How to tell if hex value is negative?
From 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
Read up on Two's complement representation: https://en.wikipedia.org/wiki/Two%27s_complement
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.
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.