# How to Convert Hexadecimal to Decimal

The hexadecimal system is a base-16 number system that uses has the digits 0 through 9 plus the six letters A, B, C, D, E, and F. It is useful in computing because numbers written in base-16 are four times shorter than numbers written in binary. Numbers written in hexadecimal are also shorter than numbers written in decimal.

If you want to convert a hexadecimal number to a decimal number by hand, use the step-by-step guide below. You can also use the easy conversion calculator.

(Step 1) Understand what each hexadecimal digit stands for. The digits 0 through 9 stand for their decimal counterparts, while A = 10, B = 11, C = 12, D = 13, E = 14, and F = 15.

(Step 2) Count the digits in the hexadecimal number you wish to convert. For example, the hexadecimal number A980C has five digits. Make a list of the decimal equivalents of each of the five digits. For example, A980C becomes {10, 9, 8, 0, 12}.

(Step 3) Multiply each number in the list by successive powers of 16, starting with 16^{0} = 1 for the rightmost element of the list. For example, 12 is the rightmost element of our list, so we obtain:

10(16^{4}) = 10(65536) = 655360

9(16^{3}) = 9(4096) = 36864

8(16^{2}) = 8(256) = 2048

0(16^{1}) = 0(16) = 0

12(16^{0}) = 12(1) = 12

(Step 4) Add the numbers you obtained in Step 3. This is the decimal equivalent of the hexadecimal number. For example, 655360 + 36864 + 2048 + 0 + 12 = 694284

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