平成28年度秋期 ITパスポート試験問78

This question's explanation and your answers so far.

問78

頻出度★☆☆

300×600ドットで構成され，1画素の情報を記録するのに24ビットを使用する画像データがある。これを150×300ドットで構成され，1画素の情報を記録するのに8ビットを使用する画像データに変換した。必要な記憶容量は何倍になるか。

出典　平成28年度秋期 ITパスポート試験問78

解説

問 78

ア
正解 The storage capacity of image data is determined by 'total number of pixels × bits per pixel'. The total number of pixels changes from 300×600 to 150×300; since both the width and the height are halved, it becomes 1/2 × 1/2 = 1/4. The bits per pixel change from 24 bits to 8 bits, so it becomes 8/24 = 1/3. Therefore the storage capacity becomes 1/4 × 1/3 = 1/12, and the correct answer is 'ア', 1/12.
Incorrectイ
1/6 comes from miscounting the change in pixel count as only one of the two dimensions (width or height) being halved (1/2), then multiplying by the 1/3 for bits, giving 1/2 × 1/3. In reality both the width and the height are halved, so the pixel count is 1/4; therefore it is wrong.
Incorrectウ
1/4 only accounts for the change in pixel count (1/4) and forgets to multiply by the factor for bits per pixel changing from 24 to 8, i.e. becoming 1/3; therefore it is wrong.
Incorrectエ
1/2 reflects only part of the change (for example, shrinking only one of the two dimensions), and does not multiply together both the change in total pixel count (1/4) and the change in bits (1/3); therefore it is wrong.

ここがポイント

The storage capacity of image (bitmap) data = total number of pixels (horizontal dots × vertical dots) × bits per pixel (color depth).
Multiply together the ratio of dots for each dimension (width and height) and the ratio of bits per pixel to obtain the overall capacity ratio.

用語

解答問78ア