Binary Calculator
Advanced tool for binary-decimal conversions and bitwise operations. Perform AND/OR/XOR operations, calculate two's complement, and convert between binary, decimal, and hexadecimal number systems.
Operation Manual
- Input binary numbers (8/16/32/64-bit supported)
- Select conversion type or bitwise operation
- View results in multiple number formats
- Use bit shift controls for advanced operations
- Toggle signed/unsigned representation
Binary Number System Basics
Binary is a base-2 number system using only 0 and 1:
2⁰ = 1
2¹ = 2
2² = 4
2³ = 8
2⁴ = 16
Example: 1101₂ = 1×2³ + 1×2² + 0×2¹ + 1×2⁰ = 13₁₀
Common Binary Operations
AND (∧): 1 if both bits are 1
OR (∨): 1 if at least one bit is 1
XOR (⊕): 1 if bits are different
NOT (¬): Inverts each bit
Shift Left (≪): Multiply by 2
Shift Right (≫): Divide by 2
Applications in Computing
Binary is fundamental to digital systems:
- Data Storage: All data stored as binary
- Digital Logic: CPU operations use binary
- Networking: Data transmission in binary
- Error Detection: Parity bits and checksums
Understanding binary is crucial for computer science and digital electronics.
Binary Patterns
Common binary patterns and their uses:
- 00000000: Null byte, string terminator
- 11111111: All bits set, broadcast address
- 10000000: Sign bit in signed integers
- 01111111: Maximum positive signed byte
These patterns are frequently used in programming and networking protocols.