Combinational Logic Circuits Reference: M. Mano, C. Kime, “Logic and Computer Design Fundamentals”, Chapter 2 Dr. Costas Kyriacou and Dr. Konstantinos Tatas (c) Costas Kyriacou

ACOE161 - Digital Logic for Computers - Frederick University Basic Logic Gates Logic Function Gate Symbol Logic Expression Truth Table ACOE161 ACOE161 - Digital Logic for Computers - Frederick University (c) Costas Kyriacou

Basic Logic Gates with Inverted Outputs ACOE161 ACOE161 - Digital Logic for Computers - Frederick University (c) Costas Kyriacou

Logic Gates with more than two inputs ACOE161 ACOE161 - Digital Logic for Computers - Frederick University (c) Costas Kyriacou

Analysis and Synthesis of Digital Circuits (1/2) There are three representations of a digital logic function Truth table (unique) Logic equation (not unique) Circuit diagram (not unique) We need to be able to go to from each representation to another ACOE161 ACOE161 - Digital Logic for Computers - Frederick University

Analysis and Synthesis of Digital Circuits (2/2) Truth table Logic equation Synthesis Circuit diagram Synthesis Analysis ACOE161 ACOE161 - Digital Logic for Computers - Frederick University

Circuit Implementation of a Logic Expression with Gates ACOE161 ACOE161 - Digital Logic for Computers - Frederick University (c) Costas Kyriacou

Circuit Implementation of Logic Expressions:- Examples ACOE161 ACOE161 - Digital Logic for Computers - Frederick University (c) Costas Kyriacou

Circuit Implementation of Logic Expressions:- Homework ACOE161 ACOE161 - Digital Logic for Computers - Frederick University (c) Costas Kyriacou

ACOE161 - Digital Logic for Computers - Frederick University Truth Tables Truth table of a logic circuit is a table showing all the possible input combinations with the corresponding value of the output. Examples: ACOE161 ACOE161 - Digital Logic for Computers - Frederick University (c) Costas Kyriacou

Truth Tables: Examples ACOE161 ACOE161 - Digital Logic for Computers - Frederick University (c) Costas Kyriacou

ACOE161 - Digital Logic for Computers - Frederick University Minterms and maxterms Row X Y Z F Minterm Maxterm F(0,0,0) X΄Y΄Z΄ Χ+Υ+Ζ 1 F(0,0,1) X΄Y΄Z Χ+Υ+Ζ΄ 2 F(0,1,0) X΄YZ΄ Χ+Υ΄+Ζ 3 F(0,1,1) X΄YZ Χ+Υ΄+Ζ΄ 4 F(1,0,0) XY΄Z΄ Χ΄+Υ+Ζ 5 F(1,0,1) XY΄Z Χ΄+Υ+Ζ΄ 6 F(1,1,0) XYZ΄ Χ΄+Υ΄+Ζ 7 F(1,1,1) XYZ Χ΄+Υ΄+Ζ΄ ACOE161 ACOE161 - Digital Logic for Computers - Frederick University

Standard forms: Sum of Products ACOE161 ACOE161 - Digital Logic for Computers - Frederick University (c) Costas Kyriacou

Logic expression and truth table of a logic circuit ACOE161 ACOE161 - Digital Logic for Computers - Frederick University (c) Costas Kyriacou

ACOE161 - Digital Logic for Computers - Frederick University Example: Find the logic expression and fill up the truth table for the circuit below. ACOE161 ACOE161 - Digital Logic for Computers - Frederick University (c) Costas Kyriacou

ACOE161 - Digital Logic for Computers - Frederick University Homework: Find the logic expression and fill up the truth table for the circuit below. ACOE161 ACOE161 - Digital Logic for Computers - Frederick University (c) Costas Kyriacou

Analyzing a logic circuit using timing diagrams ACOE161 ACOE161 - Digital Logic for Computers - Frederick University (c) Costas Kyriacou

ACOE161 - Digital Logic for Computers - Frederick University Homework: Fill up the truth table and timing diagram for the circuit below. ACOE161 ACOE161 - Digital Logic for Computers - Frederick University (c) Costas Kyriacou

ACOE161 - Digital Logic for Computers - Frederick University Boolean Algebra Basic Boolean identities: ACOE161 ACOE161 - Digital Logic for Computers - Frederick University (c) Costas Kyriacou

Boolean Algebra (Examples) Prove the following identities using Boolean algebra and truth tables: ACOE161 ACOE161 - Digital Logic for Computers - Frederick University (c) Costas Kyriacou

Digital circuit simplification using Boolean algebra Logic functions are simplified in order to reduce the number of gates required to implement them. Thus the circuit will cost less, need less space and power, be build faster with less effort. For example the expression F needs six gates to be build. If the expression is simplified then the function can be implemented with only two gates. ACOE161 ACOE161 - Digital Logic for Computers - Frederick University (c) Costas Kyriacou

Boolean Algebra (Examples) Simplify the expressions given below. Use truth tables to verify your results. ACOE161 ACOE161 - Digital Logic for Computers - Frederick University (c) Costas Kyriacou

Boolean Algebra (Examples - Cont.) Simplify the expressions given below. Use truth tables to verify your results. ACOE161 ACOE161 - Digital Logic for Computers - Frederick University (c) Costas Kyriacou

Boolean Algebra (Examples - Cont.) Simplify the expression given below. Use truth tables to verify your results. ACOE161 ACOE161 - Digital Logic for Computers - Frederick University (c) Costas Kyriacou

Boolean Algebra (Examples - Cont.) Simplify the expression given below. Use truth tables to verify your results. ACOE161 ACOE161 - Digital Logic for Computers - Frederick University (c) Costas Kyriacou