Which representation is commonly used to encode negative numbers in binary?

Which representation is commonly used to encode negative numbers in binary?

• A. Binary shift
• B. Overflow
• C. Syntax
• D. Two's complement

Answer: (D)

Two's complement is used because it lets a computer perform addition and subtraction with signed numbers using the same simple hardware. Negative numbers are obtained by flipping all the bits of the positive value and adding one, so the same adder can handle both adding positives and adding negatives. This approach also gives a unique representation for zero and a symmetrical range of positive and negative values, with overflow behaving in a predictable way that's easy to detect at the hardware level. Other ideas aren’t about how numbers are stored: a binary shift is just moving bits around, overflow is a result of arithmetic going past the representable range, and syntax is about language rules rather than encoding numbers.

Two's complement is used because it lets a computer perform addition and subtraction with signed numbers using the same simple hardware. Negative numbers are obtained by flipping all the bits of the positive value and adding one, so the same adder can handle both adding positives and adding negatives. This approach also gives a unique representation for zero and a symmetrical range of positive and negative values, with overflow behaving in a predictable way that's easy to detect at the hardware level. Other ideas aren’t about how numbers are stored: a binary shift is just moving bits around, overflow is a result of arithmetic going past the representable range, and syntax is about language rules rather than encoding numbers.