Hexadecimal To Decimal

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What Does Hexadecimal To Decimal Mean?

Hexadecimal to decimal (X2D) is a conversion process involving the two aforementioned number systems. The original number is in hexadecimal format, base 16, and it is converted to decimal format, base 10.

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The conversion can be done by multiplying the decimal equivalent of each hexadecimal digit by 15^n, where n is the place number, place numbers start at 0 from the right going to the left, and then adding up all the results.

Techopedia Explains Hexadecimal To Decimal

Hexadecimal to decimal conversion is often done for the benefit of the human reader because computers can already understand any of the given number systems. Often, hexadecimal is used for displaying values because they effectively shorten the number of characters due to its larger base value of 16. Hexadecimal values are 0 to 9 and A to F, which is essentially the same as 0 to 9 and 10 to 15 in decimal, totaling 16 values, hence the base 16.

In order to convert hexadecimal to decimal, the following mathematical equation can be used:

    Decimal equivalent = ?(Hn x 16^n)

Where "Hn" is the hexadecimal digit and "n" is the place value of that digit. The variable "n" starts as 0 from right to left so if a hexadecimal number like F34B has four places, they are numbered 3, 2, 1 and 0 respectively.

For example, here "FACE6" is converted to decimal:

    Decimal equivalent of "6" = 6 x 16^0 = [6] Decimal equivalent of "E" = (E) 14 x 16^1 = [224] Decimal equivalent of "C" = (C) 12 x 16^2 = [3072] Decimal equivalent of "A" = (A) 10 x 16^3 = [40960] Decimal equivalent of "F" = (F) 15 x 16^4 = [983040] Decimal equivalent of FACE6 = 6 + 224 + 3072 + 40960 + 983040
    FACE6 = 1,027,302

Therefore, hexadecimal effectively shortens the value from seven decimal digits to only five hexadecimal digits.

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Margaret Rouse
Senior Editor
Margaret Rouse
Senior Editor

Margaret is an award-winning technical writer and teacher known for her ability to explain complex technical subjects to a non-technical business audience. Over the past twenty years, her IT definitions have been published by Que in an encyclopedia of technology terms and cited in articles by the New York Times, Time Magazine, USA Today, ZDNet, PC Magazine, and Discovery Magazine. She joined Techopedia in 2011. Margaret's idea of a fun day is helping IT and business professionals learn to speak each other’s highly specialized languages.