# Number System

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

|D| = dn-1 rn-1 + dn-2 rn-2 + …… di ri + …… d1 r1 + d0 r0 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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