Binary Subtraction Calculator 2’s Complement Online

Binary subtraction using 2’s complement is not just a mathematical curiosity—it’s a practical solution used in almost all digital computers for subtracting binary numbers efficiently. This method simplifies the hardware design for arithmetic operations, making it an essential concept in computer architecture.

Formula

When subtracting two binary numbers, A and B, the process involves converting B to its 2’s complement and then adding it to A. The formula used is:

Step-by-step process:

1. Convert B to 2’s Complement: Start by inverting the bits of B and then adding 1 to the least significant bit (LSB).
2. Add to A: Perform binary addition of A and the 2’s complement of B.
3. Handle Overflow: Disregard any carry beyond the most significant bit as this represents overflow, which is common in fixed-size binary operations.

Table of Common Binary Calculations

To aid in understanding and for practical use, a table is provided below with examples of binary subtraction using 2’s complement. This reference helps visualize the operation and offers a quick guide for common calculations.

Binary A	Binary B	Result using 2’s Complement
0101	0011	0010
1100	1001	0011
1010	0111	0011

Example

Consider subtracting binary number 0011 from 0101 using 2’s complement:

1. Convert 0011 to its 2’s complement → 1101.
2. Add 1101 to 0101 → 0010. This simple example demonstrates the effectiveness and efficiency of using 2’s complement for binary subtraction.

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