Base-N Addition
Add two numbers in any arbitrary radix from base 2 to base 36 with column carry tracking. Designed for software developers, electrical engineers, students, and computer architecture researchers requiring deterministic client-side accuracy.
Select base (2 to 36) and enter numbers.
Calculated Output
Step-by-Step Mathematical Proof
Active DerivationWhat Is Base-N Addition?
Base-N Addition calculates the sum of two numbers expressed in any base from base 2 through base 36, carrying at the chosen base value.
How Does It Work?
Adds columns from right to left. If column sum >= base, a carry of floor(sum / base) is propagated to the next column.
Mathematical Algorithm
Step-by-Step Example
Important Rules & Edge Cases
- All digits must be strictly less than the selected base.
Practical Applications in Engineering
- Radix research in computer science.
- Non-standard positional mathematics.
Common Mistakes to Avoid
- Caution: Entering digits that exceed the selected base.
Frequently Asked Questions
What happens when two digits equal the base in base N?
The result is 0 with a carry of 1 (e.g. in base 5, 2 + 3 = 10_5).
Related Tools
View All Number System Arithmetic →Base-N Subtraction
Subtract numbers in any arbitrary radix from base 2 to base 36 with column borrow tracking.
Base-N Multiplication
Multiply numbers in any arbitrary radix (base 2 to 36) with base-N partial products.
Any Base → Any Base Converter
Convert any number between any source base (2 to 36) and any target base (2 to 36).