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) | senary (base 6) | binary (base 2) | senary (base 6) |
|---|---|---|---|
| 1 | = 1 | 1011 | = 15 |
| 10 | = 2 | 1100 | = 20 |
| 11 | = 3 | 1101 | = 21 |
| 100 | = 4 | 1110 | = 22 |
| 101 | = 5 | 1111 | = 23 |
| 110 | = 10 | 10000 | = 24 |
| 111 | = 11 | 10001 | = 25 |
| 1000 | = 12 | 10010 | = 30 |
| 1001 | = 13 | 10011 | = 31 |
| 1010 | = 14 | 10100 | = 32 |
The senary numeral system (also known as base-6 or heximal) has six as its base. It has been adopted independently by a small number of cultures. Like decimal, it is a semiprime, though being the product of the only two consecutive numbers that are both prime (2 and 3) it has a high degree of mathematical properties for its size. As six is a superior highly composite number, many of the arguments made in favor of the duodecimal system also apply to this base-6.
| senary (base 6) | binary (base 2) | senary (base 6) | binary (base 2) |
|---|---|---|---|
| 1 | ≈ 1 | 15 | ≈ 1011 |
| 2 | ≈ 10 | 20 | ≈ 1100 |
| 3 | ≈ 11 | 21 | ≈ 1101 |
| 4 | ≈ 100 | 22 | ≈ 1110 |
| 5 | ≈ 101 | 23 | ≈ 1111 |
| 10 | ≈ 110 | 24 | ≈ 10000 |
| 11 | ≈ 111 | 25 | ≈ 10001 |
| 12 | ≈ 1000 | 30 | ≈ 10010 |
| 13 | ≈ 1001 | 31 | ≈ 10011 |
| 14 | ≈ 1010 | 32 | ≈ 10100 |
| binary (base 2) | senary (base 6) |
|---|---|
| 1 | = 1 |
| 10 | = 2 |
| 11 | = 3 |
| 100 | = 4 |
| 101 | = 5 |
| 110 | = 10 |
| 111 | = 11 |
| 1000 | = 12 |
| 1001 | = 13 |
| 1010 | = 14 |