Range of signed char

Question

Why the range of signed character is -128 to 127 but not -127 to 128 ?

Answer 1

In 8-bit 2's complement encoding numbers -128 and +128 have the same representation: 10000000. So, the designer of the hardware is presented with an obvious dilemma: how to interpret bit-pattern 10000000. Formally, it will work either way. If they decide to interpret it as +128, the resultant range will be -127..+128. If they decide to interpret it as -128, the resultant range will be -128..+127.

In actual real-life 2's complement representation the latter approach is chosen because it satisfies the following nice convention: all bit-patterns with 1 in higher-order bit represent negative numbers.

It is worth noting though, that language specification does not require 2's-complement implementations to treat the 100...0 bit pattern as a valid value in any signed integer type. E.g. implementations are allowed to restrict 8-bit signed char to -127..+127 range and regard 10000000 as an invalid bit combination (trap representation).