Definition: Decimal is a base-10 numeral system using digits 0 through 9.
History/origin: The most common number system used in everyday counting, historically developed by humans.
Current use: Used universally for arithmetic, financial calculations, and general counting.
Definition: Binary is a base-2 numeral system using only two digits, 0 and 1.
History/origin: Used in digital electronics and computing as it represents two states (off/on).
Current use: Fundamental to computer systems, data representation, and digital communication.
| Decimal | Binary |
|---|---|
| 1 | 00000001 |
| 2 | 00000010 |
| 5 | 00000101 |
| 10 | 00001010 |
| 15 | 00001111 |
| 31 | 00011111 |
Formula: Binary = Decimal converted to base-2 string
Example: convert decimal 11 to binary:
11 ÷ 2 = 5 remainder 1
5 ÷ 2 = 2 remainder 1
2 ÷ 2 = 1 remainder 0
1 ÷ 2 = 0 remainder 1
So, 11 in binary = 1011