Binary → Decimal
Enter a binary integer (example: 101101 or -1110).
Decimal → Binary
Enter a decimal integer (example: 45 or -18).
Binary Arithmetic (Integer)
Decimal Arithmetic (Integer)
What this binary and decimal calculator does
This page gives you a practical binary and decimal calculator you can use for both quick conversion and basic integer arithmetic. Whether you are learning computer science, working on embedded systems, practicing for technical interviews, or teaching number systems, this tool helps you move between binary (base 2) and decimal (base 10) with clear results.
- Convert binary integers to decimal integers
- Convert decimal integers to binary integers
- Run binary arithmetic and see decimal equivalents
- Run decimal arithmetic and see binary equivalents
Why binary and decimal both matter
Decimal is the number system most people use every day. It has 10 symbols: 0 through 9. Binary, on the other hand, only uses two symbols: 0 and 1. Computers store and process data in binary, so understanding both systems helps bridge human thinking and machine logic.
Decimal place values
In decimal, each position represents a power of 10. For example, 472 means: 4×10² + 7×10¹ + 2×10⁰.
Binary place values
In binary, each position represents a power of 2. For example, 10110 means: 1×2⁴ + 0×2³ + 1×2² + 1×2¹ + 0×2⁰ = 22.
How to use the calculator
Binary to decimal conversion
Enter a binary number (such as 110011) in the Binary field and click Convert to Decimal. The tool validates your input and returns the decimal result.
Decimal to binary conversion
Enter a decimal integer (such as 51) in the Decimal field and click Convert to Binary. You can also convert negative integers like -12.
Arithmetic tools
You can perform integer arithmetic in either binary or decimal. Choose an operation (+, −, ×, ÷), provide two numbers, and calculate. Division is integer division, meaning any fractional part is dropped.
Worked examples
- Binary to decimal: 101101 = 45
- Decimal to binary: 37 = 100101
- Binary addition: 1010 + 11 = 1101 (decimal 13)
- Decimal multiplication: 14 × 3 = 42 (binary 101010)
- Binary subtraction: 10000 − 1 = 1111 (decimal 15)
Common input mistakes and fixes
- Using digits other than 0 and 1 in binary: Binary accepts only 0 and 1.
- Using decimal points: This calculator is designed for integers.
- Division by zero: Not allowed in either binary or decimal arithmetic.
- Leaving fields empty: Enter both required values before calculating.
Where this is useful in real life
Binary and decimal conversion appears in many practical workflows:
- Programming logic and bit-level operations
- Computer architecture and digital electronics courses
- Networking concepts (flags, masks, and low-level representations)
- Debugging numeric data in logs, tools, and firmware
- Classroom activities in math and STEM education
Final thoughts
If you want to get faster and more confident with number systems, use the converter repeatedly and compare each result to your manual calculations. Over time, binary patterns become intuitive, and this strengthens your overall computational thinking.