Final answer:
Negative numbers are handled in computers using two's complement notation, where the bits of the number's absolute value are inverted and 1 is added to the least significant bit to obtain the negative representation in binary.
Step-by-step explanation:
Negative numbers are represented in a computer system using two's complement notation. This is typically used to allow for negative values in binary, which otherwise has no native concept of a negative sign like in decimal notation.
To find the two's complement of a negative number, invert all bits of its absolute value in binary form (this is also known as taking the one's complement) and then add 1 to the least significant bit. For example, to find the two's complement of -5 in an 8-bit system:
- Write the binary representation of the positive number (5 in decimal is 00000101 in binary).
- Invert the bits (00000101 becomes 11111010).
- Add 1 to the inverted number (11111010 + 1 becomes 11111011).
The result, 11111011, is the two's complement representation of -5. To confirm, if we add 5 (00000101) to -5 (11111011) in binary, the result is 100000000, but since we are using an 8-bit system, we discard the carry and are left with 00000000, which represents 0, demonstrating that the two's complement representation is correct.