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Place Value and Number Bases
Each digit's value depends on its position. The base tells you how many digits there are and what each place is worth.
Place Value in Decimal
You already use a number system every day: decimal, also called denary or base 10. It has ten digits, 0 to 9.
In the number 4,725 the digit 7 does not mean seven. It means seven hundred, because of its place. Each place is worth 10 times the place to its right.
| The number 4,725 in place-value columns | ||||
|---|---|---|---|---|
The Four Number Systems You Need
| Four number systems | |||
|---|---|---|---|
Hexadecimal needs sixteen digits, but we only have ten number symbols. So it borrows letters:
| Hex digit | A | B | C | D | E | F |
|---|---|---|---|---|---|---|
| Decimal value | 10 | 11 | 12 | 13 | 14 | 15 |
Counting in Each Base
When you run out of digits in a column, you write 0 and carry 1 to the next column — exactly as 9 + 1 = 10 in decimal.
| Counting from 0 to 17 in each base | |||
|---|---|---|---|
Practice
In the octal number 352₈, what is the 3 worth in decimal?
Your answer
More lessons in Number Systems · Next: Why Computers Use Binary · Previous: Introduction