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Сколько Кбайт необходимо для хранения изображения, если ィспользуется \( 2^{14} \) цветов и з40×480 пикселей? Размер заголовка файла и палитры не учитывай.

Ask by Cox Bolton. in Russia
Feb 24,2025

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Для хранения изображения требуется около 33 Кбайт.

Solución

Чтобы узнать, сколько памяти потребуется для хранения изображения, выполним следующие расчёты. 1. Определим общее количество пикселей:   40 × 480 = 19200 пикселей. 2. Так как изображение использует 2^14 цветов, на каждый пиксель приходится:   log₂(2^14) = 14 бит. 3. Найдём общее количество бит:   19200 пикселей × 14 бит = 268800 бит. 4. Переведём биты в байты (1 байт = 8 бит):   268800 бит ÷ 8 = 33600 байт. 5. Переведём байты в килобайты (1 Кбайт = 1024 байта):   33600 байт ÷ 1024 ≈ 32.81 Кбайт. Таким образом, для хранения изображения требуется примерно 33 Кбайт (без учёта заголовка и палитры).

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The Deep Dive

Чтобы рассчитать необходимость хранения изображения, сначала определим, сколько бит нужно для хранения одного пикселя. Если используется \( 2^{14} \) цветов, это требует 14 бит на пиксель. Поскольку изображение имеет разрешение 640×480 пикселей, общее количество пикселей равно \( 640 \times 480 = 307200 \). Теперь умножаем количество пикселей на количество бит: \( 307200 \times 14 = 4291200 \) бит. Теперь переведем это значение в байты: \( 4291200 \div 8 = 536400 \) байт. Чтобы перевести байты в килобайты, делим на 1024: \( 536400 \div 1024 \approx 523.44 \) Кбайт. Таким образом, для хранения изображения потребуется примерно 524 Кбайт.

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