EE200(class 32)
Prof. M.M. Dawoud
19
EE200 DIGITAL LOGIC CIRCUIT DESIGN
Class Notes
CLASS 33
The material covered in this class will be as follows:
⇒
Boolean Algebra
⇒
Postulates
⇒
Twovalued Boolean Algebra
⇒
Basic Theorems and Properties
⇒
Venn Diagrams
Boolean Algebra:
It is defined with a set of elements, set of operators, and a number
of unproved axioms or postulates. We are interested in twovalued
Boolean Algebra.
Axiomatic Definition of Boolean Algebra:
Boole in 1854 introduced the treatment of logic and Shannon in
1938 introduced the 2valued Boolean Algebra (Switching Theory).
We define Boolean Algebra by using the following
Huntington's
postulates
defined on a set of two elements
B
and two binary
operators: +, .
1.
Closure
a.
with respect to +
b.
with respect to .
2. Identity
a.
wrt + called 0 such that x + 0 = 0 + x = x
b.
wrt . called 1 such that
x.1 = 1.x = x
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Prof. M.M. Dawoud
20
3.
Commutative
a.
x + y = y + x
b.
x.y = y.x
4.
Distributive
a.
x.(y+z) = x.y + x.z
b.
x + (y.z) = (x +
y).(x + z)
5.
For
xB
∈
there
is
′
∈
such
that
1,
.
0
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 Spring '09
 prof.ahmed
 Logic, Boolean Algebra, Axiom, Prof. M.M. Dawoud

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