Basic boolean logic

Thread Starter

fran1942

Joined Jul 26, 2010
58
Hello, I am trying to grasp this topic.
I have the following expression (see attached image).
I need to
i) simplify using deMorgans theorem
ii) then show how the expression could be implemented using only 2 input NOR gates.

I "think" I have the deMorgans simplification correct, but I am not sure how to do part ii.
Any help would be much appreciated.
 

Attachments

Thread Starter

fran1942

Joined Jul 26, 2010
58
thanks, but that is the problem.
I am not sure how to rewrite my deMorgan simplification as two NOR gates.

Can anyone please help with this ?
 

DerStrom8

Joined Feb 20, 2011
2,373
You used DeMorgan's theorem incorrectly. When you use DeMorgan's theorem, you split up the "not" bar and change the operation. For example:

(A+B)' = A'*B'

The ' symbolizes a "Not" bar. As you can see, the entire first part (A+B) is inverted, so you have a bar above all of it. You split the bar so that each part has the bar over it, and then you change the operation from OR to AND (+ to *).

EDIT: Sorry, you are correct. I misread the expression :p
 

WBahn

Joined Mar 31, 2012
24,695
You actually only need a single 2-input NOR gate.

Your simplification is wrong.

This is what you started with

J = [(G'*H')' + (H*I')]'

Applying DeMorgan's gets you

J = (G'*H')*(H*I')'

Applying DeMorgan's to the second term gets you

J = (G'*H')*(H'+I)

But at this point you just removed the parens around the second factor. You have to distribute one over the other.

Now take a step back and look at your original expression

J = [(G'*H')' + (H*I')]'

This is ALREADY a NOR gate!

J = NOR[(G'*H')', (H*I')]

So focus on the guts of this expression and in three easy steps it will reduce to the OR of just two terms.
 

DerStrom8

Joined Feb 20, 2011
2,373
You actually only need a single 2-input NOR gate.

Your simplification is wrong.

This is what you started with

J = [(G'*H')' + (H*I')]'
That is not correct. The bar goes over the entire G*H expression. It is NOT G'*H', it is (G*H)'.

The OP's simplification is done correctly.
 

WBahn

Joined Mar 31, 2012
24,695
Oops. That's what happens when a nearly blind man that sees double and triple images has to switch between windows and remember what lines he saw where.

It's a shame, too, because my incorrect version simplifies so beautifully!

But the OP's simplification is still wrong. The mistake I made does not affect the need to distribute one factor over the other.

So hopefully this is the correct starting point.

J = [(G*H)' + (H*I')]'

This is still a NOR gate at the outermost level.

Applying DeMorgan's

J = (G*H)*(H*I')'

Applying DeMorgan's to the second term

J = (G*H)*(H'+I)

The OP has this

J = G*H*H'+I

Which is wrong, since AND takes precedence over OR and this would simplify to J=I

Instead, what you have is

J = (G*H)*(H'+I)

J = (G*H)*H'+(G*H)*I

J = G*H*I
 
Top