How many digits in hex do you need to represent integers up to 1, 000?

You can convert 1000 to hex and see how many digits that requires:



So every integer below 1000 needs up to 3 digits.

Alternatively, we know that , and that requires digits in its hex representation (e.g. ). Taking the logarithm, we get , and adding 1 gives the number of digits needed to represent . Similarly,