1. What is 2's Complement?

2's complement is a mathematical operation on binary numbers, and a way to represent signed integers in computing. It's the most common method of representing signed integers on computers.

2. How Does the Calculator Work?

The calculator uses the 2's complement formula:

Where:

• Invert Bits - Flip all 0s to 1s and 1s to 0s
• Add 1 - Add 1 to the inverted binary number
• Apply negative sign - The result becomes the positive magnitude of the negative number

Explanation: For positive numbers, simply convert binary to decimal. For negative numbers (when MSB is 1), invert all bits, add 1, then apply negative sign.

3. Importance of 2's Complement

Details: 2's complement representation allows efficient arithmetic operations on signed integers and eliminates the problem of negative zero found in other representations.

4. Using the Calculator

Tips: Enter a binary number (only 0s and 1s). The calculator will automatically detect if it's a negative number (MSB = 1) and apply the 2's complement conversion.

5. Frequently Asked Questions (FAQ)

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

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

Q3: How do I convert a negative decimal to 2's complement?
A: Take the absolute value, convert to binary, invert all bits, then add 1 to the result.

Q4: What happens if I add 1 to the maximum positive value?
A: It will wrap around to the most negative value due to overflow (e.g., 127 + 1 = -128 in 8-bit 2's complement).

Q5: Are there any limitations to 2's complement?
A: The main limitation is the fixed range based on bit length, and the asymmetry between positive and negative ranges (one more negative number than positive).