Перевод из десятичной системы в double ieee-754 (черновая версия)
| Введите число в десятичной записи. | ||
| + | 0 | . | 875 | * 10^0 |
Учитываем порядок
С учетом порядка: x = + 0.875
Нормализация
Нормализуем мантиссу (приведем к виду 1.xxx...x * 2^exp)
| Шаг | Мантисса | * 2^двоичный порядок |
| 0 | 0.875 | * 2^0 |
| 1 | 1.75 | * 2^-1 |
x = +1.75 * 2^-1
Перевод в двоичный вид
Переводим нормализованную мантиссу в двоичный вид (p = 52)
| Шаг i | Двоичная мантисса | остаток * 2^-i |
| 0 | 1. | + 0.75 * 2^-0 |
| 1 | 1.1 | + 0.5 * 2^-1 |
| 2 | 1.11 | + 0.0 * 2^-2 |
| 3 | 1.110 | + 0.0 * 2^-3 |
| 4 | 1.1100 | + 0.0 * 2^-4 |
| 5 | 1.11000 | + 0.0 * 2^-5 |
| 6 | 1.110000 | + 0.0 * 2^-6 |
| 7 | 1.1100000 | + 0.0 * 2^-7 |
| 8 | 1.11000000 | + 0.0 * 2^-8 |
| 9 | 1.110000000 | + 0.0 * 2^-9 |
| 10 | 1.1100000000 | + 0.0 * 2^-10 |
| 11 | 1.11000000000 | + 0.0 * 2^-11 |
| 12 | 1.110000000000 | + 0.0 * 2^-12 |
| 13 | 1.1100000000000 | + 0.0 * 2^-13 |
| 14 | 1.11000000000000 | + 0.0 * 2^-14 |
| 15 | 1.110000000000000 | + 0.0 * 2^-15 |
| 16 | 1.1100000000000000 | + 0.0 * 2^-16 |
| 17 | 1.11000000000000000 | + 0.0 * 2^-17 |
| 18 | 1.110000000000000000 | + 0.0 * 2^-18 |
| 19 | 1.1100000000000000000 | + 0.0 * 2^-19 |
| 20 | 1.11000000000000000000 | + 0.0 * 2^-20 |
| 21 | 1.110000000000000000000 | + 0.0 * 2^-21 |
| 22 | 1.1100000000000000000000 | + 0.0 * 2^-22 |
| 23 | 1.11000000000000000000000 | + 0.0 * 2^-23 |
| 24 | 1.110000000000000000000000 | + 0.0 * 2^-24 |
| 25 | 1.1100000000000000000000000 | + 0.0 * 2^-25 |
| 26 | 1.11000000000000000000000000 | + 0.0 * 2^-26 |
| 27 | 1.110000000000000000000000000 | + 0.0 * 2^-27 |
| 28 | 1.1100000000000000000000000000 | + 0.0 * 2^-28 |
| 29 | 1.11000000000000000000000000000 | + 0.0 * 2^-29 |
| 30 | 1.110000000000000000000000000000 | + 0.0 * 2^-30 |
| 31 | 1.1100000000000000000000000000000 | + 0.0 * 2^-31 |
| 32 | 1.11000000000000000000000000000000 | + 0.0 * 2^-32 |
| 33 | 1.110000000000000000000000000000000 | + 0.0 * 2^-33 |
| 34 | 1.1100000000000000000000000000000000 | + 0.0 * 2^-34 |
| 35 | 1.11000000000000000000000000000000000 | + 0.0 * 2^-35 |
| 36 | 1.110000000000000000000000000000000000 | + 0.0 * 2^-36 |
| 37 | 1.1100000000000000000000000000000000000 | + 0.0 * 2^-37 |
| 38 | 1.11000000000000000000000000000000000000 | + 0.0 * 2^-38 |
| 39 | 1.110000000000000000000000000000000000000 | + 0.0 * 2^-39 |
| 40 | 1.1100000000000000000000000000000000000000 | + 0.0 * 2^-40 |
| 41 | 1.11000000000000000000000000000000000000000 | + 0.0 * 2^-41 |
| 42 | 1.110000000000000000000000000000000000000000 | + 0.0 * 2^-42 |
| 43 | 1.1100000000000000000000000000000000000000000 | + 0.0 * 2^-43 |
| 44 | 1.11000000000000000000000000000000000000000000 | + 0.0 * 2^-44 |
| 45 | 1.110000000000000000000000000000000000000000000 | + 0.0 * 2^-45 |
| 46 | 1.1100000000000000000000000000000000000000000000 | + 0.0 * 2^-46 |
| 47 | 1.11000000000000000000000000000000000000000000000 | + 0.0 * 2^-47 |
| 48 | 1.110000000000000000000000000000000000000000000000 | + 0.0 * 2^-48 |
| 49 | 1.1100000000000000000000000000000000000000000000000 | + 0.0 * 2^-49 |
| 50 | 1.11000000000000000000000000000000000000000000000000 | + 0.0 * 2^-50 |
| 51 | 1.110000000000000000000000000000000000000000000000000 | + 0.0 * 2^-51 |
| 52 | 1.1100000000000000000000000000000000000000000000000000 | + 0.0 * 2^-52 |
Округление (ieee-754)
| Шаг | Мантисса | Бит p + 1 (=53) | Остаток (sticky) |
| 53 | 1.1100000000000000000000000000000000000000000000000000 | 0 | 0.0 * 2^-53 |
Результат
Экспонента со смещением: -1 + 1023 = 1022
| Знак | Смещенный порядок (e + 1023) | Дробная часть мантиссы |
| 0 | 01111111110 | 1100000000000000000000000000000000000000000000000000 |
x = 0x3fec000000000000