問83
頻出度★★☆
片面 1 層記録の DVD-R は約 4.7G バイトの記憶容量をもつ。1 ページ当たり日本語 700 文字が印刷されている本の場合, 約何万ページ分をこの DVD-R に保存できるか。ここで, 日本語 1 文字を表現するのに 2 バイトが必要であるとし, 文字情報だけを記録するものとする。また, 1G バイトは 10 億バイトとする。
平成22年度 秋期 ITパスポート試験 問83
テクノロジ系基礎理論 › 情報に関する理論
This question's explanation and your answers so far.
解説
問 83
Incorrectア
With 420,000 pages, 420,000 × 1,400 bytes = about 588 million bytes, which uses only about one eighth of the 4.7-billion-byte capacity. You get exactly one eighth if you mistake the 4.7 G of capacity for “bits” and divide by 8 before converting to bytes. As a rule, the capacity of a storage device is expressed in bytes, and this question clearly states 4.7 GB, so there is no need to divide by 8.
Incorrectイ
With 710,000 pages, 710,000 × 1,400 bytes = about 994 million bytes, that is only about 1 GB worth. This is the value you get by dividing 1 GB = 1 billion bytes by 1,400 bytes, a calculation that forgets to apply the capacity of 4.7 GB (4.7 times as much). Correctly, you divide 4.7 billion bytes, not 1 billion bytes, by 1,400 bytes.
- ウ
正解 The correct answer is ウ (about 336 ten-thousand pages, that is about 3,360,000 pages). The procedure is “total capacity ÷ amount of information per page”. First, put the capacity into bytes. Since 1 GB is taken as 1 billion bytes, 4.7 GB = 4.7 × 1 billion = 4.7 billion bytes = 4,700,000,000 bytes. Next, find the amount of information for one page. One page holds 700 Japanese characters and one character is 2 bytes, so 700 × 2 = 1,400 bytes. Therefore the number of pages that can be stored is 4,700,000,000 ÷ 1,400 = about 3,357,000 pages. The question asks how many ten-thousand pages, so dividing by 10,000 gives about 335.7 ten-thousand pages, and the closest choice, 336, is the answer. To check the order of magnitude, you can also estimate 4.7 billion ÷ 1,400 ≒ 4.7 billion ÷ 1.4 thousand = about 3.36 million, which gives the same result.
Incorrectエ
With 6,710,000 pages, 6,710,000 × 1,400 bytes = about 9.39 billion bytes, which would require exactly twice the 4.7-billion-byte capacity. This is the value from 4.7 billion ÷ 700 = about 6.71 million, that is, treating one page as 700 bytes instead of 700 characters and forgetting the condition that one Japanese character is 2 bytes. A character count and a byte count are different things, so always convert to 700 characters × 2 bytes = 1,400 bytes before dividing.
ここがポイント
- Converting amounts of information: the basics are that one Japanese (full-width) character is 2 bytes and one half-width alphanumeric character is 1 byte. Do not treat a character count as a byte count; always multiply by the bytes per character before comparing it with a capacity. One page = 700 characters × 2 bytes = 1,400 bytes.
- Estimating storage capacity: “number of items that can be stored = storage capacity ÷ amount of information per item”. The iron rule is to align the units before calculating: 1 GB is 1 billion (10 to the 9th power) bytes, 1 MB is 1 million bytes, and 1 kB is 1,000 bytes. Note as well that capacity is expressed in bytes, not bits.
用語