Number System and Its Types

In digital electronics, the number system represents the information. Because number systems commonly used in digital electronics have different base values to the decimal system, they look less familiar, but work in essentially the same way.

Some important points to know:

• The base or radix of the number system is the number of symbols used to represent the numbers in the number system or we can say the total number of the digit used in the number system. Suppose if the number system representing the digit from 0 – 7 then the base of the system is the 8.
• The largest value of a digit is always one less than the base. In case the base is 10, then the largest digit is 9.
• Each digit place represents a different multiple of the base. Suppose we have a decimal number 142 (base 10), so it can be written as :
• (142.15)₁₀ = 1*10²  + 4*10¹ + 2*10⁰ + 1*10^-1 + 5*10^-2
• So a number of any base (r) can be represented as:
• N_r = …D₃*r³ + D₂*r² + D₁*r¹ + D₀*r⁰ + D_-1*r^-1 + D_-2*r^-2...
•  The left-most digit of any number is called the Most Significant Digit (MSD).
• The rightmost digit of any number is called the Least Significant Digit (LSD).

Types of Number System:

In digital electronics, with a different base, there are various number systems. Given below is the list of types of the number system used in the computer world.     

1.Binary Number:

Binary the number system is used in all digital circuits and systems. Binary number system has base 2. Hence, the numbers 0 and 1 are used in this number system. A binary digit is called a bit. A sequence of bits, which is either 1 or 0, forms a binary number.

Binary a point separates the integer and fraction part. The part that lies to the left of the binary point in the number is known as the integer part and the part that lies to the right of the binary point in the number is known as the fractional part.

 In this number system, the positions to the left of the binary point have weights of 2⁰, 2¹, 2², 2³ and so on. Similarly, the positions to the right of the binary point have weights of 2^-1, 2^-2, 2^-3 and so on. Hence each position has a specific weight, which is power of base 2.

e.g. 0101, 1111, 0010 

Applications:            

Binary number system is used in digital computers which consist of two state devices with switching circuits. These devices (such as diodes, transistors, etc.) exist in one of the possible two states: ON/OFF or OPEN/CLOSED which can be denoted by 0 and 1 (0 for OPEN or OFF and 1 for ON or CLOSED).    

2.Decimal Number System

Decimal number system is the most basic number system used in day to day life. The base of Decimal number system is 10. Hence, Decimal number system uses the numbers 0 to 9. In this number system the point separating integer part and decimal part is called decimal point. The part lying left to the decimal point is called integer part and the part lying right to the decimal point is called fraction part.

Like binary number system it is also a positional weighted system. So in this system,   the digits to the left of the decimal point have weights that are positive powers of 10 (i.e.10⁰, 10¹, 10², 10³⁾ and so on). Similarly, the successive positions to the right of the decimal point have weights that are negative powers of 10 (i.e.10^-1, 10^-2, 10^-3 and so on). That means, each position has specific weight which is power of base 10.

 e.g. 149, 28, 247

3.Octal Number System

Octal Number System was used in early mini computers. Like binary and decimal number system, it is also a positional weighted system. The base or radix of octal number system is 8. So, the numbers from 0 to 7 are used in this number system. The part of the number that lies to the left of the octal point is known as integer part. Similarly, the part of the number that lies to the right of the octal point is known as fractional part.

In this number system, the positions to the left of the octal point have weights that are positive powers of 8. Similarly, the positions to the right of the octal point have weights that are negative powers of 8. That means, each position has specific weight, which is power of base 8.

e.g. 147, 32, 70

Usefulness of octal number system:

In computer language, we have binary numbers with large number of bits such as up to 64 bits and more. Sometimes these are not mere numerical quantities but some type of code. So while dealing with large binary numbers it is much easy and convenient to deal with them in octal number system by conversions.

4.Hexadecimal Number System

As binary numbers are too lengthy to handle for human beings, hence hexadecimal number system is one number system to represent binary numbers concisely.  The base or radix of Hexa-decimal number system is 16. So, the numbers used are ranging from 0 to 9 and the letters from A to F are used in this number system. The decimal equivalents of Hexa-decimal digits from A to F are 10 to 15.

A 4-bit group is called nibble and since words come in 8, 16, 32-bits, they are easy to represent in hexadecimal.

The part of the number, which lies to the left of the hexadecimal point is known as integer part. Similarly, the part of the number, which lies to the right of the Hexadecimal point is known as fractional part. It is also a positional weighted system. Hence, each position has specific weight which is power of base 16.