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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.
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.
