Complementary outputs

Also called: Q and Q-bar, Q-bar, Q bar, inverted output, complement output

The two outputs of a latch or flip-flop, Q and Q', which are always opposite in normal operation. Q' is free to use as an inverted copy.

Most latches and flip-flops provide two outputs: Q and (read "Q bar" or "Q not"). In normal operation they are always complements: when Q = 1, = 0, and vice versa.

Why two outputs? In a cross-coupled SR latch they come for free: each gate's output is one of them. Having available also saves an inverter whenever the next logic needs the complement, for example in a frequency divider built from a D flip-flop with wired to D.

When they stop being complements: the forbidden state of an SR latch forces both outputs to the same value. On a NOR latch S = R = 1 makes both 0; on a NAND latch = = 0 makes both 1. Asserting a flip-flop's preset and clear together can do the same. This is exactly why those inputs are not allowed: the circuit no longer represents one well-defined bit.

A tracing tip: you only need to work out Q. In normal operation is simply its inverse, slot by slot.

Worked example

Example

Watching Q and Q' together

A NOR SR latch receives these inputs. Q starts at 1.

1.
Slots 1–2: set, then hold. Q = 1, Q' = 0.
2.
Slot 3: reset. Q = 0, Q' = 1.
3.
Slot 4: S = R = 1. Both NOR outputs are 0, so Q = Q' = 0. Not complements.
4.
Slot 5: R drops first, leaving a set. Q = 1, Q' = 0. Complements again.

Common mistakes

Assuming Q' is always the inverse of Q. It is not during an SR latch's forbidden input.
Building an extra inverter to get Q' when the flip-flop already provides it.