1. What is 1's Complement?

The 1's complement of a binary number is obtained by inverting all the bits (changing 0s to 1s and 1s to 0s). This representation is used in some computer systems for signed number representation.

2. How Does the Calculator Work?

The calculator uses the 1's complement formula:

Where:

• Decimal — The input integer number
• ~ — Bitwise NOT operator that inverts all bits

Explanation: The calculator first converts the decimal number to its binary representation, then inverts all bits to get the 1's complement.

3. Importance of 1's Complement

Details: 1's complement is important in digital systems for representing negative numbers and performing arithmetic operations. It's also used in error detection and checksum calculations.

4. Using the Calculator

Tips: Enter any integer decimal number. The calculator will display its 32-bit 1's complement binary representation.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between 1's complement and 2's complement?
A: 1's complement is obtained by inverting all bits, while 2's complement is 1's complement plus 1. 2's complement is more commonly used in modern computers.

Q2: How is negative zero represented in 1's complement?
A: In 1's complement, there are two representations of zero: all 0s (+0) and all 1s (-0).

Q3: What are the limitations of 1's complement?
A: The main limitation is the existence of two zeros, which complicates arithmetic operations and comparisons.

Q4: Where is 1's complement still used today?
A: While largely replaced by 2's complement, 1's complement is still used in some checksum algorithms and specialized applications.

Q5: How does endianness affect 1's complement?
A: The bitwise inversion is the same regardless of endianness, but the byte order matters when interpreting the result as a multi-byte value.