1. What is One's Complement?

One's complement is a binary number representation where negative numbers are represented by inverting all bits of the positive number's binary representation. This method was historically used in computer systems for representing signed numbers.

2. How Does the Calculator Work?

The calculator performs the following steps:

Where:

• First convert the decimal number to binary
• Then invert all bits (change 1 to 0 and 0 to 1)

Example: For decimal 5 (binary 0101), the one's complement is 1010.

3. Importance of One's Complement

Details: While modern computers typically use two's complement, understanding one's complement is important for computer science education, working with legacy systems, and understanding checksum calculations in networking.

4. Using the Calculator

Tips: Enter any non-negative integer decimal number. The calculator will display its one's complement binary representation.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between one's and two's complement?
A: Two's complement adds 1 to the one's complement, eliminating the negative zero problem and making arithmetic operations simpler.

Q2: Why was one's complement used historically?
A: It was simpler to implement in early computers as negation only required bit inversion.

Q3: Where is one's complement still used today?
A: Mainly in checksum calculations for network protocols like TCP/IP.

Q4: How is zero represented in one's complement?
A: There are two representations: +0 (all 0s) and -0 (all 1s).

Q5: What's the range of numbers in 8-bit one's complement?
A: -127 to +127 (with both +0 and -0).