Chapter 3 - Number System
Binary Number System
The binary numeral system, or base-2 number system, is a numeral system that represents numeric values
using two symbols, usually 0 and 1 and is called BIT (Binary digit). More specifically, the usual base-2
system is a positional notation with a radix of 2. Owing to its straightforward implementation in digital
electronic circuitry using logic gates, the binary system is used internally by all modern computers.
Octal Number System
The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. It is
represented by Q or O. It was once very popular number system, especially used in the Digital Equipment
Corporation PDP/8 and other old computers. It is rarely used nowadays.
Numerals can be made from binary numerals by grouping consecutive digits into groups of three (starting
from the right). For example, the binary representation for decimal 74 is 1001010, which groups into 001 001
010 — so the octal representation is 112.
Decimal Number System
The decimal (base ten or occasionally denary) numeral system has ten as its base. uses various symbols
(called digits) for no more than ten distinct values (0, 1, 2, 3, 4, 5, 6, 7, 8 and 9) to represent any numbers, no
matter how large. It is a first number system in which all the ancient and modern mathematical calculation is
done.
Hexadecimal Number System
In mathematics and computer science, hexadecimal (also base-16, hexa, or hex) is a numeral system with a
radix, or base, of 16. It is denoted by H. It uses sixteen distinct symbols, most often the symbols 0–9 to
represent values zero to nine, and A, B, C, D, E, F to represent values ten to fifteen.
Its primary use is as a human friendly representation of binary coded values, so it is often used in digital
electronics and computer engineering. Each hexadecimal digit represents four binary digits (bits)—also called
a nibble. The highest digit of base-16 is "F" whose binary equivalent is "1111".
BIT:
The smallest unit of information handled by a computer.
Byte:
A byte is a basic grouping of bits (binary digits) that the computer operates on as a single unit. It consists of 8
bits and is used to represent a character by the ASCII (American Standard Code for Information Interchange)
and EBCDIC (Extended Binary Coded Decimal Interchange Code
Nibble:
A string of four bits or half a byte is called nibble.
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