Binary Subtraction Calculator:
Binary addition is a fundamental operation in digital electronics and computer science. Just like we add decimal numbers in base 10, binary addition operates in base 2, using only the digits 0 and 1. While integer binary addition is widely understood, adding binary fractions introduces additional complexity — and it’s just as important, especially in computing systems that require precision like graphics processing, simulations, and financial algorithms.
This guide will walk you through both integer and fractional binary addition, complete with examples and a clear explanation of how it works.
Binary numbers are composed of only two digits:
Each position in a binary number represents a power of 2, starting from the right (least significant bit). In fractional binary numbers, digits to the right of the decimal point represent negative powers of 2.
Examples:
1011
= 1×2³ + 0×2² + 1×2¹ + 1×2⁰ = 1110.11
= 1×2¹ + 0×2⁰ + 1×2⁻¹ + 1×2⁻² = 2.75Binary addition follows specific rules:
A | B | Carry-in | Sum | Carry-out |
---|---|---|---|---|
0 | 0 | 0 | 0 | 0 |
0 | 1 | 0 | 1 | 0 |
1 | 0 | 0 | 1 | 0 |
1 | 1 | 0 | 0 | 1 |
1 | 1 | 1 | 1 | 1 |
Binary addition is performed from right to left, just like in base 10.
Let’s add two binary integers:
1011
(decimal 11)1101
(decimal 13)1011 + 1101 ------- 11000
Result: 11000
= 24 in decimal
Adding binary fractions works similarly, but with digits to the right of the binary point. Carry rules still apply.
Example: Add 10.1
and 1.11
10.1
= 2.51.11
= 1.7510.10 + 01.11 -------- 100.01
Result: 100.01
= 4.25 in decimal
Fractional binary addition is essential for:
Want to add binary numbers (including fractions) easily? Try our Binary Addition Calculator that supports 4, 8, 12, and 16-bit modes with decimal equivalents!