Post date: Feb 8, 2011 5:12:31 PM
Content:
Basic identities of boolean algebra;
Use truth table to prove a boolean equation;
Use algebraic manipulation to prove a boolean equation.
Assignment 7:
Use truth table and algebraic manipulation to prove the following boolean equation:
1) (xyz)' = x'+y'+z'
2) x'y' + x'y + xy = x' + y
3) A'B+B'C'+AB+B'C = 1
Answer:
Truth tables are ignored.
1)
(xyz)'
= ((xy)z)'
= (xy)' + z'
= x' + y' + z'
2)
x'y' + x'y + xy
= x'y' + x'y + x'y + xy
=(x'y' + x'y) + (yx' + yx)
=x'(y'+y) + y(x'+x)
=x'.1+y.1
=x' + y
3)
A'B+B'C'+AB+B'C
=A'B+AB+B'C'+B'C
=(BA'+BA)+(B'C'+B'C)
=B(A'+A)+B'(C'+C)
=B.1+B'.1
=B+B'
= 1