Base-N Converter – Positional Notation Steps

Positional notation is the single idea behind every numeral system: each digit contributes its face value times a power of the base. The hexadecimal number 2F3 expands as 2×16² + 15×16¹ + 3×16⁰ = 512 + 240 + 3 = 755. The converter shows this expansion line by line for any base from 2 to 36, then rebuilds the value in your target base by repeated division: 755 ÷ 16 = 47 r3, 47 ÷ 16 = 2 r15, 2 ÷ 16 = 0 r2 — remainders read upward reproduce 2F3. Fractional parts use repeated multiplication instead. The same machinery handles unusual bases: 755 in base 5 works out to 11010₅ (625+125+5), and base 20 relies on letter digits. Every step is printed so conversions can be reproduced (and graded) by hand.

1. 1

   Enter value, from-base, to-base

   Example: 2F3, base 16, to base 10

2. 2

   Expand positionally

   Each digit multiplies its base power — shown per digit

3. 3

   Divide repeatedly

   Remainders of division by the target base form new digits

4. 4

   Read the result

   Remainders bottom-up give the converted numeral

• 1

  Weights grow right-to-left: b⁰, b¹, b², …

• 2

  Repeated division remainders rebuild the number in the new base

• 3

  Cross-check via decimal: every path through 755₁₀ must agree

• Assigning weights left-to-right as b⁰, b¹, b² — reversed

• Forgetting letter digit values: F contributes 15, not 6

• Reading division remainders top-down instead of bottom-up

• Ignoring place limits: digit 7 has no home in base 7