INTRODUCTION
In this modern world of electronics, the term
digital is mostly associated with a computer. Number systems are used to
represent data in digital systems. In this chapter, we will consider the
following topics:
- Analog and digital system.
- Number systems: decimal,
binary, octal, and hexadecimal number systems
- Counting in various number
systems
- Number system
conversions
- Basic binary arithmetic:
addition, subtraction, multiplication, division.
- Complements of numbers: 1's
and 2's complement of binary number, 7's and 8's complement of octal
number, 9's and 10's complement of decimal number, 15's and 16's
complement of hexadecimal number.
- Number representation in
binary system: sign magnitude representation, 1's complement
representation, 2's complement representation.
- Complement binary, octal,
decimal, and hexadecimal arithmetic: addition and subtraction using
complement of numbers.
- Binary codes: BCD, Excess-3
code, Gray code; their conversion.
Analog
and digital systems
There are two types of electronic circuits and
systems:
Analog
System: Analog systems are those in which physical quantities are represented
over a continuous range of values.
Digital
System: Digital systems are those in which physical quantities are represented
in digital form; that is, the quantities can take on only discrete values.
The
comparison between analog and digital system are given in the following text
Advantages of Digital System
1.
Digital systems are easier to design.
2.
Storage of information is easy.
3.
Greater accuracy and precision.
4.
Digital systems are less affected by noise. 5.Operation can be controlled
by a program.
6. More
digital circuitry can be fabricated on integrated circuit (IC) devices.
7.
Digital Systems are more reliable.
Limitations
of Digital System
In real world, most physical quantities are analog in nature. These
quantities are used as input signals of system and monitored for controlling
the system. In digital system, these analog quantities are converted to digital
quantities. Because of these conversions, the processing time increases and the
system becomes more complex.
Number system
A number
system is nothing more than a code that uses symbols to represent a number. In
general, in any number system, there is an ordered set of symbols known as
digits. A number is made up of a collection of digits and it has two parts;
integer and fraction, both are separated by a radix point (.). The number is
represented as,
Where,
r = radix or base of the number system n= number of digits in the integer part
m =
number of digits in fractional part
dn-1=
most significant digit (MSD)
d-m=
least significant digit (LSD) On the basis of number of different symbols used
(radix), number systems are classified as
1.
Decimal number system
2. Binary
number
3.Octal
number system
4.
Hexadecimal number system
Now, we
discuss each number system in following sections.
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