Unit 1
Logic Minimisation
Boolean Expression:-
they are constructed by connecting the Boolean constants and variables with
Boolean operations
These Boolean expression are also known as Boolean formulas
For example if the Boolean expression (A+B)C is used to describe the function f
then Boolean function is written as f(A,B,C) = (A+B)C or. f =(A+B)C
Each occurance of a variable in either complemented or uncomplemented form is
called literal
A product term is defined as either a literal or a product (also called conjunction) or
literals
A sum term is defined as either a literals or a sum (also called as disjunction) of
literals
These literals and terms are arranged in one of two forms:
Sum of product form (SOP)Product of sum form (POS)
A product term is any group of literals that are ANDed together.
Ex. ABC, XY.
A sum term is any group of literals that are ORed together.
Ex.A+B+C, X+Y
Sum of Product form:-(a group of AND terms ORed together)
The sum of products is a group of product terms (AND terms) ORed together
The sum of product form is also known as disjunctive normal form or
disjunctive normal formula.
Unit 1 1
, Ex 1:-
Sum Terms
⇑
f(A,B,C)= ABC + ABC
⇓ ⇓
Product Terms
Ex 2:-
Sum Terms
⇑ ⇑
f(P,Q,R,S)= PQ + QR + RS
⇓ ⇓ ⇓
Product Terms
Product of Sum form:-(a group of OR terms ANDed together)
A product of sums is any groups of sum terms (OR terms) ANDed together.
The product of sum form is also known as conjunctive normal form or
conjunctive normal formula.
Ex 1:-
Product
⇑
f(A,B,C)= (A + B) . (B + C)
⇓ ⇓
Sum Terms
Ex 2:-
Sum Terms
⇑ ⇑
f(P,Q,R,S)= (P + Q) + (R + S) + (P + S)
⇓ ⇓ ⇓
Unit 1 2
Unit 1
Logic Minimisation
Boolean Expression:-
they are constructed by connecting the Boolean constants and variables with
Boolean operations
These Boolean expression are also known as Boolean formulas
For example if the Boolean expression (A+B)C is used to describe the function f
then Boolean function is written as f(A,B,C) = (A+B)C or. f =(A+B)C
Each occurance of a variable in either complemented or uncomplemented form is
called literal
A product term is defined as either a literal or a product (also called conjunction) or
literals
A sum term is defined as either a literals or a sum (also called as disjunction) of
literals
These literals and terms are arranged in one of two forms:
Sum of product form (SOP)Product of sum form (POS)
A product term is any group of literals that are ANDed together.
Ex. ABC, XY.
A sum term is any group of literals that are ORed together.
Ex.A+B+C, X+Y
Sum of Product form:-(a group of AND terms ORed together)
The sum of products is a group of product terms (AND terms) ORed together
The sum of product form is also known as disjunctive normal form or
disjunctive normal formula.
Unit 1 1
, Ex 1:-
Sum Terms
⇑
f(A,B,C)= ABC + ABC
⇓ ⇓
Product Terms
Ex 2:-
Sum Terms
⇑ ⇑
f(P,Q,R,S)= PQ + QR + RS
⇓ ⇓ ⇓
Product Terms
Product of Sum form:-(a group of OR terms ANDed together)
A product of sums is any groups of sum terms (OR terms) ANDed together.
The product of sum form is also known as conjunctive normal form or
conjunctive normal formula.
Ex 1:-
Product
⇑
f(A,B,C)= (A + B) . (B + C)
⇓ ⇓
Sum Terms
Ex 2:-
Sum Terms
⇑ ⇑
f(P,Q,R,S)= (P + Q) + (R + S) + (P + S)
⇓ ⇓ ⇓
Unit 1 2
