In number system modern method of representing numbers symbolically is based on positional notations.

In this method, each number is represented by a string of symbols where each symbol is associated with a specific weight depending upon its positions. The total number of different symbols which are used in a particular number system is called the base or radix of the system and the weight of each position of a particular number is expressed as a power of the base. When a number is formed with the combination of the symbols, each symbol is then called a digit and the position of each symbol is referred to as the digit position.

Thus if a number system has symbols starting from 0, and the digits of the system are 0, 1, 2, ….. (r - 1) then the base or radix is r. If a number D of this system be represented by

D = d₀ d₀ ……. d₀…….. d₁ d

then the magnitude of this number is given by

Where each d₀ ranges from 0 to r - 1, such that

0 ≤ d₀ ≤ r - 1, i = 0, 1, 2 ...... (n - 1).

The digit at the extreme left has the highest positional value and is generally called the **Most Significant Digit**, or in short **MSD**; similarly, the digit occupying the extreme right position has the least positional value and is referred to as the **Least Significant Digit** or **LSD**.

- Decimal Number System

- Why Binary Numbers are Used

- Binary to Decimal Conversion

- Conversion of Numbers

- Hexa-decimal Number System

- Conversion of Binary Numbers to Octal or Hexa-decimal Numbers

- Octal and Hexa-Decimal Numbers

- Signed-magnitude Representation

- Radix Complement

- Diminished Radix Complement

- Arithmetic Operations of Binary Numbers

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