number systems

Summary

Decimal (base 10): digits 0–9
Binary (base 2): digits 0,1
Octal (base 8): digits 0–7
Hexadecimal (base 16): digits 0–9, A–F

Concept

Weighted positional number systems

• each digit represents the

Base-R → Decimal

• multiply digits by powers of R

Decimal → Base-R

• repeated division by R

Between non-decimal bases convert via decimal or shortcuts (group bits).

• Binary -> Octal: groups of 3.
• Binary -> Hex: groups of

Application

Positional weights

Binary <-> Octal <-> Hexadecimal