In mathematics and digital electronics, a binary number is a number expressed in the base-2 numeral system or binary numeral system, which uses only two symbols: typically 0 (zero) and 1 (one).
Conversion to and from other numeral systems
Binary 10010101101
Decimal 1×210 +0×29 +0×28 +1×27 +0×26 +1×25 +0×24 +1×23 +1×22 +0×21 +1×20 =1197
Hexadecimal
C0E716 = (12 × 163) + (0 × 162) + (14 × 161) + (7 × 160) = (12 × 4096) + (0 × 256) + (14 × 16) + (7 × 1) = 49,38310
| 0hex | = | 0dec | = | 0oct | 0 | 0 | 0 | 0 | |
| 1hex | = | 1dec | = | 1oct | 0 | 0 | 0 | 1 | |
| 2hex | = | 2dec | = | 2oct | 0 | 0 | 1 | 0 | |
| 3hex | = | 3dec | = | 3oct | 0 | 0 | 1 | 1 | |
| 4hex | = | 4dec | = | 4oct | 0 | 1 | 0 | 0 | |
| 5hex | = | 5dec | = | 5oct | 0 | 1 | 0 | 1 | |
| 6hex | = | 6dec | = | 6oct | 0 | 1 | 1 | 0 | |
| 7hex | = | 7dec | = | 7oct | 0 | 1 | 1 | 1 | |
| 8hex | = | 8dec | = | 10oct | 1 | 0 | 0 | 0 | |
| 9hex | = | 9dec | = | 11oct | 1 | 0 | 0 | 1 | |
| Ahex | = | 10dec | = | 12oct | 1 | 0 | 1 | 0 | |
| Bhex | = | 11dec | = | 13oct | 1 | 0 | 1 | 1 | |
| Chex | = | 12dec | = | 14oct | 1 | 1 | 0 | 0 | |
| Dhex | = | 13dec | = | 15oct | 1 | 1 | 0 | 1 | |
| Ehex | = | 14dec | = | 16oct | 1 | 1 | 1 | 0 | |
| Fhex | = | 15dec | = | 17oct | 1 | 1 | 1 | 1 | |
Octal
Converting from octal to binary proceeds in the same fashion as it does for hexadecimal:
- 658 = 110 1012
- 178 = 001 1112
And from binary to octal:
- 1011002 = 101 1002 grouped = 548
- 100112 = 010 0112 grouped with padding = 238
And from octal to decimal:
- 658 = (6 × 81) + (5 × 80) = (6 × 8) + (5 × 1) = 5310
- 1278 = (1 × 82) + (2 × 81) + (7 × 80) = (1 × 64) + (2 × 8) + (7 × 1) = 8710
Representing real numbers
Non-integers can be represented by using negative powers, which are set off from the other digits by means of a radix point (called a decimal point in the decimal system). For example, the binary number 11.012 thus means:
-
1 × 21 (1 × 2 = 2) plus 1 × 20 (1 × 1 = 1) plus 0 × 2−1 (0 × 1⁄2 = 0) plus 1 × 2−2 (1 × 1⁄4 = 0.25)
For a total of 3.25 decimal.
How to convert a float number into binary?
What about
\((3.14)_{10} = (???.???????)_2\)
A tool for conversion between different bases: http://tool.oschina.net/hexconvert/
