simplify/rewrite the expression so it can be implemented with a maximum of 11 two input-NAND Gates

Thread Starter

omaralnoman

Joined Nov 10, 2017
2
X = AC'D'E' + ABC + A'D'E + CE + CD

Note : All inputs are available in both complement and uncomplemented forms.

I tried to simplify it many times but I almost always end up with 12 gates or more.
Here is What I got:
(C+D') [(C'+AB)(C+AE') + E(C+A')] + CD
 
Last edited:

WBahn

Joined Mar 31, 2012
25,914
X = AC'D'E' + ABC + A'D'E + CE + CD

Note : All inputs are available in both complement and uncomplemented forms.

I tried to simplify it many times but I almost always end up with 12 gates or more.
Here is What I got:
(C+D') [(C'+AB)(C+AE') + E(C+A')] + CD
I don't see any NAND gates in that expression.

Have you tried using a K-map on it?
 

Thread Starter

omaralnoman

Joined Nov 10, 2017
2
I don't see any NAND gates in that expression.

Have you tried using a K-map on it?
Thanks for your reply....
NAND Gate is a universal gate.... you can implement any circuit by using only nand gates.
for example (C+D') is obviously an OR gate but you can use NAND GATE since nand is equivalent to negative OR
C'---
NAND Gate -----
D---
 

WBahn

Joined Mar 31, 2012
25,914
Thanks for your reply....
NAND Gate is a universal gate.... you can implement any circuit by using only nand gates.
for example (C+D') is obviously an OR gate but you can use NAND GATE since nand is equivalent to negative OR
C'---
NAND Gate -----
D---
Yes, you can implement any logic using nothing but two-input NAND gates. There are several other gates for which this is true, as well.

But if you want to implement logic using at most 11 2-input NAND gates, then don't you think it would be a reasonable step to get your logic expression written in terms of 2-input NAND gates so that you (and us) can see how many you need?
 
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