Number System – Useful and Commonly used Number Systems

Know about Number System – Useful and Commonly used Number Systems: The computers are made up of digital electronic circuit. It is a system of hardware and performs arithmetic operations, manipulates data and makes decision.


In digital circuit like computers, the major circuit elements being transistors which are essentially bistable or binary in nature.

Binary means that the transistor can operate only in two states, fully conducting and nonconducting states. Thus a transistor can act like a switch that is either on (fully conducting) or off (non conducting).

So data in computer system is represented as a group of binary digits 0’s and 1’s and this is known as binary representation of data. The number systems used to represent data in computer is, therefore, known as binary numbers system.


Number systems play an important role in the design, organization and understanding of computers. An important feature of computers is that the data processing in a computer is based on a numbers systems different from one decimal system.

The importance of number systems is that it is the systematic and organized way of representing numbers.

It is the numbers system which does not give importance to the number of symbols used in it but what is important is concept of face value (absolute value) and the place value (value of position) of a symbol.

The knowledge of numbers systems is essential for understanding of computers.

The useful and the commonly used number systems are:

  1. Decimal Number System
  2. Binary Number System
  3. Octal Number System
  4. Hexadecimal Number System

1. Decimal Number System:

The decimal number systems are composed of 10 numbers i.e, 0, 1. 2, 3, 4, 5, 6, 7, 8, 9. And that is why these are known as base —10 numbers. The decimal number system is convenient for the users. The value of each digit in the number depends upon:

  • The face value of the digit
  • The base value of the system
  • The position of the digit in the number.

For example consider the decimal number 546. We know that digit 5 actually represents 5 hundred, the 4 represents 4 tens and the 6 represents 6 units.

In this digit the 5 carries the most weight of three digits so it is referred as Most Significant Digit (MSD) and the 6 carries the least weight and is called the Least Significant Digit (LSD).

Number systems table

In general, any number is simply the sum of the products of each digit value and its positional value. e.g. The decimal number 2789.4567 can be represented as:

decimal number system with positional value

2. Binary Number Systems:

As the decimal number does not lead itself to convenient implementation in digital system, it became very difficult to design electronic equipment that can work with 10 different voltage levels (each representing one decimal character (0 through 9).

On the other hand it became easy to design circuit, which can operate with only two voltage levels. For this reason almost every digital system uses the binary number systems (base 2).

The binary number system is exactly like decimal number except that the base is 2 because binary number system is represented by only two numbers 0 and 1, known as base 2 numbers and these can be used to represent any number that can be represented in decimal or other number system.

The binary number system is also a positional value system wherein every binary digit has its own value or weight expressed as a power of 2.

For example number 1010.0101 can be represented as:

binary numbers with positional value

Know about computer programming language in detail:

In the binary system, the binary digit is often abbreviated as bit.

The leftmost bit carries the largest weight and is known as MSB (Most Significant Bit) and the rightmost carries the smallest weight and is known as LSB (Least significant Bit).

3. Octal Number System:

Octal number systems are also very important and is known as base 8 counting number systems having digits 0 through 7 meaning that it has eight unique symbols: 0, 1, 2, 3, 4, 5, 6, and 7.

The octal number systems is also a way to express binary number. They are also positional value system, wherein each octal digit has its own weight expressed as a power of 8.

The places to the left of octal point are positive powers of 8 and places to the right are negative powers of 8. The number 4256.2678 can be represented as:

octal number system with positional value

4. Hexadecimal Number Systems:

A hexadecimal numbers system is base 16 number systems. Thus it has 16 possible digit symbols. It uses the digits 0-9 and the letters A, B, C, D, E, F. The alphabets A through F represent the numbers 10, 11, 12, 13, 14, 15.

Like other numbers systems, hexadecimal number systems is also a positional value system where in each hexadecimal digit has its own value or weight expressed as a power of 16:

hexadecimal number system

Hexadecimal digit represents a group of binary digits and digits A to F are equivalent to the decimal values 10 to 15.

Table showing relationship between various number systems:


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