Perform binary addition, subtraction, multiplication, and division. Convert between binary, decimal, octal, and hex with step-by-step explanations and bit visualization.
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Binary addition follows the same rules as decimal but with only 0 and 1: 0+0=0, 0+1=1, 1+0=1, 1+1=10 (carry 1). Work from right to left, carrying as needed.
Multiply each digit by 2 raised to its position (starting from 0 on the right). Example: 1101 = 1×8 + 1×4 + 0×2 + 1×1 = 13.
Two's complement represents negative numbers in binary. Flip all bits and add 1. For example, -5 in 8-bit is: 5=00000101, flip=11111010, +1=11111011.
The Binary Calculator is a free online tool that lets you perform binary arithmetic operations and convert between binary, decimal, octal, and hexadecimal. It is part of NexTool's collection of free tools designed to help you work faster and more efficiently.
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The Binary Calculator uses industry-standard formulas and algorithms to deliver reliable results. While the tool is designed for accuracy, results should be used as estimates and guidance. For critical decisions, always consult a qualified professional.
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Perform binary addition, subtraction, multiplication, and division. Convert between binary, decimal, octal, and hex with step-by-step explanations and bit visualization.
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= 10 (unsigned 8-bit)
= 6 (unsigned 8-bit)
0001 0000
16
0o20
0x10
| Bit | 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |
|---|---|---|---|---|---|---|---|---|
| A | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 |
| B | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 |
| + | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
0000 1010 (10) + 0000 0110 (6) ─────────── = 0001 0000 (16)
Both bits must be 1 for result 1. Used to mask/clear bits.
Either bit being 1 gives 1. Used to set specific bits.
Different bits give 1, same give 0. Used to toggle bits.
Signed integers use MSB as sign. Negate by flipping bits + 1.
Shifts bits left, fills with 0s. Equivalent to multiplying by 2^n.
Shifts bits right. Logical fills with 0s; arithmetic preserves sign.