A. Notes
In this last lesson of boolean algebra, we learned some common identities. Identities refer to the things that are always the same. For instance, A+B and B+A are always the same, so A+B and B+A are identities, we write A+B=B+A.
Some commonly used identities in Boolean Algebra are below.
#9 above is also called Law of Tautology. We can use these identities to simplify compound boolean expressions. While applying these identities, please keep in mind:
A * or a dot both means AND, and sometimes we even omit them. i.e. AB, A*B, A&&B all mean A AND B.
A bar on top of a variable means NOT, just as ! and ~. A bar on top of a compound expression means to negate the whole expression.
See the example below. Solution I and II both simplify this boolean expression.
B. HW
Simplify the following boolean expressions:
2. Use DeMorgan's Law to simplify the following:
true
A + B
not(A)+C+B
not(A) x B
not(A) x B
C x B + C x A
A x B + A x C
B
True
not (A) x B x C
(A or B) or (not B)
A or (B and C) or (B or C)
(not A) or C or (A and B)
(not A) and (B or (A and C))
(not A) and (B or A)
(B or (A and (not B)) and (C or (A and C))
(A and B and C) or (A and (not B) and C) or (A and B and (not C))
(B or (A and C)) and (B or (not A))
~A + ~B + ~C
A + ~B + ~C