Did I write this logic expression correctly?

Question

This is what I came up with. $$Y=A+AB+B+C'+B+C'D+D$$ Is it safe to say that it is correct or did I make a mistake?

Answer 1

Your answer can't be right because it depends on $D$. Note the following:

• If $D$ is on, then the NOR gate it feeds into is off;
• If $D$ is off, then the NAND gate it feeds into is on, so the NOR gate is off again.

So we can actually eliminate the NOR gate completely from the circuit without having any effect.

Then the expression is much simpler to analyse:

• If $A$ is on, then $Y$ is on.
• If $A$ is off, then the AND gate it feeds into is off, so the circuit reduces to "$B$ or not $C$".

So a simplified expression is $Y = A + B + C'$.