Number Systems
Understand binary, decimal, octal and hexadecimal bases used in digital electronics.
Why several bases?
A digital circuit manipulates electrical levels interpreted as bits: 0 and 1. For humans, long binary strings quickly become hard to read. Hexadecimal and octal are compact notations that still map directly to bits.
| Base | Digits | Common use |
|---|---|---|
| 2, binary | 0, 1 | Real value seen by hardware |
| 10, decimal | 0 to 9 | Human reading, everyday calculations |
| 8, octal | 0 to 7 | Groups of 3 bits |
| 16, hexadecimal | 0 to 9, A to F | Groups of 4 bits, registers, buses |
The rule is always the same: each position has a weight. In base 2, the weights are 1, , , , , and so on.