Number System - Base r

General Number in base r is expressed as:

where,

• Allowed values of a_i (digits) are 0, 1, 2, ......., r-1 ONLY
• a_n is the MSD (Most Significant Digit)
• a_-m is the LSD (Least Significant Digit)

A number with base r with form/shape as

is equal to

 Example:

(1234.5)₁₀ = 1X10³ + 2X10² + 3X10³ + 4X10⁴ + 5X10^-1

Table 1 : Numbers with Different Bases

 

Note: Numbers in base r can use only r allowable digits. 

Example:

• 10 allowable digits (0, 1, 2, ....., 9) for decimal numbers (base 10)
• 2 allowable digits (0 and 1) for binary numbers (base 2)
• 8 allowable digits (0, 1, 2, ......., 7) for octal numbers (base 8)
• 16 allowable digits (0, 1, 2, ......, 9, A, B, ....., F) for hexadecimal numbers (base 16)

Previous