Simplify using Boolean Algebra and DeMorgan's Theorems

WC_demon

Joined Dec 16, 2007
2
I'd like to get some insight as to how to complete this: (X''+Y')+XYZ+X''Y''+Z'
Here are my steps:
(X''+Y')+XYZ+X''Y''+Z'
(X+Y')+XYZ+XY+Z'
(X+Y')+XYZ+Y+Z'
(X+Y')+XYZ+Z'
(XY')+XYZ+Z'
(XY')+XYZ+Z'

This is as far as i could get.

hgmjr

Joined Jan 28, 2005
9,029
Review the material in this section of the AAC e-book.

Several members have commented on the clarity of the explanation it provides for boolean expression manipulation.

hgmjr

agentofdarkness

Joined Oct 9, 2007
42
What does X" mean?

WC_demon

Joined Dec 16, 2007
2
that it's like two NOT gates, so it equals X

hgmjr

Joined Jan 28, 2005
9,029
Each tick merk equates to an overbar which is used to indicate negation. A double tick as WC_demon has indicated is the same as a double negation and therefore it equates to the non-negated variable.

hgmjr

agentofdarkness

Joined Oct 9, 2007
42
Thats what I figured. Whats the reasoning behind double negating a variable? I know its sometimes used when doing a NOR/NOR or NAND/NAND circuit like [F']' where F is some function (like ABC) but what about just one variable.

Management

Joined Sep 18, 2007
306
Maybe it is acting like some sort of buffer. The double negation that is.