# Boolean expression

Discussion in 'Homework Help' started by thisonedude, Jun 29, 2014.

1. ### thisonedude Thread Starter Member

Apr 20, 2014
52
0
Hi all.

I was wondering if i could get some help in implementing my equations into shematics. So my bojective is to use 3-input NAND gates, 2-input NAND gates, and inverters. this design will be based on the minimum SOP equations.

INPUT OUTPUT
S2 S1 S0 | X0 X1 X5 X6
0 0 0 1 0 0 0
0 0 1 0 0 1 0
0 1 0 0 0 0 1
0 1 1 0 1 0 0
1 0 0 0 1 1 1
1 0 1 1 1 0 1
1 1 0 1 1 1 0
1 1 1 1 0 1 1

For SOP, my equations (Simplified) are:
X0 = S2'^S1'^S0' + S2^S1 + S2^S0
X1 = S2'^S1'^S0 + S2^S0' + S2^S1'
X5 = S2'^S1'^S0 + S2^S1 + S2^S0'
X6 = S2'^S1^S0 + S2^S0 + S2^S1'

I'm having a hard time designing the schematic. So far all i have is three inputs each separately being inverted and then they combing going into a NAND gate. Can anyone help me from here?

2. ### MrCarlos Active Member

Jan 2, 2010
400
134
Hello thisonedude

Let me give you a little push.

You have to make 3 horizontal lines naming them: S0, S1 and S2.
Below these, 3 NOT gates, naming the other 3 lines As: S0', S1' and S2'

Analyzes the image below to have a better idea.

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3. ### thisonedude Thread Starter Member

Apr 20, 2014
52
0
That was how i originally thought about doing it. But the constraints are that we are only allowed to use 3-input NANDS, 2-input NANDS, and inverters.

I came out with the following. Would you mind checking my work? This is for the function X0 only. I used the DeMorgans Theorem to use the NANDS instead or the OR.

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4. ### MrCarlos Active Member

Jan 2, 2010
400
134
Hello thisonedude

You say:
Would you mind checking my work?

Well, I'd like to see it to check it

5. ### thisonedude Thread Starter Member

Apr 20, 2014
52
0
My schematic is attached attached to my reply post. Is it not showing up?

6. ### thisonedude Thread Starter Member

Apr 20, 2014
52
0
I have reattached the image.

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7. ### MrCarlos Active Member

Jan 2, 2010
400
134
Hello thisonedude

What if you remove the red NOT gates and you add the blue wire ?

You tried it ?

• ###### Some Help (2).jpg
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thisonedude likes this.
8. ### thisonedude Thread Starter Member

Apr 20, 2014
52
0
Hi MrCarlos,
Thank you for your help. I was able to figure out the schematic. my problem was that i had those extra NOT gates (The red ones) and i also have three extra NOT gates that i did not need to have. Thank you again for your help!

9. ### MrCarlos Active Member

Jan 2, 2010
400
134
Hello thisonedude

You say:
Thank you for your help. I was able to figure out the schematic.
Probably your schematic is similar to mine.

Let me see, if possible.
It could serve as a sample for other members.

Meanwhile, I'll make a recommendation.
There is a computer program named Boole-Deusto. Search it on google.com.
Is NOT the eighth wonder but I have been very useful to learn.

The point that it is not designed to handle many variables either input or output.
I'm not selling it but I'm recommending it as a very good programming tool to develop combinational circuits, decoders, and so on.

Anyway, with this Software (Boole-Deusto) you can develop your design with only gates
NAND,
NOR,
AND & OR.

With it, I developed you did with only NAND gates.
All material is attached.
Take a look.