What is the name of the system that stores positive and negative integers where the most significant bit has a negative value?

The system that stores positive and negative integers with the most significant bit representing a negative value is commonly referred to as two's complement. In this representation, the most significant bit (MSB) serves as the sign bit, where 0 indicates a positive number and 1 indicates a negative number.

Two's complement allows for straightforward arithmetic operations such as addition and subtraction, since both positive and negative values can be treated in a unified way without the need for separate handling of sign. For instance, to obtain the two's complement of a binary number, you invert all the bits and add one to the result. This method effectively enables the representation of negative numbers while keeping the bit-length consistent, maximizing efficiency in computer calculations.

The other systems mentioned serve different purposes or handle integer representation differently. For example, sign and magnitude also uses a sign bit, but it does not eliminate the complexity involved in arithmetic operations, as it requires separate logic to handle the signs. Thus, two's complement remains the most widely utilized system for representing signed integers in computer systems due to its effectiveness for calculations.