Fracciones binarias
Cómo funcionan
Como programador, deberías estar familiarizado con el conceptro de enteros binarios, esto es, la representación de números enteros como series de bits:
Decimal (base 10) |
|
Binario (base 2) |
1 |
⋅ |
101 |
+ |
3 |
⋅ |
100 |
= |
1310 |
= |
11012 |
= |
1 |
⋅ |
23 |
+ |
1 |
⋅ |
22 |
+ |
0 |
⋅ |
21 |
+ |
1 |
⋅ |
20 |
1 |
⋅ |
10 |
+ |
3 |
⋅ |
1 |
= |
1310 |
= |
11012 |
= |
1 |
⋅ |
8 |
+ |
1 |
⋅ |
4 |
+ |
0 |
⋅ |
2 |
+ |
1 |
⋅ |
1 |
Así almacenan números internamente los ordenadores. Y para números racionales en notación posicional, hacen lo mismo:
Decimal (base 10) |
|
Binario (base 2) |
6 |
⋅ |
10-1 |
+ |
2 |
⋅ |
10-2 |
+ |
5 |
⋅ |
10-3 |
= |
0.62510 |
= |
0.1012 |
= |
1 |
⋅ |
2-1 |
+ |
0 |
⋅ |
2-2 |
+ |
1 |
⋅ |
2-3 |
6 |
⋅ |
1/10 |
+ |
2 |
⋅ |
1/100 |
+ |
5 |
⋅ |
1/1000 |
= |
0.62510 |
= |
0.1012 |
= |
1 |
⋅ |
1/2 |
+ |
0 |
⋅ |
1/4 |
+ |
1 |
⋅ |
1/8 |
|
