combinational logic digital design department of software development faculty of information...

Combinational LogicCombinational Logic

Digital DesignDigital Design

Department of Software DevelopmentDepartment of Software Development

Faculty of Information TechnologyFaculty of Information Technology

Islamic University of GazaIslamic University of Gaza

Dr. Rebhi BarakaDr. Rebhi Baraka

rbaraka@iugaza.edu

Basic Combinational Logic CircuitsBasic Combinational Logic Circuits

• AND-OR LogicAND-OR Logic• AND-OR-Invert LogicAND-OR-Invert Logic• Exclusive-OR LogicExclusive-OR Logic

Basic Combinational Logic CircuitsBasic Combinational Logic Circuits

• AND-OR LogicAND-OR Logic

Basic Combinational Logic CircuitsBasic Combinational Logic Circuits

• AND-OR Invert LogicAND-OR Invert Logic

Basic Combinational Logic CircuitsBasic Combinational Logic Circuits

• Exclusive-OR LogicExclusive-OR Logic

Basic Combinational Logic CircuitsBasic Combinational Logic Circuits

• Exclusive-NOR LogicExclusive-NOR Logic

Implementing Combinational LogicImplementing Combinational Logic

• From Boolean expression to logic From Boolean expression to logic circuitcircuit– Given a Boolean expression, create a Given a Boolean expression, create a

logic circuit that implements that logic circuit that implements that expression.expression.

• From truth table to logic circuitFrom truth table to logic circuit– Given a truth table, create a logic circuit Given a truth table, create a logic circuit

that implements that table.that implements that table.

Implementing Combinational LogicImplementing Combinational Logic

• From Boolean expression to logic circuitFrom Boolean expression to logic circuit

Logic circuit for Logic circuit for XX = = ABAB + + CDECDE . .

Implementing Combinational LogicImplementing Combinational Logic

• Implement the following Boolean expression:Implement the following Boolean expression:

Implementing Combinational LogicImplementing Combinational Logic

• From truth table to logic circuitFrom truth table to logic circuit– Given a truth table, create a logic circuit that Given a truth table, create a logic circuit that

implements that table.implements that table.Input Output

A B C X

00001111

00110011

01010101

00011000

A’BCAB’C’

The SOP expression obtained from the truth table is

Implementing Combinational LogicImplementing Combinational Logic

• From truth table to logic circuit (continued)From truth table to logic circuit (continued)

Implementing Combinational LogicImplementing Combinational Logic

• Example: Design a logic circuit to implement the operation specified in the truth tableExample: Design a logic circuit to implement the operation specified in the truth table

Input Output

A B C X

00001111

00110011

01010101

00010110

A’BC

AB’CABC’

Implementing Combinational LogicImplementing Combinational Logic

• Example: Design a logic circuit with 4 inputs that will only produce a 1 output when exactly Example: Design a logic circuit with 4 inputs that will only produce a 1 output when exactly 3 inputs are 1s.3 inputs are 1s.

The combinations in which there are exactly 3 1s are listed in the table with their product termsThe combinations in which there are exactly 3 1s are listed in the table with their product terms

A B C D

0111

1011

1101

1110

A’BCDAB’CDABC’DABCD’

X = A’BCD + AB’CD + ABC’D + ABCD’

The Universal Property The Universal Property of NAND and NOR Gatesof NAND and NOR Gates

NAND and NOR gates are “universal” because they can be NAND and NOR gates are “universal” because they can be used to produce any of the other logic functions.used to produce any of the other logic functions.

The Universal Property of NAND GatesThe Universal Property of NAND Gates

The Universal Property of NOR GatesThe Universal Property of NOR Gates

These slides are based on Digital Fundamentals 9These slides are based on Digital Fundamentals 9 thth ed. By Thomas Floyd ed. By Thomas Floyd