Combinational Logic Circuits Reference M Mano C Kime
Combinational Logic Circuits Reference: M. Mano, C. Kime, “Logic and Computer Design Fundamentals”, Chapter 2 Dr. Costas Kyriacou and Dr. Konstantinos Tatas ACOE 161 - Digital Logic for Computers - Frederick University
Basic Logic Gates Logic Function Gate Symbol Logic Expression Truth Table ACOE 161 - Digital Logic for Computers - Frederick University 2
Basic Logic Gates with Inverted Outputs ACOE 161 - Digital Logic for Computers - Frederick University 3
Logic Gates with more than two inputs ACOE 161 - Digital Logic for Computers - Frederick University 4
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 ACOE 161 - Digital Logic for Computers - Frederick University 5
Analysis and Synthesis of Digital Circuits (2/2) Truth table Analysis Synthesis Logic equation ACOE 161 Circuit diagram Analysis ACOE 161 - Digital Logic for Computers - Frederick University 6
Circuit Implementation of a Logic Expression with Gates ACOE 161 - Digital Logic for Computers - Frederick University 7
Circuit Implementation of Logic Expressions: - Examples ACOE 161 - Digital Logic for Computers - Frederick University 8
Circuit Implementation of Logic Expressions: - Homework ACOE 161 - Digital Logic for Computers - Frederick University 9
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: ACOE 161 - Digital Logic for Computers - Frederick University 10
Truth Tables: Examples ACOE 161 - Digital Logic for Computers - Frederick University 11
Minterms and maxterms Row X Y Z ACOE 161 F Minterm Maxterm 0 0 F(0, 0, 0) X΄Y΄Z΄ Χ+Υ+Ζ 1 0 0 1 F(0, 0, 1) X΄Y΄Z Χ+Υ+Ζ΄ 2 0 1 0 F(0, 1, 0) X΄YZ΄ Χ+Υ΄+Ζ 3 0 1 1 F(0, 1, 1) X΄YZ Χ+Υ΄+Ζ΄ 4 1 0 0 F(1, 0, 0) XY΄Z΄ Χ΄+Υ+Ζ 5 1 0 1 F(1, 0, 1) XY΄Z Χ΄+Υ+Ζ΄ 6 1 1 0 F(1, 1, 0) XYZ΄ Χ΄+Υ΄+Ζ 7 1 1 1 F(1, 1, 1) XYZ Χ΄+Υ΄+Ζ΄ ACOE 161 - Digital Logic for Computers - Frederick University 12
Standard forms: Sum of Products ACOE 161 - Digital Logic for Computers - Frederick University 13
Logic expression and truth table of a logic circuit ACOE 161 - Digital Logic for Computers - Frederick University 14
Example: Find the logic expression and fill up the truth table for the circuit below. ACOE 161 - Digital Logic for Computers - Frederick University 15
Homework: Find the logic expression and fill up the truth table for the circuit below. ACOE 161 - Digital Logic for Computers - Frederick University 16
Analyzing a logic circuit using timing diagrams Logic 1 Logic 0 ACOE 161 - Digital Logic for Computers - Frederick University 17
Homework: Fill up the truth table and timing diagram for the circuit below. ACOE 161 - Digital Logic for Computers - Frederick University 18
Boolean Algebra Basic Boolean identities: ACOE 161 - Digital Logic for Computers - Frederick University 19
Boolean Algebra (Examples) Prove the following identities using Boolean algebra and truth tables: ACOE 161 - Digital Logic for Computers - Frederick University 20
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. ACOE 161 - Digital Logic for Computers - Frederick University 21
Boolean Algebra (Examples) Simplify the expressions given below. Use truth tables to verify your results. ACOE 161 - Digital Logic for Computers - Frederick University 22
Boolean Algebra (Examples - Cont. ) Simplify the expressions given below. Use truth tables to verify your results. ACOE 161 - Digital Logic for Computers - Frederick University 23
Boolean Algebra (Examples - Cont. ) Simplify the expression given below. Use truth tables to verify your results. ACOE 161 - Digital Logic for Computers - Frederick University 24
Boolean Algebra (Examples - Cont. ) Simplify the expression given below. Use truth tables to verify your results. ACOE 161 - Digital Logic for Computers - Frederick University 25
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