Saturday, 24 November 2012

Simplification of Boolean Expressions


By on 22:16

Note:-Learn the rules/laws of Boolean Algebra.

Q)Simplify the below Boolean expressions

1) x+(x'y)
2)xy+xy'

Ans 1) x+(x'y)
=(x+x')(x+y)
=1.(x+y)
=(x+y)

Ans 2)xy+xy'
=x(y+y')
=x.1
=x

This above examples are quite simple,so now we discuss some good/quite tough questions.

Q)Simplify the below Boolean expressions

1)x'y'z'+x'yz'+xy'z'+xyz'
2)a[b+c(ab+ac)']
3)(A+B)(A+B')(A'+B)

Ans 1)x'y'z'+x'yz'+xy'z'+xyz'
=x'z'(y'+y)+xz'(y'+y)
=x'z'1+x.z'.1
=z'.1
=z'

Ans 2)a[b+c(ab+ac)'
=a[b+c(ab+ac)']
=a[b+c(b+c(ab)'.(ac)']
=a[b+c(a'a'+a'c'+a'b'+b'c')]
=a[b+c(a'(1+c')+a'b'+b'c')]
=a[b+c(a'.1+a'b'+b'c')]
=a[b+c(a'(1+b')+b'c')]
=a[b+a'c+a'b'c+0]
=ab+aa'c+aa'b'c
=ab+0+0
=ab

Ans 3)(A+B)(A+B')(A'+B)
=(A.A+AB'+AB+B.B')(A'+B)
=(A+AB'(B'+B)+0)(A'+B)
=(A+A+B)(A'+B)
=AA'+AB+AA'+AB
=AB+AB
=AB



If you have any query then leave your comments and don't forgot to follow me on Google+,Facebook,Twitter.

0 comments:

Post a Comment

Related Posts Plugin for WordPress, Blogger...