Conversion from the Decimal system to the Natural Binary Code
The conversion of a decimal number to the binary format is very simple. The decimal value is simply divided by 2 and then the remainder is written down, the process is repeated until the number cannot be divided by 2 anymore. The next step requires rewriting the remainders in the reverse order and by this obtaining the result in binary code.
Example:
157
| 157 | 2 | 1 (LSB) |
| 78 | 2 | 0 |
| 39 | 2 | 1 |
| 19 | 2 | 1 |
| 9 | 2 | 1 |
| 4 | 2 | 0 |
| 2 | 2 | 0 |
| 1 | 2 | 1 (MSB) |
10011101 = 157
In the natural binary code it is also possible to convert fractions of a decimal number. Conversion algorithm in this case differs from the one performed on integers. Instead of division, multiplication of the fraction by 2 is performed. The process repeats until the result is equal to zero.
Example:
0.625
| 0.625* 2 = 1.25 | 1 |
| 0.25 *2 =0.5 | 0 |
| 0.5 * 2 = 1 | 1 |
The binary result is produced by rewriting the remainders in order.
0.625=0.101