A number system is an agreement about how to write an amount down. It fixes which digit symbols you may use and what each digit is worth depending on where it sits.
The amount itself doesn't depend on the system. Twelve marbles are twelve marbles whether you write 12 in decimal, 1100 in binary or C in hexadecimal. Only the spelling changes.
The systems in this course are all positional (see positional notation): each position has a weight that is a power of the radix.
- Decimal, base 10: digits 0–9. What people use.
- Binary, base 2: digits 0 and 1. What hardware stores, because a wire is either low or high.
- Octal, base 8: digits 0–7. A short way to write binary in groups of 3 bits.
- Hexadecimal, base 16: digits 0–9 and A–F. A short way to write binary in groups of 4 bits.
Not every number system is positional. Roman numerals give each symbol a fixed value (X is always ten), which is why they're so clumsy for arithmetic. Positional systems make adding, carrying and converting follow the same few rules in every base.
1
8
1
4
0
2
0
1