This document provides an overview of digital logic circuits and Boolean algebra. It discusses minimization techniques for Boolean expressions including Karnaugh maps. The basic types of logic gates like AND, OR, and NOT are described. Boolean algebra is defined as the algebra of binary variables and logic operations. Some key theorems of Boolean algebra are also summarized such as De Morgan's theorems.

1. 19EI4251
Digital Logic Circuits

3. Unit 1 –
MINIMIZATION TECHNIQUES AND
LOGIC GATES
• Boolean Algebra
• Demorgan’s Theorem
• Minimization of Boolean Expressions
• Minterms, Maxterms
• Sum Of Products (SOP)
• Products Of Sums(POS)

4. • Karnaugh Map Minimization
• Dont Care Conditions
• Simplification of Boolean expression using logic gates
NAND,NOR
• Implementation of Boolean functions using K Maps

5. Digital Electronics
• Digital electronics is a field of electronics involving the study
of digital signals and the engineering of devices that use or
produce them.
• Digital electronic circuits are usually made from large assemblies
of logic gates , often packaged in integrated circuits.
• Complex devices may have simple electronic representations
of Boolean logic functions

6. BASIC LOGIC BLOCK - GATE
Types of Basic Logic Blocks
- Combinational Logic Block
Logic Blocks whose output logic value
depends only on the input logic values
- Sequential Logic Block
Logic Blocks whose output logic value
depends on the input values and the
state (stored information) of the blocks
Functions of Gates can be described by
- Truth Table
- Boolean Function
- Karnaugh Map
Gate
.
.
.
Binary
Digital
Input
Signal
Binary
Digital
Output
Signal

7. BOOLEAN ALGEBRA
Boolean Algebra
* Algebra with Binary(Boolean) Variable and Logic Operations
* Boolean Algebra is useful in Analysis and Synthesis of
Digital Logic Circuits
- Input and Output signals can be
represented by Boolean Variables, and
- Function of the Digital Logic Circuits can be represented by
Logic Operations, i.e., Boolean Function(s)
- From a Boolean function, a logic diagram
can be constructed using AND, OR, and I
Truth Table
* The most elementary specification of the function of a Digital Logic
Circuit is the Truth Table
Boolean Algebra

8. LOGIC CIRCUIT DESIGN
x y z F
0 0 0 0
0 0 1 1
0 1 0 0
0 1 1 0
1 0 0 1
1 0 1 1
1 1 0 1
1 1 1 1
F = x + y’z
x
y
z
F
Truth
Table
Boolean
Function
Logic
Diagram

13. Boolean Function
• Constructed by connecting Boolean constants and variables
• Boolean expressions are used to describe Boolean functions
F(A,B.C) = (A + B’) C

14. Postulates Comment
A + 0 = 0 + A = A Identity Element
A . 1= 1 . A = A
(A+B) = (B+A) Commutative Law
(A.B) = (B.A)
A.(B+C) = (A.B) + (A.C) Distributive Law
A+(B.C) = (A+B) . (A+C)
A+A’ = 1 Complement
A.A’ = 0
A+(B+C) = (A+B) + C Associative Law
(A.B) .C = A.(B.C)

15. Boolean Theorems
• Duality
• Basic Theorems
• De Morgan’s Theorem

16. Duality Principle
• Starting with boolean relation can derive another boolean
relation
• Example : A+A’=1 A. A’=0
Changing each OR sign to AND sign
Changing each AND sign to an OR sign
Complementing any 0 or 1 appearing in expression

17. Postulates
Postulates (a) (b)
Postulate 2 A+0=A A.1=A
Postulate 5 A + A’ =1 A.A’ = 0
Commutative A+B=B+A AB=BA
Distributive A(B+C)=AB+AC A+BC=(A+B)(A+C)

18. Theorems
Theorems (a) (b)
Theorem 1 (Idempotency)
A + A= A A.A=A
Theorem 2 A+1=1 A.0 =A
Theorem 3 (Involution) A’’ = A
Theorem 4 (Absorption) A + AB=A A(A+B)=A
Theorem 5 A + A’B = A+B A.(A’+B)=AB
Theorem 6 (Associative) A+(B+C)=(A+B)+C A(BC) = (AB)C

19. DeMorgan’s Theorems