Hex to Decimal Converter

A hex numeral is a polynomial in 16. Converting hexadecimal to decimal is just evaluating that polynomial, which you can do on paper with nothing harder than multiplication by a few fixed weights.

1. Write the hex number and number its digits from the right, starting at 0.
2. Replace each letter with its value: A is 10, B 11, C 12, D 13, E 14, F 15.
3. Multiply each digit by 16 raised to its position number.
4. Add the products; the total is the decimal value.

If you prefer fewer large numbers, there is an equivalent running form: start with the leftmost digit, then for each next digit multiply what you have by 16 and add the digit. For 2AF3 that is 2, then 2 × 16 + 10 = 42, then 42 × 16 + 15 = 687, then 687 × 16 + 3 = 10995. It is the same arithmetic grouped differently, and it is how most parsers do it.

Powers of 16 worth remembering

Every hex place is worth sixteen of the place to its right. Knowing the first few weights by sight makes a mental estimate quick: a five-digit hex number is somewhere between 65,536 and about a million, and an eight-digit one never exceeds 4,294,967,295.

The weight of each place is also a power of two, four times the position: 16³ is 2¹², which is why 1000 in hex marks a 4 KiB boundary in memory maps and page tables.

When the same hex means a negative number

The sum of powers gives the unsigned value. A program that stores the bits in a signed 32-bit integer reads the top bit as −2³¹ instead of +2³¹, so patterns from 80000000 up wrap around to negative numbers. 7FFFFFFF is the last positive value; one step past it the sign flips.

To read a value the way a signed type does, pick its width in the converter. The decimal row then shows the signed reading, with the unsigned one underneath. A value from a debugger that looks absurdly large, like 4294967286, is often just −10 seen without a width.