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). It's a method of representing signed numbers in binary form.

2. How Does the Calculator Work?

The calculator uses the Python formula:

Where:

• \( dec \) — Decimal integer to convert
• \( bits \) — Number of bits for the representation
• \( \sim \) — Bitwise NOT operator (inverts all bits)
• \( \& \) — Bitwise AND operator

Explanation: The formula first inverts all bits of the number, then masks it to the specified bit length to get the proper 1's complement representation.

3. Importance of 1's Complement

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

4. Using the Calculator

Tips: Enter a decimal integer and the number of bits you want for the representation. The calculator will show the 1's complement binary form.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between 1's and 2's complement?
A: 1's complement simply inverts all bits, while 2's complement inverts all bits and adds 1. 2's complement is more commonly used in modern computers.

Q2: Why do we need to specify bit length?
A: The bit length determines how many bits are used to represent the number, which affects the range of numbers that can be represented and ensures proper sign extension.

Q3: What happens if my number is too large for the bit length?
A: The number will be truncated to fit within the specified bit length, which may give unexpected results. Always ensure your bit length is sufficient.

Q4: Can I represent floating-point numbers in 1's complement?
A: No, 1's complement is only for integer representation. Floating-point numbers use a different representation scheme.

Q5: Where is 1's complement used today?
A: While 2's complement is more common, 1's complement is still used in some checksum algorithms and in certain legacy systems.