問64
頻出度★★☆
次の真理値表で示される入力x，yに対する出力zが得られる論理演算式はどれか。
| x | y | z |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 0 |
平成25年度 秋期 ITパスポート試験 問64
テクノロジ系基礎理論 › 離散数学
This question's explanation and your answers so far.
解説
問 64
Incorrectア
x AND y (logical AND) is 1 only when both inputs are 1, so the output is 0, 0, 0, 1 in order. This is exactly the reverse of the table: the row where x = y = 0 gives 0 and the row where x = y = 1 gives 1, so it does not match.
Incorrectイ
NOT(x AND y) is NAND (negated AND), and its output is 1, 1, 1, 0 in order. The z = 1 of the first row does match, but the second row (0, 1) and the third row (1, 0) become 1, which conflicts with the 0 in the table.
- ウ
正解 Reading the truth table, the output z is 1 in only one row, where x = 0 and y = 0; whenever either x or y is 1, z is always 0. The behavior “1 only when both inputs are 0” is obtained by first computing x OR y and then inverting that result, that is, NOT(x OR y). Checking it: x OR y gives 0, 1, 1, 1 in order, and inverting with NOT gives 1, 0, 0, 0, which matches the z column of the table exactly. This operation is called NOR (negated OR). Therefore the correct answer is ウ.
Incorrectエ
x OR y (logical OR) is 1 if either input is 1, so the output is 0, 1, 1, 1 in order, which is the reverse of the table's z column (1, 0, 0, 0) in every row. It is the form with the NOT left off, so as it stands it is not the correct answer.
ここがポイント
- To identify a logical expression from a truth table, focus on the pattern of the rows where the output is 1 (or 0). If it is 1 only when both inputs are 0, that corresponds to NOR = NOT(x OR y); if it is 1 only when both inputs are 1, that corresponds to AND, and so on.
- It is faster if you remember the value sequences of the basic logical operations (for x, y in the order 00, 01, 10, 11): AND is 0, 0, 0, 1; OR is 0, 1, 1, 1; NAND is 1, 1, 1, 0; NOR is 1, 0, 0, 0. Applying each candidate expression in turn and comparing it with the table lets you narrow things down reliably.
用語