Since the 256 possible bit patterns for 8 bits (2⁸ = 256) are to represent both positive and negative values, half of them must be negative.

So the range is

      -128 to +127
   

So overflow occurs if mathematically a sum is > 127 or < -128.

For the 8 bit signed type char, binary addition works the same way as for unsigned char.

That is, if there is a carry out of the 7^th bit, it is discarded.

This carry in to the 8^th bit position has value 256 (= 2⁸). So discarding it is the same mathematically as subtracting 256.

Examples

char x	char y	char z = x + y (mathematically)	(z <= 127)? z : z - 256
126	1	127	127
126	2	128	-128 (= 128 - 256)
126	3	129	-127 (= 129 - 256)

(If z is negative mathematically, then as signed char, the value is (z >= -128) ? z : z + 256.)