Base-N Arithmetic Simulator
Add, subtract, multiply, and divide in any base from 2 to 36—binary through hex and beyond.
Base-N Arithmetic Simulator
Perform arithmetic operations in any number base from 2 to 36. Learn how arithmetic works in different numeral systems.
Quick Examples
Same rules, different radix
In base N, digits run 0 … N−1 (A–Z for 10–35). Place values are powers of N. Column arithmetic still carries when a sum reaches N—exactly like carrying at 10 in decimal.
Why bother: machines run binary; programmers debug hex dumps; networking and octal permissions still show up. Doing the ops in-base beats converting everything to decimal for every step when you are learning the notation.
Worked idea (hex add)
Multiplication and long division follow the same place-value logic; only the digit alphabet and the carry threshold change.
Common mistakes
- Using a digit ≥ N (e.g. "8" in octal)
- Carrying at 10 instead of at N
- Mixing bases mid-problem without converting
- Forgetting leading zeros matter less than place alignment
Related tools
Frequently Asked Questions
Base-N vs decimal arithmetic?
Same place-value addition/subtraction/multiplication/division. Digit set and carry size equal the base.
Why learn other bases?
Binary for hardware, hex for compact machine words, octal in some legacy and Unix contexts.
How do I check an answer?
Convert operands and result to decimal once, or reverse the operation in the same base.
Practice tip?
Drill small adds in binary and hex until carry feels automatic, then multiply.
Related tools
Related tools
Related Number Tools
Add/Subtract Percentage
Add or subtract percentages from numbers
Age Calculator
Calculate age from birth date
Angle Converter
Convert between angle units
Area Converter
Convert between area units
Armstrong Number Checker
Check if a number is an Armstrong number
Average Calculator
Calculate average of numbers
Binary ↔ Decimal Converter
Convert between binary and decimal
BMI Calculator
Calculate your Body Mass Index (BMI) using metric or imperial units. Get instant health category classification and personalized weight range recommendations.
Box Plot Generator
Generate box plots from data
Combinations Calculator
Calculate combinations