Combinational circuit

Also called: combinational logic, combinational, combinatorial logic, combinatorial circuit, combinational network

A digital circuit whose outputs depend only on its present inputs. It has no memory, so one truth table describes it completely.

A combinational circuit computes its outputs from the inputs it sees right now, and nothing else. Give it the same inputs tomorrow and you get the same outputs. It has no idea what happened a moment ago.

That property comes from how it's built: logic gates wired from inputs toward outputs, with no feedback loops. Because nothing is remembered, a single truth table lists its complete behavior, one row per input combination.

The opposite is a sequential circuit, which contains memory (latches or flip-flops). Its output also depends on what it has stored, so the same inputs can give different outputs at different times.

Common combinational building blocks:

Multiplexers and demultiplexers, which route signals
Decoders and encoders, which convert between codes
Comparators and adders, which do arithmetic on numbers

One subtlety: "depends only on present inputs" describes the settled result. Real gates need a little time, the propagation delay, so after an input changes the output is briefly in transition before it settles.

Worked examples

Example

Combinational or sequential?

Ask one question of each device: can the same inputs ever produce different outputs?

1.
A circuit that lights the segments for the 4-bit digit on its inputs right now: each digit always gives the same segments. Combinational.
2.
A circuit that outputs 1 when its 3-bit input is a prime number: the answer depends only on the number. Combinational.
3.
A push-button that switches a lamp on, then off, then on again: the same input (a press) gives different results, so the circuit must remember the lamp's state. Sequential.
4.
A circuit that counts how many cars have entered a parking garage: the count is history. Sequential.

Example

Reading the diagram above

The circuit computes F = . Every gate feeds forward toward F, and no output wire loops back into an earlier gate.

1.
S = 1, D = 0, W = 1: = 1, then F = 1 · 1 = 1.
2.
Apply the same inputs again later: F = 1 again. Nothing in the circuit can store a different answer.
3.
So the circuit is combinational, and its 8-row truth table says everything about it.

Common mistakes

Thinking a big circuit must be sequential. Size doesn't matter: thousands of gates with no feedback are still combinational.
Calling a circuit combinational because it's made only of gates. Two gates wired in a loop (like an SR latch) can store a bit, so the circuit is sequential.
Expecting outputs to change instantly. A combinational output is a function of the inputs only after the propagation delay has passed.

Practice Combinational circuit

Interactive questions with instant feedback and a worked solution for every wrong answer.

Combinational Logic lesson full course

Adders and ALUs lesson full course

An ALU computes AND, OR, ADD or SUB of its inputs A and B, chosen by an opcode. What kind of circuit is it?

Latches and Flip-Flops lesson full course

Practice exams

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Combinational circuit is taught in Combinational Logic.

Combinational Logic →

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