Which concept describes encoding negative numbers using a specific form of complement?

Which concept describes encoding negative numbers using a specific form of complement?

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

Answer: (C)

Two's complement is the method used to encode negative integers in a fixed-width binary system. In an n-bit system, a negative number -x is represented by the bit pattern that equals 2^n minus x. Practically, you obtain it by inverting all bits of x and adding one. For example, in four bits, the positive 3 is 0011, and its two's complement representation for -3 is 1101. This encoding lets addition and subtraction use the same hardware: you can add numbers regardless of sign, and overflow behavior naturally indicates when results fall outside the representable range. The representable range in n bits is from -2^(n-1) to 2^(n-1) - 1. Other concepts like binary shift describe moving bits, overflow is about results that don’t fit, and syntax relates to programming language structure, not number representation.

Two's complement is the method used to encode negative integers in a fixed-width binary system. In an n-bit system, a negative number -x is represented by the bit pattern that equals 2^n minus x. Practically, you obtain it by inverting all bits of x and adding one. For example, in four bits, the positive 3 is 0011, and its two's complement representation for -3 is 1101. This encoding lets addition and subtraction use the same hardware: you can add numbers regardless of sign, and overflow behavior naturally indicates when results fall outside the representable range. The representable range in n bits is from -2^(n-1) to 2^(n-1) - 1. Other concepts like binary shift describe moving bits, overflow is about results that don’t fit, and syntax relates to programming language structure, not number representation.