A computational tool performs binary arithmetic using a specific method where the negative of a number is obtained by inverting its bits (changing 0s to 1s and 1s to 0s). Addition is then carried out following binary addition rules, with any carry-out from the most significant bit added back to the least significant bit in a process called end-around carry. For example, to add -5 and 3 using 4-bit representation, -5 is represented as the 1s complement of 5 (1010), and 3 is represented as 0011. Adding these yields 1101. An end-around carry is not needed here because there is no carry out. 1101 is 1s complement of -2 which is the correct answer.
This arithmetic technique simplifies the hardware design for early computers by eliminating the need for separate adder and subtractor circuits. Implementing subtraction through the addition of a complemented number reduces the complexity of the central processing unit. While largely superseded by other methods in modern systems, it provides an illustrative example of binary arithmetic and holds historical significance in computer architecture. Its use allowed for cost-effective and relatively simple arithmetic operations in early computing devices.
