Number Base Arithmetic Calculator

Arithmetic in any base

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About Number Base Arithmetic Calculator

A number base arithmetic calculator performing add/subtract/multiply/divide in any base 2–36. Enter numbers in the selected base, see results in the same base, and convert between bases. Handles hexadecimal, octal, binary, and custom bases. Client-side.

Number Base Arithmetic Calculator Features

  • Add/Sub/Mul/Div
  • Any base 2–36
  • Step display
  • Cross-base
  • Conversion
Perform arithmetic directly in any base. Binary (base 2): 1011+110=10001. Hex (base 16): FF+1=100. Octal (base 8): 77+1=100. Works like decimal arithmetic but carries at the base value instead of 10.

How to Use

Select base and operation:

  • Base: 2 to 36
  • Numbers: Enter in selected base
  • Result: Answer in same base

Carrying in Bases

Carry when digit ≥ base. Binary: 1+1=10 (carry). Hex: F+1=10 (carry). Octal: 7+1=10 (carry). Same principle as decimal (9+1=10) but threshold changes.

Common Bases

  • Binary (2): computing fundamentals
  • Octal (8): Unix file permissions
  • Decimal (10): everyday use
  • Hexadecimal (16): memory addresses, colors

Step-by-Step Instructions

  1. 1Select base.
  2. 2Enter first number.
  3. 3Choose operation.
  4. 4Enter second number.
  5. 5View result.

Number Base Arithmetic Calculator — Frequently Asked Questions

How does carrying work in different bases?+

Same as decimal but carry at the base. In base 5: 3+4=12₅ (7 decimal = 1×5+2). In base 16: A+B=15₁₆ (10+11=21 decimal = 1×16+5). The algorithm is identical to grade school arithmetic.

What digits are used for bases > 10?+

Bases 11-36 use letters: A=10, B=11, ..., Z=35. Hexadecimal uses 0-9,A-F. Base 36 (maximum single-character) uses 0-9,A-Z. This convention allows any base up to 36 with single characters.

Why are certain bases common in computing?+

Binary (2): hardware logic gates. Octal (8): groups of 3 binary digits. Hex (16): groups of 4 binary digits, compact representation. Each hex digit = exactly 4 bits, making hex↔binary conversion trivial.

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