Final answer:
2's complement is a method used in computing to represent negative numbers in binary. It involves inverting the bits of the number and adding 1 to the result. This allows for straightforward binary arithmetic operations between positive and negative numbers.
Step-by-step explanation:
The 2's complement is a mathematical operation used in computer science to represent negative numbers in binary form. It is widely used because it allows for simple binary addition and subtraction of positive and negative integers, eliminating the need for separate subtraction operations.
To find the 2's complement of a binary number, follow two steps: First, invert all the bits in the number, transforming every 0 to a 1 and every 1 to a 0. This is known as the 1's complement. Second, add 1 to the resulting number. For example, the 2's complement of the binary number 0110 (which is 6 in decimal) would be 1010, which represents -6 in 2's complement form.
This method ensures that when a binary number and its 2's complement are added together, the sum equals zero, showing that they are indeed opposite values. Thus, 2's complement facilitates the handling of arithmetic operations in binary systems employed by computers and digital systems.