Binary Calculator
Perform binary operations and convert between number systems
How to Use This Binary Calculator
- Choose 'Binary Operations' to perform math on binary numbers
- Enter two binary numbers using only 0s and 1s
- Select an operation (+, -, x, /) by clicking the button
- View results in binary, decimal, hexadecimal, and octal
- Use 'Number Converter' tab to convert between bases
Example: Add binary 1010 (decimal 10) + 1100 (decimal 12): Result is 10110 in binary, which equals 22 in decimal, 16 in hex, and 26 in octal.
Tip: Binary 1010 = 8+2 = 10 in decimal. Each position from right is 1, 2, 4, 8, 16... (powers of 2).
Why Use a Binary Calculator?
Binary is the language of computers. Understanding binary operations is essential for programming, networking, and computer science coursework.
- Learning computer science fundamentals and digital logic
- Debugging bitwise operations in programming code
- Understanding IP addresses and subnet masks in networking
- Working with file permissions in Unix/Linux systems
- Converting between number systems for embedded programming
- Analyzing memory addresses and data structures
Understanding Your Results
Results appear in multiple number systems to help you understand the relationships between bases.
| Result | Meaning | Action |
|---|---|---|
| Binary (Base 2) | Native computer representation | Each digit is one bit - useful for understanding data storage |
| Hexadecimal (Base 16) | Compact binary representation | One hex digit = 4 bits. Used in color codes (#FF0000), memory addresses |
| Decimal (Base 10) | Human-readable form | What we normally use - easier to understand magnitude |
Meaning: Native computer representation
Action: Each digit is one bit - useful for understanding data storage
Meaning: Compact binary representation
Action: One hex digit = 4 bits. Used in color codes (#FF0000), memory addresses
Meaning: Human-readable form
Action: What we normally use - easier to understand magnitude
Note: Hex uses A-F for values 10-15. So FF in hex = 1111 1111 in binary = 255 in decimal.
About Binary Calculator
Formula
Binary place values: ... 16, 8, 4, 2, 1 (powers of 2 from right) Binary 1101 = 1x8 + 1x4 + 0x2 + 1x1 = 8 + 4 + 0 + 1 = 13 in decimal. Each position doubles in value moving left.
Current Standards: Modern computers use 8-bit bytes, 32-bit or 64-bit integers. IPv4 addresses are 32 bits (4 octets). File permissions in Unix use 3 octal digits (9 bits total).
Frequently Asked Questions
How do I convert binary to decimal manually?
Write the powers of 2 above each digit from right to left: 1, 2, 4, 8, 16, 32... Then add the values where there's a 1. For 101101: 32 + 0 + 8 + 4 + 0 + 1 = 45. Or: 1x32 + 0x16 + 1x8 + 1x4 + 0x2 + 1x1 = 45.
What are common binary values programmers memorize?
Key values: 255 = 1111 1111 (max 8-bit value), 256 = 1 0000 0000, 1024 = 2^10 (kilobyte origin), 65535 = max 16-bit. Common hex: 0xFF = 255, 0x100 = 256, 0xFFFF = 65535. Byte boundaries: 8, 16, 32, 64 bits.
How do computers do binary addition?
Same as decimal but carry at 2 instead of 10. 0+0=0, 0+1=1, 1+0=1, 1+1=10 (write 0, carry 1). For 1011+1101: rightmost column 1+1=10 (write 0, carry 1), then 1+0+1=10 (write 0, carry 1), etc. Result: 11000 (binary) = 24 (decimal).
Why do programmers prefer hexadecimal?
Hex is compact and aligns perfectly with binary. One hex digit = exactly 4 bits, so one byte = exactly 2 hex digits. The binary 1111 0010 is F2 in hex versus 242 in decimal. Memory addresses, color codes, and debugging all use hex because it's easier to read and directly maps to binary.
What's the difference between signed and unsigned binary?
Unsigned binary is always positive (8 bits = 0 to 255). Signed binary uses the leftmost bit for sign (8 bits = -128 to +127). This calculator uses unsigned values. Negative results in subtraction may show unexpected values if the result goes below zero.