1.0
DIGITAL LOGIC
1.1 Basic Revision of Logic
Gates
Principles of logic.
Any Boolean algebra operation can be associated
with an electronic
circuit in which the inputs and outputs represent
the statements of
Boolean algebra. Although these circuits may be
complex, they may all
be constructed from six devices. These
are the AND gate, the OR gate, the NOT gate, the NAND gate, the XOR gate
and the NOR gate.
1.2 Boolen Equation
Form
1.2.1 Sum of Product and Product of Sum
Boolen equation form can be represent in two forms :
A) Sum-of-product is a
sum of three product terms
When two or more product terms
are summed by Boolean addition,
the resulting expression is a
sum-of-products (SOP). Some examples are:
AB + ABC
ABC + CDE + BCD
AB + BCD + AC
Also, an SOP expression can
contain a single-variable term, as in
A + ABC + BCD.
In an
SOP expression a single overbar cannot extend over more than
B) Product-of –sum is a
product of three sum terms
A
sum term was defined before as a term consisting of the sum
(Boolean
addition) of literals (variables or their complements). When two or
more
sum terms are multiplied, the resulting expression is a product-of-sums
(POS).
Some examples are
(A
+ B)(A + B + C)
(A
+ B + C)( C + D + E)(B + C + D)
(A
+ B)(A + B + C)(A + C)
A
POS expression can contain a single-variable term, as in
A(A
+ B + C)(B + C + D).
In
a POS expression, a single overbar cannot extend over more than one
variable;
however, more than one variable in a term can have an overbar. For
example, a
POS expression can have the term A + B + C but not A + B + C.
1.3 Simplication Of Boolean
Equation
1.3.1 Laws of boolean Algebra
The basic laws of Boolean algebra-the
commutative laws for addition and
multiplication, the associative laws
for addition and multiplication, and the
distributive law-are the same as in ordinary
algebra.
