# reducing minterms of a nand gate

Thread Starter

#### blpanther

Joined Nov 23, 2015
5
From the truth table of a nand gate we have following minterms:
(NOT A AND NOT B) OR (NOT A AND B) OR (A AND NOT B)=X
how can that be reduced to the nand gate bolean equation which is
NOT (A AND B)=X ?
I'm trying to get my head around how it was reduced to that?

#### WBahn

Joined Mar 31, 2012
26,398
Sounds like a homework problem. Even if it's not, you'll get a lot more out of it if you show us your best shot at it and let us use that as a jumping off point to give you hints on how to make the next step.

Here's a hint -- (A) OR (NOT A) = 1 (i.e., TRUE)

Thread Starter

#### blpanther

Joined Nov 23, 2015
5
If I consider A to be 1 than not A will be '0'
anything times 0 is zero so based on that assumption (NOT A And B) and also (A AND NOT B) can be removed as they will have zero value... ?

#### WBahn

Joined Mar 31, 2012
26,398
If I consider A to be 1 than not A will be '0'
anything times 0 is zero so based on that assumption (NOT A And B) and also (A AND NOT B) can be removed as they will have zero value... ?
It helps if you are very explicit about the order of operations.

[(NOT A) AND (NOT B)] OR [(NOT A) AND (B)] OR [(A) AND (NOT B)] = X

You can consider A to be a 1 all day long, but you can't go removing terms based on that consideration because A may not be a 1. You have to show that you can remove those terms whatever the value of A is.