Short Answer

1’s complement and 2’s complement are methods used to represent negative numbers in binary form. In 1’s complement, we change all 0s to 1s and all 1s to 0s. It is simply the inversion of the binary number.

In 2’s complement, we first find the 1’s complement and then add 1 to the result. This method is widely used in digital systems because it makes arithmetic operations like addition and subtraction easier and more efficient.

Detailed Explanation

1’s Complement

1’s complement is a simple method used to represent negative binary numbers. It is obtained by flipping all the bits of a binary number. That means every 0 becomes 1, and every 1 becomes 0.

How to Find 1’s Complement

To find the 1’s complement of a binary number, follow these steps:

1. Write the binary number.
2. Replace all 0s with 1s.
3. Replace all 1s with 0s.

Example

Let us take a binary number: 1010

1’s complement of 1010 is: 0101

Here, each bit is reversed. This method is easy to understand and apply.

Use of 1’s Complement

1’s complement is used to represent negative numbers in binary form. For example, if 1010 represents a positive number, then its 1’s complement (0101) can represent the negative form.

However, 1’s complement has a drawback. It has two representations of zero:

• Positive zero (0000)
• Negative zero (1111)

This creates confusion in digital systems, so it is not commonly used in modern computers.

2’s Complement

2’s complement is an improved method of representing negative numbers. It is widely used in digital electronics and computer systems.

How to Find 2’s Complement

To find the 2’s complement of a binary number, follow these steps:

1. Find the 1’s complement of the number.
2. Add 1 to the result.

Example

Let us take the binary number: 1010

Step 1: Find 1’s complement → 0101
Step 2: Add 1 → 0101 + 1 = 0110

So, the 2’s complement of 1010 is 0110

Use of 2’s Complement

2’s complement is widely used because it solves the problems of 1’s complement. It has only one representation of zero, which avoids confusion.

It also makes arithmetic operations easier. Subtraction can be performed using addition, which simplifies the design of digital circuits and processors.

Importance in Digital Electronics

Both 1’s and 2’s complement are important for representing signed numbers in digital systems. They allow computers to perform operations with both positive and negative numbers.

2’s complement is preferred in modern systems because it is efficient and reduces hardware complexity. It is used in processors, microcontrollers, and digital communication systems.

Understanding these concepts is essential for students and engineers working in electronics and communication fields.

Conclusion

1’s complement and 2’s complement are methods used to represent negative binary numbers. 1’s complement is obtained by inverting bits, while 2’s complement is found by adding 1 to the 1’s complement. Due to its advantages like single zero representation and easy arithmetic operations, 2’s complement is widely used in digital electronics.