One's Complement

The sign-magnitude representation has limitations, such as the duplication of zero representations and increased complexity in comparison operations. The inversion-based representation overcomes these limitations and simplifies comparison and arithmetic operations.

What is one’s complement?

One’s complement representation is another way of representing signed numbers. A number’s representation in one’s complement has the same number of bits as the original number, plus a bit called the sign bit on the extreme left (the MSB). The sign bit denotes that the number is negative if it is set to $1$, and positive if it is set to $0$. To represent a negative number, the other bits hold the complement of the original number in binary. To represent a positive number, the bits hold the number as it is in binary.

Note: The complement of a binary number is the number with all the individual bits inverted. That means that every $1$ turns into a $0$ ...