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Radix Explained – What Is Radix in the Numeral System?

Radix indicates the number of unique digits from zero (0) that you can use to express numbers in a standard positional numeral system.

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Radix is sometimes called "base."

How to Write a Number and Its Radix

Whenever you wish to express a number and its radix, do the following:

  1. Enclose the numeral in parentheses.
  2. Write the radix—as a subscript—immediately after the closing parentheses.

Example 1: Express Forty-Five as a Binary Numeral

(101101)2

In the example above, 101101 is a numeral, while 2 is the radix. In other words, we used (101101)2 to express that 101101 is a number in the binary (base 2) numeral system.

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  • A radix of 2 means that you can use only two digits (0 and 1) to express numbers in the binary numeral system.
  • The decimal numeral equivalent of (101101)2 is 45. (1 x 25 + 0 x 24 + 1 x 23 + 1 x 22 + 0 x 21 + 1 x 20 = 45)
  • Humans prefer reading letters and decimal digits. However, computers can only read binary digits.

Example 2: Express Forty-Five as an Octal Numeral

(55)8

In the example above, 55 is a numeral, while 8 is the radix. In other words, we used (55)8 to express that 55 is a number in the octal (base 8) numeral system.

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  • A radix of 8 means that you can use only eight digits (0, 1, 2, 3, 4, 5, 6, and 7) to express numbers in the octal numeral system.
  • The decimal numeral equivalent of (55)8 is 45. (5 x 81 + 5 x 80 = 45)

Example 3: Express Forty-Five as a Hexadecimal Numeral

(2D)16

In the example above, 2D is a numeral, while 16 is the radix. In other words, we used (2D)16 to express that 2D is a number in the hexadecimal (base 16) numeral system.

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  • A radix of 16 means that you can use only sixteen digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F) to express numbers in the hexadecimal numeral system.
  • The hexadecimal letters A, B, C, D, E, and F represent 10, 11, 12, 13, 14, and 15, respectively.
  • The decimal numeral equivalent of (2D)16 is 45. (2 x 161 + 13 x 80 = 45)

Overview

This article discussed what radix means in the standard positional numeral system. We also used examples to see how to use it.

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