2. Contents
• Types of digital circuit
• Combinational circuit
• Block diagram of combinational circuit
• Sum of product form
• Product of sum form
• Standard SOP form
• Standard POS form
• Conversion of non standard SOP to standard SOP
• Conversion of non standard POS to standard POS
• Minterm and Maxterm
3. Types of circuits
• In digital Electronics
Two types of circuits
1. combinational circuit
2. sequential circuit
4. Introduction of Combinational circuit
• a circuit whose output is dependent only on the state of its
inputs
• The output of combinational circuit at any instant of time,
depends only on the levels present at input terminals.
• The combinational circuit do not use any memory.
• The previous state of input does not have any effect on
the present state of the circuit.
• A combinational circuit can have an n number of inputs
and m number of outputs.
• for example: Adder, subtractor,encoder, decoder,
multiplexer and demultiplexer.
6. 3.1 Standard Boolean representation
• Sum of Product (SOP) & Product of Sum (POS),
• Maxterm and Minterm ,
• Conversion between SOP and POS forms,
• Realization using NAND/NOR gates.
Unit outcome:
• Develop logic circuits in standard SOP/POS form for the
given logical expression.
7. Standard
Any logical expression can be expressed in the following
two forms:
• Sum of Product (SOP) Form
• Product of Sum (POS) Form
10. Standard or canonical form means?
• A logic expression is said to be in the standard (or
canonical) SOP or POS form if each product term (for
SOP) and sum term (for POS) consists of all the literals in
their complemented or uncomplemented form.
• std. SOP form
• std. POS form
12. Conversion of non standard SOP form to
Standard SOP
Steps:
1. Write down all the terms.
2. If one or more variables are missing in any product term,
expand the term by multiplying it with the sum of each one
of the missing variable and its complement .
3. Drop out the redundant terms
18. Conversion of POS form to Standard
POS
• Steps:
1. Write down all the terms.
2. If one or more variables are missing in any sum term,
expand the term by adding the products of each one of the
missing variable and its complement .
3. Drop out the redundant terms
22. minterm and Maxterm
• A minterm is a Boolean expression resulting in 1 for the
output of a single cell, and 0s for all other cells in a
Karnaugh map, or truth table.
• If a minterm has a single 1 and the remaining cells as 0s,
it would appear to cover a minimum area of 1s.
• minterm ABC a single product term, as a single 1 in a
map
• A Maxterm is a Boolean expression resulting in a 0 for the
output of a single cell expression, and 1s for all other cells
in the Karnaugh map, or truth table.
• Maxterm (A+B+C), a single sum term, as a single 0 in a
map
