Hexadecimal question

[Hood]

I was reading through the tutorial on ASM hacking earlier. Midway through it gives an example of converting hex values like 0xFFB2 (this is the particular example I am trying to work the math on) to decimal. I understand that part, but I don't understand the process of converting it to a signed value. The unsigned values comes out to 65,458, and it says the signed value is -78. If anyone could help me understand the math behind this I would greatly appreciate it.

[ffta707]

That's a good tutorial to start with, since barely anyone ASM hacks. I was looking through that about a month ago. I'm sure Zodiac could help, if you PM him. Also, senitalBlade is very good with this stuff.

"Welcome to ffhacktics, were all your dreams come true!"

[Xifanie]

The number is 0x8000+, so it will be negative.
subtract the whole number from 0x10000, which is basically the total number of values a half-word can hold
0x10000 - 0xFFB2 = 0x4E = 78
and since we know it's signed, -78.

[Hood]

Thank you for the replies. I'm still a bit lost though. I see how..

0xFFB2 =

0x0F = 16^3 * 15 = 61,440
0x0F = 16^2 * 15 = 3,840
0x0B = 16^1 * 11 = 176
0x02 = 16^0 * 2 = 2

61,440 + 3,840 + 176 + 2 = 65,458

I just don't understand the process of converting it to a signed number.