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How to Convert Hexadecimal to Decimal

The hexadecimal system is a base-16 number system. It has the regular ten 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 our regular base-10 system. That is, every number can be written with as many or fewer digits in hexadecimal than in decimal.

If you want to convert a hexadecimal number to a decimal number, use the simple step-by-step instructions below. This is handy if you do not have a conversion calculator at hand.

Instructions

    • 1

      First 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.

    • 2

      Next, make a table with as many columns as there are digits in your hexadecimal number. Label each column with the digits in order. See figure. We will use the number B61F as an example

    • 3

      Below each digit, write its decimal equivalent below. So, B = 11, 6 = 6, 1 = 1, and F = 15. See figure.

    • 4

      Next, make a row for the powers of 16 starting with 1 in the rightmost column and continuing to the leftmost column. In our example we write 1, 16, 16^2 = 256, 16^3 = 4096 in the third row. If you have a longer number, continue on with 16^4 = 65536, etc.

    • 5

      Now, for each column, multiply the numbers in the second and third rows, and write those products in a fourth row. In our example, we get 11x4096 = 45056, 6x256 = 1536, 1x16 = 16, and 15x1 = 15.

    • 6

      And finally, add up all the numbers in the 4th row. So 45056 + 1536 + 16 + 15 = 46623. Thus, 46623 is the decimal equivalent of B61F.

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