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
9.
10.
11.
12.
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)
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
