Number System Continued ...

Base of a Number System :

Base or radix of a number system is defined as the number of digits used to represent the number system. Example decimal number system uses ten digits (0,1,2,3,4,5,6,7,8,9) so, its base is 10. The base of number system is indicated by a subscript and followed by the value of the number.

(1101)₂ is of base 2 number system.

(1607)₈ is of base 8 number system.

(1809)₁₀ is of base 10 number system.

(190F)₁₆ is of base 16 number system.

Types of Number System :

There are different types of number system. We are going to know about four types of number systems. Depending upon the base of number, number systems are categorized into the followings:

Decimal or Denary Number System

Binary Number System

Octal Number System

Hexadecimal Number System

Decimal or Denary Number System:

A number system that uses ten different digits is known as Decimal Number System. It is also known as Base-Ten number system. The digits of decimal number system are 0,1,2,3,4,5,6,7,8 and 9. The decimal number system is used in our daily life but not used in a computer. The other numbers in the decimal number system are formed by combining its two or more digits like 11 (combination of 1 and 1), 123(combination of 1, 2 and 3). A decimal number can be expressed by using powers of 10.

For example, a decimal number 345 can be expressed as:

345      = 300 + 40 + 5

            = 3 x 100 + 4 x 10 + 5 x 1

            = 3 x 10² + 4 x 10¹ + 5 x 10⁰

The number 3, 4 and 5 are the face values of 345. The number 1, 10 and 100 represent place values of 345.

Binary Number System:

A Binary Number System uses two different digits: 0 (zero) and 1 (none zero). It is also known as Base-Two number system. Each digit of the binary number system is called Binary Digit (BIT). The other numbers in the binary number system are formed by combining its digits two or more times like 11(combination of 1 and 1), 101(combination of 1, 0 and 1). The binary number is read digit by digit. For example a binary number 1001 is read as one zero zero one.

A computer is based on two states of electricity(i.e. On or Off) which can be only represented by the binary number system. The 0 bit represents Off state and the 1 bit represents On state of electricity. So, the binary number system is used in the computer to represent data and instructions.

The place values in the binary number can be expressed by using powers of 2 like 2⁰, 2¹, 2², 2³, etc. When you express the binary number by using powers of 2, you get equivalent decimal number.

For example: a binary number 1110 can be expressed as:

(1110)²      = 1 x 2³ + 1 x 2² +1 x 2¹ + 0 x 2⁰

                 = 8 + 4 + 2 + 0

                 = 14

Therefore (1110)₂ is equivalent to (14)₁₀.

 

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Number System

Number system is a set of values used to represent different quantities and other special characters. In other words it is a system of number that deals about the numbers and their representation(such as base and exponents) in different systems.

Number system have been around for thousands of years. The common system is the existing system based on number ten(10). Apart from this number system, there are in use the Arabic system, binary system(base two), ternary system(base three), quaternary system(base four), quinary system(base five), octal system(base eight), decimal system(base ten), due-decimal system(base twelve), hexadecimal system(base sixteen),etc.

All these number system can be used to count the number of students in a class or number of viewers watching a certain TV program etc.

The number systems can be categorized in two categories:

1. Non-Positional Number Systems

2. Positional Number Systems

 

 1. Non-Positional Number Systems

In ancient time, people used to count on their fingers. When these fingers became insufficient for counting then stones, pebbles or sticks were used to signify the values. This method of counting is known as the Non-Positional Number System. It was very difficult to perform arithmetic operation, and it had no symbol for zero. The most common non-positional number system is the Roman Number System. In this number system, only a few characters are used to represent the numbers. The characters that are use in this number system are I,V,X,L(fifty),C(hundred),D(thousand),etc. Furthermore, it is very difficult to perform arithmetic operation, logical operation as well as positional techniques.

 

 2. Positional Number Systems

In positional number system, the value of each digit in a number is defined not only by the system but also by the position of symbol. Positional number system have a base or radix. The first positional number system was invented by the Babylonians. They used a base 60 system. The positional number system, which is being used nowadays is known as the decimal number system. The system is base ten(10) system that contains ten(10) digits 0,1,2,3,4,5,6,7,8,9. 

The digital computer represents all kinds of data and information in binary numbers 0 and 1. It includes audio, graphics, video, text and number. Actually to a computer everything is a number. Numbers are numbers, letters are numbers, sound and pictures are also numbers. Even the computer's own instructions are numbers. Computer represents alphabets in ASCII code(American Standard Code for Information Interchange).