🔢 Radix and Positional Number Systems

🧠 What Is Radix?

Radix (also called base) is the number of unique digits used in a positional numeral system.

• Decimal → radix = 10 → digits: 0–9
• Binary → radix = 2 → digits: 0, 1
• Hexadecimal → radix = 16 → digits: 0–9, A–F

🔧 Positional Value Logic

Each digit’s value is weighted by a power of the radix:

Number:  3  4  7   (in base 10)
Weights: 10² 10¹ 10⁰
Value:   3×100 + 4×10 + 7×1 = 347

Number:  1  0  1  1   (in base 2)
Weights: 2³  2²  2¹  2⁰
Value:   1×8 + 0×4 + 1×2 + 1×1 = 11

🧩 Semantic Vault Insight

“Radix defines the scaling law behind digits. It’s the root of positional meaning and the foundation of all base conversions and complement systems.”

This principle underpins all positional number systems, from binary logic to historical sexagesimal timekeeping.

🔍 Common Radices