# Pos (/a+b)(a+/b)(/b+c)

Discussion in 'Homework Help' started by GGerardo2010, Dec 11, 2010.

1. ### GGerardo2010 Thread Starter New Member

Dec 11, 2010
4
0
I am working on this circuit and I have a few questions.

First I have (/A+B)(A+/B)(/B+C)

I want to use all NOR gates for this project.

ABC F
000 1
001 1
010 0
011 1
100 0
101 1
110 1
111 1

This is my truth table so I made the design with NAND gates which was wrong I need to create design with all NOR gates, I read somewhere that I need to use inverters before and after each gate.

How can I just use all NOR gates and do I use inverters or can I short the NOR gates as I go along?

I am not sure if the truth table is right?

How can the equation be solved, direct method or Demorgan's theorem?

Can anyone help?

G.

2. ### Wendy Moderator

Mar 24, 2008
20,772
2,540
Another way to go about it is to convert the gates in the layout. You will likely have to have inverters (which is a NOR gate with the inputs connected), but it is actually pretty easy.

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3. ### GGerardo2010 Thread Starter New Member

Dec 11, 2010
4
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Is this truth table correct? If so then its my design that is not working. I did make a design using NAND gates which that worked fine it follows the truth table, but I could be wrong.

Thanks!

4. ### tyblu Member

Nov 29, 2010
199
16
Just verify it.. feed in inputs, calculate output.

5. ### GGerardo2010 Thread Starter New Member

Dec 11, 2010
4
0
I think that is the question, how to verify it multiply the variables together or by inputting zeros to the location of the variables.

(/A+B) is located @ 011, 010
(A+/B) is located @ 100, 101

(/B+C) is located @ 001. 101

In the POS method do you place a 1 in the KMAP to these locations or place a 0 where these variables are located?

The designing the circuit is no problem its the equation is what I am concerned about.

Can some tell me if the truth table is correct or is the a simpler way to do this?

6. ### tyblu Member

Nov 29, 2010
199
16
It's just "plug and chug":

$F(A,B,C) = (\not A + B)(A + \not B)(\not B + C)$
F(0,0,0) = (1 + 0)(0 + 1)(1 + 0) = (1)(1)(1) = 1
F(0,0,1) = (1 + 0)(0 + 1)(1 + 1) = (1)(1)(1) = 1
F(0,1,0) = (1 + 1)(0 + 0)(0 + 0) = (1)(0)(0) = 0
F(0,1,1) = (1 + 1)(0 + 0)(0 + 1) = (1)(0)(1) = 0
F(1,0,0) = (0 + 0)(1 + 1)(1 + 0) = (0)(1)(1) = 0
F(1,0,1) = (0 + 0)(1 + 1)(1 + 1) = (0)(1)(1) = 0
F(1,1,0) = (0 + 1)(1 + 0)(0 + 0) = (1)(1)(0) = 0
F(1,1,1) = (0 + 1)(1 + 0)(0 + 1) = (1)(1)(1) = 1

7. ### GGerardo2010 Thread Starter New Member

Dec 11, 2010
4
0
I have done that so many times I thought I was wrong! I thought I need to do something else like foil the variables out term by term.

Thank you. let me see I'll post the design up when I am done.