The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. Octal numerals can be made from binary numerals by grouping consecutive binary digits into groups of three (starting from the right). For example, the binary representation for decimal 74 is 1001010. Two zeroes can be added at the left: (00)1 001 010, corresponding the octal digits 1 1 2, yielding the octal representation 112.
| octal (base 8) | binary (base 2) | octal (base 8) | binary (base 2) |
|---|---|---|---|
| 1 | = 1 | 13 | = 1011 |
| 2 | = 10 | 14 | = 1100 |
| 3 | = 11 | 15 | = 1101 |
| 4 | = 100 | 16 | = 1110 |
| 5 | = 101 | 17 | = 1111 |
| 6 | = 110 | 20 | = 10000 |
| 7 | = 111 | 21 | = 10001 |
| 10 | = 1000 | 22 | = 10010 |
| 11 | = 1001 | 23 | = 10011 |
| 12 | = 1010 | 24 | = 10100 |
In mathematics and digital electronics, a binary number is a number expressed in the binary numeral system or base-2 numeral system which represents numeric values using two different symbols: typically 0 (zero) and 1 (one). The base-2 system is a positional notation with a radix of 2. Because of its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used internally by almost all modern computers and computer-based devices. Each digit is referred to as a bit.
| binary (base 2) | octal (base 8) | binary (base 2) | octal (base 8) |
|---|---|---|---|
| 1 | ≈ 1 | 1011 | ≈ 13 |
| 10 | ≈ 2 | 1100 | ≈ 14 |
| 11 | ≈ 3 | 1101 | ≈ 15 |
| 100 | ≈ 4 | 1110 | ≈ 16 |
| 101 | ≈ 5 | 1111 | ≈ 17 |
| 110 | ≈ 6 | 10000 | ≈ 20 |
| 111 | ≈ 7 | 10001 | ≈ 21 |
| 1000 | ≈ 10 | 10010 | ≈ 22 |
| 1001 | ≈ 11 | 10011 | ≈ 23 |
| 1010 | ≈ 12 | 10100 | ≈ 24 |
| octal (base 8) | binary (base 2) |
|---|---|
| 1 | = 1 |
| 2 | = 10 |
| 3 | = 11 |
| 4 | = 100 |
| 5 | = 101 |
| 6 | = 110 |
| 7 | = 111 |
| 10 | = 1 000 |
| 11 | = 1 001 |
| 12 | = 1 010 |