# Drawing a circuit diagram

#### Yami

Joined Jan 18, 2016
337
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?

#### Alec_t

Joined Sep 17, 2013
11,817
What logic functions do you have available? AND, NAND, NOR .........?

#### WBahn

Joined Mar 31, 2012
26,398
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?
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'

#### Yami

Joined Jan 18, 2016
337
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'
The bit about the DeMorgan's theorem is the a bit I don't really get. This is a Homework question that I got, and correct me if I'm wrong the question doesn't ask to simplify the circuit so should I break up the expression as DeMorgan's theorm. Or does it make sense to draw the logic diagram as it is and just put an inverter after the final OR gate?

#### WBahn

Joined Mar 31, 2012
26,398