1. What is 2's Complement Subtraction?

2's complement is a mathematical operation on binary numbers that allows for efficient subtraction in digital systems. It's the most common method of representing signed integers in computers.

2. How Does the Calculator Work?

The calculator uses the 2's complement subtraction formula:

Where:

• \( A \) — First binary number (minuend)
• \( B \) — Second binary number (subtrahend)
• \( \sim B \) — Bitwise NOT of B
• \( \sim B + 1 \) — 2's complement of B

Explanation: The formula converts subtraction to addition by using the 2's complement of the subtrahend.

3. Importance of 2's Complement

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

4. Using the Calculator

Tips: Enter binary numbers (containing only 0s and 1s) for both A and B. The calculator will compute A - B using 2's complement method.

5. Frequently Asked Questions (FAQ)

Q1: Why use 2's complement for subtraction?
A: It simplifies hardware design by allowing the same circuit to handle both addition and subtraction.

Q2: How is overflow detected in 2's complement?
A: Overflow occurs when the sign of the result differs from what's expected given the signs of the inputs.

Q3: What's the range of numbers representable in n-bit 2's complement?
A: From \(-2^{n-1}\) to \(2^{n-1}-1\).

Q4: How is the 2's complement of a number calculated?
A: Invert all bits (1's complement) and then add 1.

Q5: What's the advantage over 1's complement?
A: 2's complement has a single representation of zero and simpler arithmetic operations.