Binary Calculator
Perform binary arithmetic and convert between binary, decimal, hexadecimal, and octal number systems instantly.
Enter digits 0 and 1 only.
Enter digits 0 and 1 only.
Result
Enter a valid number in the selected base.
Conversion Results
How to Use the Binary Calculator
Select a Mode: Choose between Binary Arithmetic (add, subtract, multiply, divide) or Number Base Conversion using the mode tabs at the top of the tool.
Enter Your Values: For arithmetic, enter two binary numbers in the input fields. For conversion, enter a number and select its source base (binary, decimal, hex, or octal).
Choose an Operation: For arithmetic mode, select the operation: addition (+), subtraction (â), multiplication (Ã), or division (Ãˇ).
Click Calculate: Press the Calculate button to instantly see the result in binary, decimal, hexadecimal, and octal formats.
Review Step-by-Step Output: The results panel shows the answer across all four number bases plus a breakdown of the calculation for learning purposes.
Clear and Start Again: Use the Clear button to reset all fields and perform a new calculation without reloading the page.
Key Features
Full Binary Arithmetic
Supports addition, subtraction, multiplication, and division of binary numbers with accurate results every time.
4-Base Conversion
Convert any number between binary, decimal, hexadecimal, and octal in a single click â all four outputs shown simultaneously.
Step-by-Step Breakdown
Arithmetic results include a readable calculation summary showing how the answer was derived â ideal for learning and verification.
Instant Results
No delays or server calls. All calculations run entirely in your browser for immediate, always-available results.
Strong Validation
Invalid inputs (non-binary characters, empty fields, division by zero) are caught immediately with clear error messages.
Works on All Devices
Fully responsive layout works on any screen size â phone, tablet, or desktop â with no app download needed.
How Binary Arithmetic & Conversion Works
Binary is a base-2 number system. Every digit (called a bit) is either 0 or 1. All arithmetic follows the same rules as decimal, but carries happen at 2 instead of 10. Here are the fundamental rules:
| Operation | Binary Example | Decimal Equivalent |
|---|---|---|
| Addition | 1010 + 0110 = 10000 | 10 + 6 = 16 |
| Subtraction | 1101 â 0101 = 1000 | 13 â 5 = 8 |
| Multiplication | 1011 Ã 0011 = 100001 | 11 Ã 3 = 33 |
| Division | 1100 Ãˇ 0011 = 0100 | 12 Ãˇ 3 = 4 |
For base conversions, the tool converts any input to its decimal (base-10) integer representation first, then formats that integer into binary (base-2), hexadecimal (base-16), and octal (base-8) output strings using standard positional notation.
Practical Examples
Arjun needs to add two binary numbers for his Digital Logic assignment.
Input: 10110101 + 01101110
Decimal: 181 + 110 = 291
â Result: Binary = 100100011 | Decimal = 291 | Hex = 123 | Octal = 443
Sneha wants to convert decimal 255 to all bases to teach her students about byte boundaries.
Input: 255 (Decimal) â Convert
â Binary = 11111111 | Hex = FF | Octal = 377 | Decimal = 255
Rohit needs to verify a binary subtraction for a microcontroller register calculation.
Input: 11110000 â 00001111
Decimal: 240 â 15 = 225
â Result: Binary = 11100001 | Decimal = 225 | Hex = E1 | Octal = 341
Marcus converts hex color code 1A to binary to debug a bitwise flag in his application.
Input: 1A (Hexadecimal) â Convert
â Binary = 11010 | Decimal = 26 | Octal = 32 | Hex = 1A
What Is a Binary Calculator?
A binary calculator is a tool that performs mathematical operations and number-base conversions using the binary (base-2) number system â the fundamental language of every digital computer. Unlike the decimal system we use daily with digits 0â9, binary uses only two digits: 0 and 1. Each digit represents a physical state in electronics â off or on, false or true, low voltage or high voltage.
Binary arithmetic is at the core of computer science, digital electronics, networking, and programming. Students studying BCA, B.Tech (CS/IT/ECE), NIELIT, or any IT certification will encounter binary operations constantly â from understanding CPU registers and memory addressing to network subnetting and data encoding.
This tool combines both common use cases: performing arithmetic on binary values and converting numbers across the four standard bases â binary (base-2), octal (base-8), decimal (base-10), and hexadecimal (base-16). All results are displayed simultaneously so you can understand the relationship between each base representation.
Binary Calculator in Multiple Languages
Want to understand binary numbers from scratch? Read our complete guide on how binary arithmetic and base conversions work.
Read the Full Guide âFrequently Asked Questions
Is this binary calculator free to use?
What operations does the binary calculator support?
Can I enter decimal numbers to convert to binary?
What happens if I divide by zero in binary?
Does the tool support negative binary numbers?
What is the maximum binary number I can enter?
Can I convert hexadecimal to binary?
What is the difference between binary and decimal number systems?
Is this tool useful for computer science students?
Does my data get saved anywhere?
Can I use this tool on a mobile phone?
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