# How to show all false outputs in a circuit?

I have 3 input variables and the output for all 8 possible combinations is 0 (false). When making a circuit, how would I show this using gates or no gates at all? Thanks!

• You mean, how do you draw a signal that is always false? I'd just write 0 or F and draw a line to it, probably. Oct 23 '19 at 11:47

Hint: $$A \land \lnot A$$ is always False, no matter whether $$A$$ is True or False.

First you can write down the truth table of your circuit, in this case it will be entirely composed of $$0$$s. Then you will build up a Boolean expression in the form you prefer (if you have no limitations) which reproduces the behavior (relation input/output) observed in the truth table.

Note that every operator of your boolean expression correspond to a logic gate:

$$\land$$ = AND

$$\lor$$ = OR

$$\neg$$ = NOT

$$\oplus$$ = XOR