Binary Calculator - Add, Subtract, Multiply Binary Numbers

Binary Calculator

Number System Converter

Enter a value in any base to see conversions

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About Binary Numbers

Binary is a base-2 number system that uses only two digits: 0 and 1. Each digit in a binary number represents a power of 2, making it fundamental to computer systems and digital electronics.

How Binary Works

In binary, each position represents an increasing power of 2 from right to left. For example, the binary number 1011 breaks down as:

• 1 × 2³ = 8
• 0 × 2² = 0
• 1 × 2¹ = 2
• 1 × 2⁰ = 1
• Total: 8 + 0 + 2 + 1 = 11 (decimal)

Binary Addition Rules

• 0 + 0 = 0
• 0 + 1 = 1
• 1 + 0 = 1
• 1 + 1 = 10 (0 with carry of 1)
• 1 + 1 + 1 = 11 (1 with carry of 1)

Bitwise Operations

Bitwise operations work on individual bits:

• AND: Result is 1 only if both bits are 1
• OR: Result is 1 if either bit is 1
• XOR: Result is 1 if bits are different
• NOT: Flips all bits (0 becomes 1, 1 becomes 0)

Common Applications

• Computer Science: All digital data is stored and processed in binary
• Networking: IP addresses, subnet masks, and protocols use binary
• Programming: Bitwise operations for flags, permissions, and optimization
• Electronics: Digital circuits operate on binary logic
• Data Compression: Binary encoding for efficient storage

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Binary Calculator FAQ