1. What Is 2's Complement?

2's complement is a mathematical operation on binary numbers, widely used in computing systems to represent signed integers. It allows for efficient arithmetic operations and simplifies hardware design.

2. How The Conversion Works

The conversion process from 2's complement to decimal involves:

Where:

• Bitwise NOT - Invert all bits (0 becomes 1, 1 becomes 0)
• Add 1 - Perform binary addition of 1 to the inverted number
• Convert to Decimal - Interpret the result as a binary number
• Apply Sign - If the original number's MSB was 1, the result is negative

Explanation: This process effectively reverses the 2's complement encoding to retrieve the original signed decimal value.

3. Applications Of 2's Complement

Details: 2's complement representation is fundamental in computer architecture, digital systems, and programming for handling signed integer arithmetic efficiently.

4. Using The Calculator

Tips: Enter a valid binary string in 2's complement format. The calculator will automatically detect the sign from the most significant bit and perform the conversion.

5. Frequently Asked Questions (FAQ)

Q1: Why is 2's complement used instead of sign-magnitude?
A: 2's complement allows for simpler arithmetic operations and eliminates the problem of negative zero, making hardware implementation more efficient.

Q2: What's the range of numbers representable in n-bit 2's complement?
A: The range is from -2^(n-1) to 2^(n-1)-1. For example, 8-bit can represent -128 to 127.

Q3: How do I recognize a negative number in 2's complement?
A: The most significant bit (leftmost bit) will be 1 for negative numbers and 0 for positive numbers.

Q4: Can this calculator handle different bit lengths?
A: Yes, the calculator automatically detects the bit length from your input and performs the appropriate conversion.

Q5: What happens if I enter an invalid binary string?
A: The calculator will show an error or empty result. Only strings containing 0s and 1s are valid inputs.