I have just learned how to read hexadecimal values. Until now, I was only reading them as positive numbers. I heard you could also write negative hex values.
My issue is that I can't tell if a value is negative or positive. I found a few explanations here and there but if I try to verify them by using online hex to decimal converters, they always give me different results.
Sources I found:
If I understand correctly it means that:
If a hex value written with all its bits having something > 7 as its first hex digit, it is negative.
All 'F' at the beginning or the first digit means is that the value is negative, it is not calculated.
For exemple if the hex value is written in 32 bits:
FFFFF63C => negative ( -2500 ?)
844fc0bb => negative ( -196099909 ?)
F44fc0bb => negative ( -196099909 ?)
FFFFFFFF => negative ( -1 ?)
7FFFFFFF => positive
Am I correct? If not, could you tell me what I am not getting right?
44 Answers
Read up on Two's complement representation:
I think that the easiest way to understand how negative numbers (usually) are treated is to write down a small binary number and then figure out how to do subtraction by one. When you reach 0 and apply that method once again - you'll see that you suddenly get all 1's. And that is how "-1" is (usually) represented: all ones in binary or all f's in hexadecimal. Commonly, if you work with signed numbers, they are represented by the first (most significant) bit being one. That is to say that if you work with a number of bits that is a multiple of four, then a number is negative if the first hexadecimal digit is 8,9,A,B,C,D,E or F.
The method to do negation is:
- invert all the bits
- add 1
Another benefit from this representation (two's complement) is that you only get one representation for zero, which would not be the case if you marked signed numbers by setting the MSB or just inverting them.
1From what I understand, you always need to look at the left-most digit to tell the sign. If in hex, then anything from 0-7 is positive and 8-f is negative. Alternatively, you can convert from hex to binary, and if there's a 1 in the left-most digit, then the number is negative.
HEX <-> BINARY <-> SIGN
0-7 <-> 0000-0111 <-> pos
8-F <-> 1000-1111 <-> neg
The answer here in the forum looks good:
Each hexadecimal "digit" is 4 bits. The d in the high order position is 1101. So you see it's got a high bit of one, therefore the whole number is negative.
and
A hex number is always positive (unless you specifically put a minus sign in front of it). It might be interpreted as a negative number once you store it in a particular data type. Only then does the most significant bit (MSB) matter, but it's the MSB of the number "as stored in that data type". In that respect the answers above are only partially correct: only in the context of an actual data type (like an int or a long) does the MSB matter.
If you store "0xdcafe" in an int, the representation of it would be "0000 0000 0000 1101 1100 1010 1111 1110" - the MSB is 0. Whereas the representation of "0xdeadcafe" is "1101 1110 1010 1101 1100 1010 1111 1110" - the MSB is 1.
You can tell whether a hexadecimal integer is positive or negative by inspecting its most significant (highest) digit. If the digit is ≥ 8, the number is negative; if the digit is ≤ 7, the number is positive. For example, hexadecimal 8A20 is negative and 7FD9 is positive
