## Recent Post

Notation

Using, everywhere for AND is laborious
We will quietly drop. If the intention is clear
For Example
f = x1'.x2' + x1'.x2 + x1.x2
is better written as
f = x1'x2' + x1'x2 + x1x2
Usual precedence rules of + and . apply
- Do . before + just like in multiplication
- For example 5x + 3y is (5x) + (3y) and not 5(x+3)y

Some Definition

A literal is a complemented or uncomplemented boolean variables.
- Examples: a and ā are distinct literals. ā+cd is not.

A Product term is a single literal or a logical product (AND) of two or more literals.
- Examples: a, ā, ac, ācd, aaāb are product terms; ā+cd is not a product term.

A Sum term is a single literal or a logical sum (OR) of two or more literals.
- Examples: a, ā, a+c, ā+c+d are sum terms; ā+cd is not a sum term.

A normal term is a product or sum term in which no variable appears more than once.
- Example: a, ā, a+c, ācd are normal terms; ā+a, āa are not normal terms.

A minterm of n variables is a normal product term with n literals. There are 2 to the power n such product terms.
- Examples of 3-variables minterms: ābc, abc
- Examples: āb is not a 3-variable minterm.

A maxterm of n variable is a normal sum term with n literals. There are 2 to the power n such sum terms.
- Example of 3-variables maxterms: ā+b+c, a+b+c

A sum of product (SOP) expressions is a set of product (AND) terms connected with logical sum (OR) operators.
- Examples: a,ā,ab+c,āc+bde,a+b are SOP expressions.

A product of sum (POS)expressions is a set of sum (OR) terms connected with logical product (AND) operators.
- Examples: a,ā,a+b+c, (ā+c)(b+d) are POS expressions.

A canonical sum of products (CSOP) form of an expression refers to rewriting the expression as a sum of minterms.
- Examples for 3-variables: ābc+abc is a CSOP expression; āb+c is not.

The canonical products of sum (CPOS) form of an expression refers to rewriting the expression as a product of maxterms.
- Examples for 3-variables: (ā+b+c)(a+b+c) is a CPOS expressions; (ā+b)c is not.

There is a close correspondence between the truth table and minterms and maxterms.

DeMorgan's Theorem (revisited)

Complement of Sum of Product is equivalent to Product of Complements.
Complement of Product of Sum is equivalent to Sum of Complements.