1. What is One's Complement?

One's complement is a method of representing signed numbers in binary form. In this representation, the negative of a number is obtained by inverting all of its bits (changing 0s to 1s and 1s to 0s).

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \sim \) — Bitwise NOT operator (inverts all bits)
• \( \text{bin}() \) — Converts to binary string
• \( [2:] \) — Takes the binary string from position 2 onward (skipping '0b' prefix)

Explanation: The calculator first performs a bitwise NOT operation on the decimal number, then converts the result to binary representation.

3. Importance of One's Complement

Details: One's complement is important in computer systems for representing signed numbers and performing arithmetic operations. It's used in some checksum algorithms and error detection methods.

4. Using the Calculator

Tips: Enter a decimal integer (positive or negative). Optionally specify the number of bits to constrain the output length. The calculator will show the one's complement representation.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between one's complement and two's complement?
A: One's complement simply inverts all bits, while two's complement inverts bits and adds 1. Two's complement is more commonly used today.

Q2: Why does one's complement have two representations of zero?
A: In one's complement, +0 is all 0s and -0 is all 1s, which is one of its disadvantages.

Q3: When would I need to use one's complement?
A: Mostly in legacy systems or specific applications like checksum calculations in network protocols.

Q4: How does the bit length affect the result?
A: Specifying bit length ensures the output has exactly that many bits, padding with 1s if necessary for negative numbers.

Q5: Can I convert back from one's complement to decimal?
A: Yes, by converting the binary to decimal and applying the same inversion if the number is negative.