How do you Convert decimal 65535 to its hexadecimal?

Answer 1

In any numbering system each numeral is a power of the base number.

For example, in base-10 (Decimal), the first decimal place on the right is that number times 10 to the 0th power. (Just talking about Integers right now.)

The next digit is that number times ten to the 1st power, and so on.

For example: The decimal number 635 is represented as (6*10^2)+(3*10+1)+(5*10^0)

So in Base 16, each number place would be that number times 16 to the nth power.

To make 16 numbers, we have to add some numerals to go beyond 9... The common convention is to use Letters. So in hexadecimal, you could 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F.

The decimal values of a hexadecimal number starting from the left at the 5th digit would be:

65536 4096 256 16 1

So to come up with a value equal to decimal 65535, we would have to find numbers that add up to that value.

Obviously the first digit won't work. It's already over 65535 just for one. Let's look at the next digit with value 4096. If we take that times the maximum value of the place (15 in decimal, or F in hex), we can get up to 61440. So we'll put F in that place. Our number is currently Fxxx.

The next digit has a value of 256 times the number in that place. So we check the maximum value of 15*256 = 3840. Add that to the 61440 from the first digit, and we get a total of 65280. Still below 65535 so we'll drop another F value there as well. Our number is now FFxx.

Next to last digit! It has a place value of 16. The maximum value then is 15*16, or 240. We add that to the 65280 from the last calculation and get 65520. Pretty close, but not quite up to 65535 yet. Our number is now FFFx.

Final digit! It has a value of 1, so maximum value for this first digit is 1*15, or 15. Add 15 to the prior calculation of 65520 and we get... 65535! Ta da!

So the final calculation is that 0xFFFF = 65,535 in decimal. (The 0x is an indicator that the number following is in Hexadecimal.)

Hope that helps!