# Digital Logic Circuit

#### copper_pipe

Joined Sep 30, 2014
18
Hi all,

Have a few problems with my assignment.

Circuit is as follows: Ive derived a truth table and come up with this : Can someone verify if the above is correct?

Ive then got these 2 logic expressions :

Y = A'D' + C'D' + B'D'
Z = D+ B

What I want to know is (if the above is correct) Is it possible to implement the above circuit using fewer logic gates?

#### copper_pipe

Joined Sep 30, 2014
18 This is the correct circuit

#### dl324

Joined Mar 30, 2015
10,736
If the complemented inputs are available, how many gates does your solution use? How many gates were used in the original circuit?

#### copper_pipe

Joined Sep 30, 2014
18
If the complemented inputs are available, how many gates does your solution use? How many gates were used in the original circuit?
The circuit provided uses 3 logic gates as shown above.

I think I need a minimum 3 gates so therefore it would not be possible to implement the circuit with a few number of gates

#### dl324

Joined Mar 30, 2015
10,736

#### copper_pipe

Joined Sep 30, 2014
18

#### dl324

Joined Mar 30, 2015
10,736
Can you explain?

I see an AND, NOR and OR
Y = A'D' + C'D' + B'D'
Z = D+ B
I was referring to your solution.

The Y expression is 4 gates, the Z expression is 1 gate; 4 + 1 = 5.

#### copper_pipe

Joined Sep 30, 2014
18
I was referring to your solution.

The Y expression is 4 gates, the Z expression is 1 gate; 4 + 1 = 5.
Could the Y be simplified to ABCD' ?

#### WBahn

Joined Mar 31, 2012
25,757
Part of the issue is what counts as one gate? Does a three input AND gate count as a single gate?

#### copper_pipe

Joined Sep 30, 2014
18
Part of the issue is what counts as one gate? Does a three input AND gate count as a single gate?
Yes it would.

#### WBahn

Joined Mar 31, 2012
25,757
Yes it would.
That's a shame because it is a poor metric, both in terms of real estate (number of transistors), and speed (propagation delay). But if it's the metric you have to work with, then it is what it is.

#### WBahn

Joined Mar 31, 2012
25,757
Could the Y be simplified to ABCD' ?
You tell us. ABCD' says that in order for Y to be HI, that A, B and C must be HI and D must be LO. Is that what you need for the Y signal?