Simplify using Boolean Algebra and DeMorgan's Theorems

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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
 

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
 
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.
 
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