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...
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
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