Boolean algebra

[Spyros13]

Simplify this Boolean expression please: F(a,b,c)=((c+a)^' *(c⊕b)^')^'

 

⊕=XOR

Edited February 10, 2011 by Spyros13

[khaled]

Boolean Algebra is the most basic algebra in mathematics, you should be able to do this ...

 

http://en.wikipedia.org/wiki/Boolean_algebra_%28logic%29

 

I'll take * as AND, + as OR, and ⊕ as XOR, and ' as NOT

 

Following De Morgan Laws, we get the following ...

 

while NOT AND = OR, and NOT OR = AND

 

(a+a') = 1 :: always true (something can happen or not)

 

(a*a') = 0 :: always false (something can happen and not)

 

(c+a)' = c' * a'

 

(c⊕b)' = ( (c * b') + (c' * b) )' = (c * b')' * (c' * b)' = (c' + b) * (c + b')

 

we get ...

 

((c+a)' * (c⊕b)')' = ( (c' * a') * ((c' + b) * (c + b')) )' = (c' * a')' + ((c' + b) * (c + b'))'

 

= (c + a) + ( (c' + b)' + (c + b')' ) = (c + a) + ( (c * b') + (c' * b') )

 

= c + a + ((c * b') + (c' * b')) = c + a + (b' * (c + c'))

 

= c + a + b'