1. What is 2's Complement?

2's complement is a mathematical operation on binary numbers used to represent signed integers in computer systems. It's the most common method of representing signed numbers in digital systems.

2. How Does the Calculator Work?

The calculator uses the 2's complement to decimal formula:

Where:

• \( Complement \) — Binary number in 2's complement form
• \( bits \) — Number of bits in the representation
• \( \& \) — Bitwise AND operation
• \( \ll \) — Bitwise left shift operation

Explanation: The formula checks the sign bit (most significant bit) and calculates the decimal value accordingly.

3. Importance of 2's Complement

Details: 2's complement representation simplifies arithmetic operations in digital systems and eliminates the need for separate subtraction circuits.

4. Using the Calculator

Tips: Enter a valid binary number and specify the number of bits. The binary should only contain 0s and 1s, and its length shouldn't exceed the specified bit length.

5. Frequently Asked Questions (FAQ)

Q1: Why use 2's complement?
A: It simplifies hardware design by using the same circuits for addition and subtraction, and it has a single representation for zero.

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

Q3: How to detect overflow in 2's complement?
A: Overflow occurs when adding two positives gives a negative, or adding two negatives gives a positive.

Q4: What's the difference between 1's and 2's complement?
A: 2's complement is 1's complement plus 1, which eliminates the negative zero problem in 1's complement.

Q5: How to convert negative decimal to 2's complement?
A: Convert the absolute value to binary, invert the bits (1's complement), then add 1 (2's complement).