Скачать или смотреть Digital Electronics || 1's complement & 2's complement || Unsigned and signed Binary number System

1's complement involves inverting every bit of a binary number (0s become 1s, and 1s become 0s), while 2's complement is found by taking the 1's complement and adding 1 to the least significant bit. The primary use of both is to perform subtraction by adding the complement of a number, but 2's complement is more efficient for modern computers as it simplifies arithmetic operations and provides a single representation for zero.
1's Complement
How to find it: Invert all the bits of the binary number.
Example: The 1's complement of 0110 (decimal 6) is 1001.
Purpose: Primarily used in some digital systems for arithmetic operations, especially subtraction, by converting subtraction into an addition problem.
Disadvantage:
Two zeros: It has two representations for zero (a positive and a negative zero), which can complicate arithmetic operations.
End-around carry: Requires adding the carry bit to the least significant bit (LSB) after addition, which is an extra step and makes operations less efficient.
2's Complement
How to find it: Take the 1's complement and add 1 to the result.
Example: The 1's complement of 0110 is 1001. Adding 1 to 1001 gives 1010, which is the 2's complement.
Purpose: Used by most modern computers to represent negative integers and perform arithmetic efficiently.
Advantage:
One zero: Has only one representation for zero, simplifying calculations.
Efficient subtraction: Simplifies subtraction as it can be performed by directly adding the 2's complement of the subtrahend.
No end-around carry handling: Discards the final carry bit after an addition, which streamlines arithmetic operations.