Binary Calculator
Perform binary arithmetic operations and convert between binary, decimal, hexadecimal, and octal number systems
Binary Calculator
Binary Arithmetic
Enter only 0s and 1s
Results
Enter values and click "Calculate" to see the results
Quick Reference
Binary: 0, 1
Octal: 0-7
Decimal: 0-9
Hex: 0-9, A-F
Understanding Binary Numbers
What is Binary?
Binary is a base-2 number system that uses only two digits: 0 and 1. Each digit represents a power of 2, making it fundamental to computer systems and digital electronics.
Binary Place Values
128 | 64 | 32 | 16 | 8 | 4 | 2 | 1
2⁷ | 2⁶ | 2⁵ | 2⁴ | 2³ | 2² | 2¹ | 2⁰
Number System Comparison
Different number systems use different bases and digit sets. Understanding these relationships is key to number system conversions.
Binary (Base 2): 0, 1
Octal (Base 8): 0, 1, 2, 3, 4, 5, 6, 7
Decimal (Base 10): 0-9
Hexadecimal (Base 16): 0-9, A-F
Binary Arithmetic Operations
Addition Rules
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 10 (carry 1)
Subtraction Rules
0 - 0 = 0
1 - 0 = 1
1 - 1 = 0
0 - 1 = 1 (borrow 1)
Bitwise Operations
Logic Gates
AND: Both bits must be 1
OR: Either bit can be 1
XOR: Bits must be different
NOT: Inverts all bits
Shift Operations
Left Shift: Multiply by 2ⁿ
Right Shift: Divide by 2ⁿ
Example: 1100 << 2 = 110000
Applications
• Fast multiplication/division
• Bit manipulation
• Flags and permissions
• Cryptography
Conversion Methods
- • Decimal to binary: Division by 2
- • Binary to decimal: Powers of 2
- • Binary to hex: Group by 4 bits
- • Binary to octal: Group by 3 bits
- • Use positional notation
Real-World Uses
- • Computer programming
- • Digital electronics
- • Network addressing
- • Image processing
- • Data compression
Tips & Tricks
- • Use grouping for readability
- • Practice with small numbers
- • Memorize powers of 2
- • Use online tools for verification
- • Understand two's complement
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