1. What is One's Complement?

One's complement is a method of representing signed numbers in binary. In this system, positive numbers are represented as usual, while negative numbers are represented by inverting all bits of the corresponding positive number.

2. How Does the Calculator Work?

The calculator uses the one's complement formula:

Where:

• \( Decimal \) — The positive integer to convert
• \( n \) — Number of bits in the representation
• \( 2^n - 1 \) — Maximum value representable with n bits

Explanation: The formula calculates the bitwise inversion of the decimal number for the given bit length.

3. Importance of One's Complement

Details: One's complement is used in some computer systems for arithmetic operations and error detection. It's fundamental to understanding binary number representations.

4. Using the Calculator

Tips: Enter a positive decimal integer and the number of bits for the representation. The decimal must be within the range representable by the given number of bits (0 to 2ⁿ-1).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between one's complement and two's complement?
A: Two's complement is more commonly used today as it has a single representation for zero and simpler arithmetic operations.

Q2: What is the range of numbers representable in one's complement?
A: For n bits: from -(2^n-1-1) to +(2^n-1-1).

Q3: 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 can cause complications in arithmetic.

Q4: Where is one's complement still used today?
A: Primarily in checksum calculations for network protocols and some legacy systems.

Q5: How is negative one's complement calculated?
A: For negative numbers, first represent the absolute value in binary, then invert all bits.