# Simplfying Boolean Expression

Thread Starter

#### frisbee4all

Joined Feb 22, 2009
13
Here's the expression:

X = A_bar *B*C+(A+B)*C_bar

- Could you please help me get started on it?
I distributed the C_bar, but I don't see any laws or identities that would help further simplify it. The end goal is to draw a logic circuit with only NAND gates and inverters, where the NAND gates can only have two inputs. But I want to get the simplified expression first. Thanks

#### mentaaal

Joined Oct 17, 2005
451
De-Morgans theorems can be applied here and you begin by double complementing the entire expression (i.e. not doing anything to it all)

you can then break the lower complement "bar" and when you do this the expression can then be implemented using only inverters and nand gates

Thread Starter

#### frisbee4all

Joined Feb 22, 2009
13
Alright, I think I got it. The logic circuit is really long though. I have 5 inverters and 6 NANDs.

The final expression I got for X:

X = (A'*B*C)' * (A*C')' * (B*C')' ; where the ' indicates a the variable is inverted (has a bar over it)

Let me know if the terminology is correct, I'm not familiar with the standard representation of these expressions on this forum. Sorry

Attached is a jpeg of my colorfully drawn circuit

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Thread Starter

#### frisbee4all

Joined Feb 22, 2009
13
Just realized I forgot to invert the outputs of the NAND...I think this is the final logic circuit.

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