# DeMorgans Laws

#### mztrordinary

Joined May 25, 2016
35
Hi I need some guidance with converting the boolean expression A and B or Not C into a NOR gate circuit I am totally lost with this and the steps i have attached in the pics are below as to my steps with DeMorgans breaking the line changing the sign etc but i dont know where to go after that

#### MrChips

Joined Oct 2, 2009
22,505
You managed to utilize two bars as in the second line. Why not place it over the first line?

#### mztrordinary

Joined May 25, 2016
35
I am totally confused with this

#### WBahn

Joined Mar 31, 2012
26,398
I am totally confused with this
Take a step back and consider the more basic cases.

How would you transform X + Y so that it used only NOR gates?

How would you similarly transform X + Y' ?

#### RBR1317

Joined Nov 13, 2010
591
So you got the red-shaded area to look like a NOR gate. How would you make the blue-shaded area look like a NOR gate (without changing the logic function)?

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#### mztrordinary

Joined May 25, 2016
35
So you got the red-shaded area to look like a NOR gate. How would you make the blue-shaded area look like a NOR gate (without changing the logic function)?

I think i am almost there the green ticks are from my professor he said it is almost correct i just cannot wrap my head around this

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#### MrChips

Joined Oct 2, 2009
22,505
You are good up to the fourth line, why the fifth line?
You need to convert all your dot operators (AND) to + operators (OR).
If you already have OR operator, leave it at that.

A + B = NOT ( NOT (A + B) )

#### mztrordinary

Joined May 25, 2016
35
You are good up to the fourth line, why the fifth line?
You need to convert all your dot operators (AND) to + operators (OR).
If you already have OR operator, leave it at that.

A + B = NOT ( NOT (A + B) )

Well i suffer with dyslexia so trying to understand these things can sometimes be a big task hence why i thought i was correct with the first 4 lines and then no more.

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#### mztrordinary

Joined May 25, 2016
35
Think i have it

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#### MrChips

Joined Oct 2, 2009
22,505

#### mztrordinary

Joined May 25, 2016
35
Whats the difference with 9 and 10. Sorry i see it there but the equation in ten is same is it not as in the long line over the final step represents NOR anyway as too does the plus sign with a line over it? But please inform me if i am wrong

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#### MrChips

Joined Oct 2, 2009
22,505
I thought that you had to use only NOR gates.

#### mztrordinary

Joined May 25, 2016
35
yes just Nor gates

#### MrChips

Joined Oct 2, 2009
22,505
yes just Nor gates
Then post #9 is the correct answer.
How do you implement a NOT gate using a NOR gate?

#### mztrordinary

Joined May 25, 2016
35
9 and 10 are the same the only difference is the word nor between the expressions instead of the + symbol in 10. but the line over the plus represents the NOR no?

#### MrChips

Joined Oct 2, 2009
22,505
#9 and #10 are not the same.
The fourth line in #10 is the correct answer.
You made a mistake in the last line of #10. It should be C, not /C.
But now you have replaced the NOR gate with a NAND gate.
Keep the + operator, not the dot operator.

In this exercise, I find it is easier to work with digital logic symbols rather than boolean algebra. Your answer to this question would appear immediately in one step.

#### MrChips

Joined Oct 2, 2009
22,505
Look at these diagrams.

U1 and U1B are equivalent.

U2 and U2B are equivalent.

#### MrChips

Joined Oct 2, 2009
22,505
This is what was given to you:

Now convert the AND gate to an OR gate using U2 = U2B from my previous post.
Replace F with //F.