1. What is One's Complement?

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

2. How Does the Calculator Work?

The calculator performs these steps:

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, low-level programming, and working with legacy systems.

4. Using the Calculator

Tips: Enter a decimal number and specify the number of bits for the representation. The calculator will show both the binary representation and its one's complement as lists of bits.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between one's and two's complement?
A: One's complement simply inverts bits, while two's complement inverts bits and adds 1. Two's complement avoids the +0/-0 problem.

Q2: When would I need one's complement?
A: Mostly in educational contexts or when working with older systems that used this representation.

Q3: How does negative numbers work in one's complement?
A: The sign is represented by the most significant bit, and the magnitude is represented by the remaining bits in inverted form.

Q4: What's the range of numbers in n-bit one's complement?
A: From -(2^(n-1)-1) to +(2^(n-1)-1).

Q5: Why is two's complement more common today?
A: It simplifies arithmetic operations and eliminates the negative zero problem present in one's complement.