unit 8 digital logic. (1) to study and understand boolean algebra and boolean properties. (2) to...

VTU Syllabus

BASIC ELECTRONICS P. S. AITHAL

UNIT 8

DIGITAL LOGIC

(1) To study and understand Boolean algebra and Boolean properties.

(2) To design and analyze Logic gates.

(3) To design and analyze Half-adder, Full-adder, and Parallel Binary adder.

OBJECTIVES

8.1.1 Digital Signal

(i) Digital systems are easier to design (ii) Information storage is easy (iii) Accuracy and precision are greater (iv) Digital systems are more versatile (v) Digital circuits are less affected by

noise (vi) More digital circuitry can be

fabricated on IC chips

8.1.2 Digital Systems

Digital systems use the binary number system. Therefore, two-state devices are used to represent the two binary digits 1 and 0 by two different voltage levels, called HIGH and LOW.

If the HIGH voltage level is used to represent 1 and the LOW voltage level is used to represent 0, the system is called the positive logic system.

On the other hand, if the HIGH voltage level represents 0 and the LOW voltage level represents 1, the system is called the negative logic system.

8.1.3 Logic Levels

Boolean algebra is a kind of logical mathematics developed by George Boole in the late 1830s. It resembles the algebra of real numbers but the basic numeric operations of multiplication, addition, and negation are replaced by basic logical operations of conjunction, disjunction, and complement and are also called OR operation, AND operation and NOT operation respectively.

8.2 BOOLEAN ALGEBRA

OR Logical Operation:

8.2.1 Boolean Arithmetic

AND Logical Operation:

NOT Logical Operation:

8.2.2 Boolean Identities

Boolean algebraic identities of additive type :

Boolean algebraic identities of multiplicative type

8.2.3 Properties of Boolean Algebra

8.2.4 Boolean Rules for Simplification

8.2.5 De-Morgan’s Theorems

8.3 LOGIC GATES

8.3.1 OR Gate

OR gate using Diodes:

8.3.2 AND Gate :

AND gate using Diodes:

8.3.3 NOT Gate

NOT gate using Transistor:

8.3.4 NOR Gate

NOR gate using Transistors:

8.3.5 NAND Gate

NAND gate using Transistors:

8.3.6 XOR Gate

8.3.7 XNOR Gate

(1) NAND gate as Universal Gate:

8.3.8 Universal Gate

(2) NOR gate as Universal Gate:

8.3.9 Equivalent Gate

The digital system consists of two types of circuits, namely (i) Combinational circuits and (ii) Sequential circuits

A combinational circuit consists of logic gates, where outputs at any instant and are determined only by the present combination of inputs without regard to previous inputs or previous state of outputs.

A combinational circuit performs a specific information-processing operation assigned logically by a set of Boolean functions.

Sequential circuits contain logic gates as well as memory cells. Their outputs depend on the present inputs and also on the states of memory elements.

8.4 BINARY ADDERS

8.4.1 Half-Adder

(1) Half Adder using NAND gates:

(2) Half Adder using NOR gates:

8.4.2 Full-Adder :

(1) Full Adder using NAND gates:

(2) Full Adder using NOR gates:

8.4.3 Parallel Binary Adder

END