Decimal to Other Bases

Decimal to Other Bases Converter:

• Converts between decimal and base-2 to base-36
• Supports bidirectional conversion
• Uses standard digit representation (0-9, A-Z)
• Validates input for each base

Number Systems:

• Base-2 (Binary): 0, 1 - Computer systems
• Base-8 (Octal): 0-7 - Unix permissions, older computers
• Base-10 (Decimal): 0-9 - Everyday use
• Base-16 (Hexadecimal): 0-9, A-F - Memory addresses, colors
• Base-32: 0-9, A-V - Data encoding
• Base-36: 0-9, A-Z - Compact encoding

Conversion Method:

• Decimal to Base-N: Repeated division by base
• Base-N to Decimal: Positional value calculation
• Digits: 0-9 for values 0-9, A-Z for values 10-35
• Validation: Checks for valid digits in each base

Common Applications:

• Binary: Computer programming, digital electronics
• Octal: Unix file permissions, legacy systems
• Hexadecimal: Web colors, memory addresses
• Base-32/36: Data compression, URL shortening

Digit Mapping:

• 0-9 → Values 0-9
• A → 10, B → 11, C → 12, D → 13
• E → 14, F → 15, G → 16, H → 17
• I → 18, J → 19, K → 20, L → 21
• M → 22, N → 23, O → 24, P → 25
• Q → 26, R → 27, S → 28, T → 29
• U → 30, V → 31, W → 32, X → 33
• Y → 34, Z → 35

Examples:

• 255 (Decimal) =
• 11111111 (Base-2)
• 377 (Base-8)
• FF (Base-16)
• 73 (Base-36)

Mathematical Properties:

• Base-N representation is unique for each number
• Positional notation: digit × base^position
• Higher bases use fewer digits for large numbers
• Base-36 is most compact alphanumeric system

Programming Context:

• Binary: Fundamental to computer architecture
• Hexadecimal: Common in programming and debugging
• Base-64: Used in data encoding (not supported here)
• Base conversions are essential for data representation

Limitations:

• Maximum base is 36 (0-9, A-Z)
• No support for negative numbers
• No support for fractional numbers
• Large numbers may have many digits in low bases

Validation Rules:

• Decimal input must be non-negative integer
• Base-N input must contain valid digits only
• Base must be between 2 and 36
• Empty input returns error message