# Drawing a circuit diagram

Discussion in 'Homework Help' started by Yami, May 14, 2016.

1. ### Yami Thread Starter Member

Jan 18, 2016
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Hi I've got this question to draw a circuit diagram for X=AB+BCD+AC (the whole expression is complemented) so do i need to draw an invertor after every input?

2. ### Alec_t AAC Fanatic!

Sep 17, 2013
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What logic functions do you have available? AND, NAND, NOR .........?

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3. ### WBahn Moderator

Mar 31, 2012
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So, in other words, you have X = (AB + BCD + AC)' ?

There are many logic circuit that implement this. As Alec_t indicated, it depends on what gates you have available. Not only what the underlying function happens to be (AND vs NAND, for instance), but also any limitations on how many inputs each gate has.

As to the question of whether you need to draw an inverter after every input, that depends on how you manipulate the circuit. For instance:

Y = (A+B)' = (A')(B')

So in that case the answer is yes, but it is not a complete answer -- you must also swap the underlying logic function from OR to AND. This is the heart of DeMorgan's theorem.

However, you can't just blindly apply this to multi-term inputs such as

Y = (AB + C)' = (A')(B')(C') -- this is WRONG.

It is term by term

Y = (AB + C)' = ((AB)')(C') = (A' + B')(C') = A'C' + B'C'

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Jan 18, 2016
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