Binary Calculator
Perform arithmetic and logical operations across different number bases.
Binary Calculator
Binary (base-2) is the foundation of all digital computing. This calculator lets you perform binary arithmetic (add, subtract, multiply, divide) and convert between binary, decimal, octal, and hexadecimal number systems.
How to Use This Calculator
- Enter numbers in binary format (digits 0 and 1 only).
- Select the operation: +, −, ×, ÷.
- Click Calculate to see the result in binary, with the decimal equivalent shown.
- Use the conversion tab to convert any number between binary, decimal, octal, and hex.
Binary Number System Basics
Binary uses only digits 0 and 1. Each position represents a power of 2:
Binary 1011 = (1×2³) + (0×2²) + (1×2¹) + (1×2⁰) = 8 + 0 + 2 + 1 = 11 in decimal
Binary Arithmetic Examples
Addition: 1011 + 0110 = 10001 (11 + 6 = 17)
Subtraction: 1100 − 0101 = 0111 (12 − 5 = 7)
Carry rules: 0+0=0, 0+1=1, 1+1=10 (0 carry 1), 1+1+1=11 (1 carry 1)
Decimal to Binary Conversion
Divide by 2 repeatedly, recording remainders bottom-to-top:
25 ÷ 2 = 12 R1 | 12 ÷ 2 = 6 R0 | 6 ÷ 2 = 3 R0 | 3 ÷ 2 = 1 R1 | 1 ÷ 2 = 0 R1 → 25 = 11001₂
Common Mistakes to Avoid
- Using digits other than 0 and 1 in binary — Binary only has two digits. Any other digit is invalid.
- Forgetting to carry in binary addition — 1 + 1 = 10 in binary (not 2). Always carry into the next position.
- Confusing binary with hex shorthand — Hex digits A–F represent values 10–15. They don't appear in binary.
Frequently Asked Questions
Why do computers use binary?
Electronic circuits are most reliable with two states: on (1) and off (0). Binary maps perfectly to these physical states — making binary the natural language of digital electronics.
What is a bit? What is a byte?
A bit is a single binary digit (0 or 1). A byte is 8 bits, capable of representing 256 different values (0–255 in decimal, 00000000–11111111 in binary).
How is binary used in color codes?
RGB colors use 8 bits per channel (0–255). A color like #FF0000 (red) is 11111111 00000000 00000000 in binary — maximum red, no green, no blue. See our Hex Calculator.
What is two's complement?
The standard way computers represent negative numbers in binary. To negate: flip all bits, then add 1. −5 in 8-bit two's complement = 11111011.
Conclusion
Whether you're studying computer science, debugging low-level code, or just satisfying curiosity, this binary calculator makes binary arithmetic and number conversion fast and error-free.
Related: Hex Calculator | Scientific Notation Calculator | Big Number Calculator
Dev Tip
Hexadecimal is commonly used in development to represent bytes. One Hex character represents exactly 4 bits (a nibble), making it very easy to read memory values.
