How to Convert Hexadecimal to Decimal

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Hexadecimal values represent a base-16 numbering system. It has the regular 10 digits -- 0 through 9 -- plus the six letters -- A, B, C, D, E and F. It is used to encode larger numbers because it is more compact than the base-10 system. That is, every number can be written with as many or fewer digits in hexadecimal than in decimal.

You can convert a hexadecimal number to a decimal number with basic instructions, but a calculator makes the process faster.

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

    Make a table with as many columns as there are digits in your hexadecimal number. Label each column with the digits in order. Use the number B61F as an example.

    Write the decimal equivalent below each digit. So, B = 11, 6 = 6, 1 = 1 and F = 15.

    Next, make a row for the powers of 16 starting with 1 in the rightmost column and continuing to the leftmost column. In the example, you would write "1," 16," "16^2 = 256" and "16^3 = 4,096" in the third row. If you have a longer number, continue on with "16^4 = 65,536" and so on.

    Multiply the numbers in the second and third rows for each column. Write those products in a fourth row. In the example, you get 11 x 4,096 = 45,056, 6 x 256 = 1,536, 1 x 16 = 16 and 15 x 1 = 15.

    Add up all the numbers in the fourth row. So 45,056 + 1,536 + 16 + 15 = 46,623. Thus, 46,623 is the decimal equivalent of B61F.


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