Digital Logic

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.