How do you convert hex to decimal?


Quick Answer

From right to left, take each digit in the base 16 number and multiply it by 16^n, where "n" is the number of places to the left of the rightmost digit, then sum the results together to get the base 10, or decimal, value. For the rightmost digit, n is 0.

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Full Answer

  1. Convert each individual hex digit to base 10 by going right to left

    Start with the rightmost hex digit and multiply it by 16^0, remembering that any number to the power 0 is 1. Then, take the next digit to the left, and multiply it by 16^1. Multiply the next digit to the left by 16^2, and so on, until you reach the leftmost digit. If a hex digit is A, B, C, D, E, or F then treat it as 10, 11, 12, 13, 14 or 15, respectively. For example, suppose you have the number A5F3 and you want to convert this from hex to decimal. Start with the rightmost digit, 3, and multiply it by 16^0. You get 3 * (16^0) = 3. Then, multiply F by 16^1. Since F represents 15 in hex, this is 15 * (16^1) = 240. Then, multiply 5 by 16^2. You get 5 * (16^2) = 1280. Then, multiply A by 16^3. Since A represents 10 in hex, this is 10 * (16^3) = 40960.

  2. Sum up each digit that was converted to base 10

    After taking each individual hex digit and converting it to base 10, sum up the individual values to get the final result in decimal form. For example, in converting the hex number A5F3, the individual hex digits from right to left represent the decimal numbers 3, 240, 1280, and 40960. Sum these together to get the decimal or base 10 number 42483.

  3. Check your work

    A variety of websites such as Binary Hex Converter can convert hex numbers to decimal. Using these helps determine that your calculations are correct.

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