Digital Logic Design covers topics such as number systems, Boolean algebra, logic gates, and Boolean functions. Boolean algebra uses basic identities and DeMorgan's theorem to simplify digital circuits. Circuits can be represented by Boolean expressions and truth tables, which can then be algebraically manipulated to reduce complexity and implement functions using fewer logic gates. Taking the complement of a function inverts its output, while complementing using duals interchanges ANDs and ORs.

1. Digital Logic Design
PROF. SHEHZAD ALI

2. Overview
Number system
Binary Numbers
Boolean Algebra
Switching Algebra
Logic Gates
Boolean Function

3. Basic Identities of Boolean Algebra
The basic rules listed in the table have been arranged into two
columns that demonstrate the property of duality of Boolean
algebra.
The dual of an algebraic expression is obtained by interchanging OR
and AND operations and replacing 1s by 0s and 0s by 1s.

4. Basic Identities of Boolean Algebra

5. DeMorgan’s Theorem

6. Algebraic Manipulation
Boolean algebra is a useful tool for simplifying digital circuits. Consider, for example, the Boolean
function represented by
The expression is reduced to only two terms and can be implemented with
gates as shown in Figure 4(b).

7. Algebraic Manipulation

8. Truth Table for Boolean Function

9. Algebraic Manipulation Examples

10. Algebraic Manipulation Examples

11. Complement of a Function

12. EXAMPLE Complementing Functions

13. EXAMPLE Complementing Functions by Using Duals