Toggle Toggle

Logic Level 3

Consider the following logic circuit:

When we toggle A, we would like the output to toggle as well. i.e. We would like the signal to propagate from A to X.

How many different ways can we set the remaining inputs so that this happens?

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The answer is 15.

2 solutions

Geoff Pilling
Aug 23, 2019

B, C, and D must each be set to one.

And E, F, G, H can be set to anything but all ones.

$\implies 15$ ways

David Vreken
Aug 24, 2019

If any of $B$ , $C$ , or $D$ were $0$ , then $ABCD$ would be $0$ no matter what $A$ is, which would mean $A$ could not toggle the output. Therefore, $B = C = D = 1$ .

If $EFGH$ is $1$ , then $X$ would be $1$ no matter what $A$ is, which would mean $A$ could not toggle the output. Therefore, $EFGH = 0$ .

Since $EFGH = 0$ , at least one of $E$ , $F$ , $G$ , and $H$ is $0$ , which is all possible combinations except one (when $E = F = G = H = 1$ ), for a total of $2^4 - 1 = \boxed{15}$ different ways.

Toggle Toggle

The answer is 15.

2 solutions

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