ is next.

There are two common layouts. A compact one lists only the inputs and an action ("Q", "0", "1", ""). A full one adds Q as an input column so every row has a definite 0 or 1. The full layout can be turned straight into the characteristic equation.

The tables for the main types:

D: Q⁺ = D.
T: T = 0 holds, T = 1 toggles.
JK: 00 hold, 01 reset, 10 set, 11 toggle.
D latch with enable E: E = 0 holds, E = 1 passes D.

The reverse question, which inputs do I need to get from Q to a chosen Q⁺?, is answered by the excitation table. You use characteristic tables to analyze a circuit and excitation tables to design one.


0	0	0
0	1	1
1	0	1
1	1	0

Worked examples

Example

Building the full table for a set-dominant flip-flop

A set-dominant SR flip-flop treats S = R = 1 as a set instead of forbidding it. Fill in Q⁺ for all eight rows of (S, R, Q).

1.
S = 0, R = 0 (hold): (0,0,0) → 0, (0,0,1) → 1.
2.
S = 0, R = 1 (reset): (0,1,0) → 0, (0,1,1) → 0.
3.
S = 1, R = 0 (set): (1,0,0) → 1, (1,0,1) → 1.
4.
S = 1, R = 1 (set wins): (1,1,0) → 1, (1,1,1) → 1.
5.
Q⁺ is 1 whenever S = 1, or when R = 0 and Q = 1: Q⁺ = .

Example

Reading the T table above

Use the table in the diagram to find Q⁺ for T = 1, Q = 1 and for T = 0, Q = 1.

1.
T = 1, Q = 1: Q⁺ = 1 ⊕ 1 = 0. The flip-flop toggles from 1 to 0.
2.
T = 0, Q = 1: Q⁺ = 0 ⊕ 1 = 1. It holds.

Common mistakes

Mixing up Q and Q⁺. Q is the present value going in; Q⁺ is the result after the edge.
Using the characteristic table to answer a design question. To find the inputs that produce a transition, use the excitation table.
Leaving the hold and toggle rows without looking at Q. Those rows depend on the present state.

Practice Characteristic table

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Latches and Flip-Flops lesson full course

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Learn it step by step

Characteristic table is taught in Latches and Flip-Flops and Finite State Machines.

Latches and Flip-Flops →Finite State Machines →

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