What is the primary use of 2's complement in binary numbers?

What is the primary use of 2's complement in binary numbers?

• A. Representing only positive numbers
• B. Storing decimal numbers
• C. Representing negative numbers and enabling subtraction by addition
• D. Replacing 1's complement

Answer: (C)

Two's complement provides a practical way to encode negative numbers in binary and makes subtraction align with addition, so a single binary adder can handle both operations. In an N-bit system, the representable range is from -2^(N-1) to 2^(N-1) - 1. A negative value is obtained by inverting all bits of its positive form and adding one. This setup means you can perform subtraction by adding the two's complement of the subtrahend: A - B = A + (two's complement of B). A compact example in 8 bits shows this: the two's complement of 3 is 11111101, and adding that to 5 (00000101) yields 00000010, which is 2, with any carry out ignored. This behavior simplifies hardware design and is why two's complement is used for representing negative numbers and performing subtraction. It’s not about storing decimal numbers, and it doesn’t represent only positives; it’s specifically the clean way to handle negatives and arithmetic.

Two's complement provides a practical way to encode negative numbers in binary and makes subtraction align with addition, so a single binary adder can handle both operations. In an N-bit system, the representable range is from -2^(N-1) to 2^(N-1) - 1. A negative value is obtained by inverting all bits of its positive form and adding one. This setup means you can perform subtraction by adding the two's complement of the subtrahend: A - B = A + (two's complement of B). A compact example in 8 bits shows this: the two's complement of 3 is 11111101, and adding that to 5 (00000101) yields 00000010, which is 2, with any carry out ignored. This behavior simplifies hardware design and is why two's complement is used for representing negative numbers and performing subtraction. It’s not about storing decimal numbers, and it doesn’t represent only positives; it’s specifically the clean way to handle negatives and arithmetic.