In the book I am reading it says that:
The standard does not define how signed types are represented, but does specify that range should be evenly divided between positive and negative values. Hence, an 8-bit signed char is guaranteed to be able to hold values from -127 through 127; most modern machines use representations that allow values from -128 through 127.
I presume that [-128;127] range arises from method called "twos-complement" in which negative number is !A+1 (e.g. 0111 is 7, and 1001 is then -7). But I cannot wrap my head around why in some older(?) machines the values range [-127;127]. Can anyone clarify this?
Both one's complement and signed magnitude are representations that provide the range [-127,127] with an 8 bit number. Both have a different representation for +0 and -0. Both have been used by (mostly) early computer systems.
The signed magnitude representation is perhaps the simplest for humans to imagine and was probably used for the same reason as why people first created decimal computers, rather than binary.
I would imagine that the only reason why one's complement was ever used, was because two's complement hadn't yet been considered by the creators of early computers. Then later on, because of backwards compatibility. Although, this is just my conjecture, so take it with a grain of salt.
Further information: https://en.wikipedia.org/wiki/Signed_number_representations
As a slightly related factoid: In the IEEE floating point representation, the signed exponent uses excess-K representation and the fractional part is represented by signed magnitude.