Subtraction operation on unsigned char

Question

I have a curiosity about unsigned char. I have a curiosity about unsigned char. I did a subtraction operation on unsigned char accidentally.I know i am not supposed to do that. But i am bit curious about how a particular answer came. Can anybody explain this at bit level?

unsigned char x = 150;
unsigned char y = 229;

unsigned char z = x - y;

finally i got 177 for z during the debugging

I am running this code in visual studio 2008.

Answer 1

Unsigned integers, declared unsigned, shall obey the laws of arithmetic modulo 2^n where n is the number of bits in the value representation of that particular size of integer.

(C++11 standard, 3.9.1.5)

On most platforms an unsigned char is 8 bits, so the result is 150 - 229 mod 256 = -79 mod 256 = 177.

Answer 2

Yes, if you subtract 229 from 150, you end up with -79. However, since you're limited to the range 0..255 (assuming 8 bits) because of the destination, it wraps around to ensure that range is maintained. Hence you basically add 256 to -79 to end up with 177.

In other words, 9 - 10 which would give you -1 in a signed value, actually gives you 255 for an 8-bit unsigned char. Similarly, 9 - 11 would give you 254.

It's no different to addition, with 255 + 7 giving you 6 because it wraps back to 0 following 255.

Now, the rules are a little more complex than that insofar as the values may be promoted to a larger data type, then the subtraction done, then the result truncated. But mathematically, that first paragraph is correct.