Representation of Number System

In this article, we will discuss the representation of the following number systems

• Decimal
• Binary
• Hexadecimal
• Octal

Radix or Base of a Number System

The number of independent digits used in the number system is known as Radix or Base of the number system.

• Decimal: a radix-10 number system and therefore has 10 different digits or symbols. These are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. All higher numbers after ‘9’ are represented in terms of these 10 digits only.
• Binary: a radix-2 number system (2 different digits are 0 and 1).
• Hexadecimal: a radix-16 number system (16 different digits are 0 to 9 and A,B,C,D,E,F representing 10, 11, 12,13,14,15 respectively).
• Octal: a radix-8 number system (8 different digits are 0 to 7).
• Radix-r: digits are 0,1,…,r-1

Positional or Weighted Number System

The traditional number systems that we learned in school and use every day (decimal, binary, hexadecimal, octal etc.) are positional number system. In such a system, a number is represented by a string of digits where each digit position has an associated weight. The value of a number is a weighted sum of the digits.

Example 1: 1734 = (1 x 1000) + (7 x 100) + (3 x 10) + (4 x 1)

Example 2: 568.23 = (5 x 100) + (6 x 10) + (8 x 1) + (2 x 0.1) + (3 x 0.01)

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