Encoding in number system-
Encoding in
a number system refers to the representation of data (such as characters,
symbols, or instructions) using a specific numerical format or base. In
computer science, encoding is crucial because computers inherently understand
data in binary (base-2) form, and encoding schemes are used to convert
human-readable information into binary digits.
Common
Encoding Schemes in Number Systems
1.
Binary Encoding:
Directly uses binary digits (0 and 1) to represent data.
2.
BCD (Binary-Coded Decimal): Represents each decimal digit (0-9) in a 4-bit binary form.
3.
Gray Code: A
binary numeral system where two successive values differ in only one bit.
4.
ASCII (American Standard Code for Information Interchange): Encodes characters as binary
numbers using 7 or 8 bits.
5.
EBCDIC (Extended Binary Coded Decimal Interchange Code): An 8-bit character encoding used
primarily on IBM mainframes.
6.
Base64 Encoding:
Represents binary data in an ASCII string format using 64 characters.
7.
Unicode: An
encoding standard that allows for the representation of text in most of the
world's writing systems.
Let's
explore these encoding schemes in more detail.
1. Binary
Encoding
- Description: Binary encoding uses the
binary number system (0 and 1) to represent data. Each piece of data, like
a character or number, is represented as a sequence of bits (binary
digits).
- Usage: It is the most fundamental
encoding since computers operate in binary at the hardware level.
Example
The binary
representation of the decimal number 5 is 101.
2. BCD
(Binary-Coded Decimal)
- Description: In BCD encoding, each decimal
digit is represented separately by its 4-bit binary equivalent.
- Usage: Used in applications where
numerical precision is important, such as financial calculations, digital
clocks, and calculators.
Example
The decimal
number 259 in BCD would be:
- 2 → 0010
- 5 → 0101
- 9 → 1001
So, 259 in
BCD is 0010 0101 1001.
3. Gray
Code
- Description: Gray code is a binary numeral
system where two successive values differ by only one bit. This is useful
in minimizing errors in digital communication and hardware encoding.
- Usage: Used in digital systems like
rotary encoders and error correction schemes.
Example
4. ASCII
(American Standard Code for Information Interchange)
- Description: ASCII is a character encoding
standard that represents text in computers. Each character is encoded
using 7 or 8 bits, allowing for 128 or 256 possible characters,
respectively.
- Usage: ASCII is widely used for text
files, basic data representation, and network protocols.
Example
The ASCII
encoding for the character A is 65 in decimal or 01000001 in binary.
Table 2.2
ASCII and Binary values for word DATA
D A T A
ASCII Code 68 65 84 65
Binary Code 1000100 1000001 1010100 1000001
5. EBCDIC
(Extended Binary Coded Decimal Interchange Code)
- Description: EBCDIC is an 8-bit character
encoding used primarily on IBM mainframes. It was developed to extend the
6-bit BCD encoding to support a larger character set.
- Usage: Mainly used in legacy systems,
particularly IBM mainframes.
Example
The EBCDIC
code for the character A is C1 in hexadecimal or 11000001 in binary.
6. Base64
Encoding
- Description: Base64 is a binary-to-text
encoding scheme that represents binary data in an ASCII string format
using 64 printable characters (A-Z, a-z, 0-9, +, /).
- Usage: Used in email encoding (MIME),
storing complex data in XML or JSON, and embedding binary files like
images in HTML or CSS.
Example
The string
Man encoded in Base64 is TWFu.
7.
Unicode
- Description: Unicode is an encoding
standard that supports the representation of text in most of the world's
writing systems. It can use different encoding forms, such as UTF-8,
UTF-16, and UTF-32.
- Usage: Used globally to support
internationalization and localization of software and web applications.
Example
The Unicode
code point for the character A is U+0041.
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