Combinational Logic Digital Design Department of Software Development

Combinational Logic Digital Design Department of Software Development Faculty of Information Technology Islamic University of Gaza Dr. Rebhi Baraka rbaraka@iugaza. edu

Basic Combinational Logic Circuits • • • AND-OR Logic AND-OR-Invert Logic Exclusive-OR Logic

Basic Combinational Logic Circuits • AND-OR Logic

Basic Combinational Logic Circuits • AND-OR Invert Logic

Basic Combinational Logic Circuits • Exclusive-OR Logic

Basic Combinational Logic Circuits • Exclusive-NOR Logic

Implementing Combinational Logic • From Boolean expression to logic circuit – Given a Boolean expression, create a logic circuit that implements that expression. • From truth table to logic circuit – Given a truth table, create a logic circuit that implements that table.

Implementing Combinational Logic • From Boolean expression to logic circuit Logic circuit for X = AB + CDE.

Implementing Combinational Logic • Implement the following Boolean expression:

Implementing Combinational Logic • From truth table to logic circuit – Given a truth table, create a logic circuit that implements that table. Input Output A B C X 0 0 1 1 0 1 0 1 0 0 0 1 1 0 0 0 The SOP expression obtained from the truth table is A’BC AB’C’

Implementing Combinational Logic • From truth table to logic circuit (continued)

Implementing Combinational Logic • Example: Design a logic circuit to implement the operation specified in the truth table Input Output A B C X 0 0 1 1 0 1 0 1 0 0 0 1 1 0 A’BC AB’C ABC’

Implementing Combinational Logic • Example: Design a logic circuit with 4 inputs that will only produce a 1 output when exactly 3 inputs are 1 s. The combinations in which there are exactly 3 1 s are listed in the table with their product terms A B C D 0 1 1 1 1 0 A’BCD AB’CD ABC’D ABCD’ X = A’BCD + AB’CD + ABC’D + ABCD’

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

The Universal Property of NAND Gates

The Universal Property of NOR Gates

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