2/8 Content + Assignment 7

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.

(xyz)'

= ((xy)z)'

= (xy)' + z'

= x' + y' + z'

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

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