Another representation of binary integers that is sometimes encountered is ones complement. Positive integers are represented in the same way as sign magnitude. A negative integer is represented by taking the Boolean complement of each bit of the corresponding positive number.

Provide a definition of ones complement numbers using a weighted sum of bits.

What is the range of numbers that can be represented in ones complement?

Define an algorithm for performing addition in ones complement arithmetic.

Note: Ones complement arithmetic disappeared from hardware in the $1960$s$,$ but still survives checksum calculations for the Internet Protocol $($IP$)$ and the Transmission Control Protocol $($TCP$).$