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

  1. Input binary numbers (8/16/32/64-bit supported)
  2. Select conversion type or bitwise operation
  3. View results in multiple number formats
  4. Use bit shift controls for advanced operations
  5. 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.