Binary Calculator
Convert between binary, decimal, hexadecimal, and octal number systems with arithmetic operations and detailed explanations.
Calculator
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Converting 10 from decimal
Conversion Details
Decimal Value: 10
Binary Breakdown: 1 × 2^3 + 0 × 2^2 + 1 × 2^1 + 0 × 2^0
Hex Digits: A = 10
Number System Comparison
| System | Base | Digits | Value |
|---|---|---|---|
| Decimal | 10 | 0-9 | 10 |
| Binary | 2 | 0-1 | 1010 |
| Hexadecimal | 16 | 0-9, A-F | A |
| Octal | 8 | 0-7 | 12 |
How It Works
The binary calculator converts between different number systems and performs arithmetic operations:
Number Systems:
- Binary (Base 2): Uses digits 0 and 1
- Decimal (Base 10): Uses digits 0-9
- Hexadecimal (Base 16): Uses digits 0-9 and A-F
- Octal (Base 8): Uses digits 0-7
Each position in a number represents a power of the base. For example, in binary 1011:
1×2³ + 0×2² + 1×2¹ + 1×2⁰ = 8 + 0 + 2 + 1 = 11 (decimal)
Examples
Conversion Example
Decimal 25:
• Binary: 11001
• Hexadecimal: 19
• Octal: 31
Binary Addition
1010 (10 decimal)
+ 0110 (6 decimal)
------
10000 (16 decimal)
Compare
Applications:
- Computer Science: Binary is the foundation of all digital systems
- Programming: Hexadecimal for memory addresses and color codes
- Networking: IP addresses often use different number systems
- Digital Electronics: Logic gates operate on binary values
Conversion Tips:
- Binary to Decimal: Sum powers of 2 for each 1 bit
- Decimal to Binary: Repeatedly divide by 2, track remainders
- Hex to Binary: Each hex digit = 4 binary digits
- Octal to Binary: Each octal digit = 3 binary digits
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