Feedback loop

Also called: feedback, combinational loop, feedback path

A path where a gate's output is wired back to an earlier gate's input. Feedback gives a circuit memory, so it is never found in combinational logic.

A feedback loop is a wire that carries a circuit's output back to its own input, directly or through other gates. Follow the signal and you come back to where you started.

Feedback is what separates the two big families of circuits:

A combinational circuit has no loops. Signals flow one way, inputs to outputs, so the outputs depend only on the present inputs.
A sequential circuit uses feedback. The output helps decide itself, so the circuit can hold on to a value: it has memory.

The classic example is two cross-coupled NOR gates, the sr latch. Each gate's output feeds the other's input. Once the loop settles into a state, it keeps it after the inputs return to rest. That's one stored bit, and every latch, flip flop and register is built on the same idea.

Not every loop stores a bit. A single inverter (or any odd number of inverters) wired in a ring can never settle: the value chases itself round and the circuit oscillates.

So when you analyze a schematic, look for loops first. If you find one, a truth table alone won't describe the circuit.

Worked examples

Example

A NOR loop remembers

Two NOR gates: Q = NOR(R, Q̄) and Q̄ = NOR(S, Q). Start with S = R = 0 and Q = 0.

1.
Pulse S to 1: Q̄ = NOR(1, Q) = 0. Then Q = NOR(0, 0) = 1.
2.
Return S to 0: Q̄ = NOR(0, 1) = 0 and Q = NOR(0, 0) = 1. Nothing changes.
3.
Now S = R = 0 with Q = 1, while at the start S = R = 0 gave Q = 0.
4.
Same inputs, different outputs: the loop is remembering the last pulse.

Example

An inverter loop oscillates

One NOT gate with its output wired to its input.

1.
Suppose the output is 0. Then the input is 0, so after one gate delay the output becomes 1.
2.
Now the input is 1, so after another delay the output becomes 0.
3.
It never settles. The output toggles every gate delay: a crude oscillator.

Common mistakes

Assuming a circuit built only of gates is combinational. Gates wired in a loop make a latch.
Thinking every loop stores a bit. An odd ring of inverters oscillates instead.
Describing a circuit with feedback by a truth table of its inputs alone. Its output also depends on what it is storing.

Practice Feedback loop

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

Combinational Logic lesson full course

Which feature would turn a gate circuit into a sequential one?

Latches and Flip-Flops lesson full course

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Learn it step by step

Feedback loop is taught in Combinational Logic and Latches and Flip-Flops.

Combinational Logic →Latches and Flip-Flops →

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