NumForge LogoNumForge
Explore
Number System ArithmeticFree Interactive Tool

Base-N Subtraction

Subtract numbers in any arbitrary radix from base 2 to base 36 with column borrow tracking. Designed for software developers, electrical engineers, students, and computer architecture researchers requiring deterministic client-side accuracy.

Engine: Client-Side Verified (0ms Latency)

Select base and enter numbers.

Calculated Output

Primary Representation
Calculating...

Step-by-Step Mathematical Proof

Active Derivation
Ready. Enter input above to generate derivation.
Concept

What Is Base-N Subtraction?

Base-N Subtraction computes the difference between two numbers in any base from 2 to 36, where each borrow provides the numerical value of base N.

Methodology

How Does It Work?

Subtract digits column by column. If top digit < bottom digit, borrow 1 from the next higher column (adding base N to the current digit).

Formula & Rules

Mathematical Algorithm

A_N - B_N = \text{Diff}_N \quad \text{with borrow of } N
Worked Problem

Step-by-Step Example

Subtract 52_6 - 24_6 in base 6: Col 0: 2 - 4 (borrow 1 from 5 -> 5 becomes 4, 2 becomes 2+6=8) -> 8 - 4 = 4 Col 1: 4 - 2 = 2 Result: 24_6.

Important Rules & Edge Cases

  • All digits must be less than the selected base.

Practical Applications in Engineering

  • Multi-radix arithmetic solvers.
  • Digital logic simulation.

Common Mistakes to Avoid

  • Caution: Borrowing 10 instead of base N.
FAQ

Frequently Asked Questions

How much does a borrow add in base N?

A borrow from the adjacent column to the left always adds exactly N to the borrowing column.