1. 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

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

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

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

5. 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
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ACOE161 - Digital Logic for Computers - Frederick University

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

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

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

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

10. 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

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

12. 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

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

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

15. 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

16. 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

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

18. 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

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

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

21. 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

22. 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

23. 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

24. 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

25. 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