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Sagot :
Let's analyze the given truth table to determine which logic gate it represents. The truth table is as follows:
[tex]\[ \begin{array}{|c|c|c|} \hline A & B & \text{Output} \\ \hline 0 & 0 & 0 \\ \hline 0 & 1 & 0 \\ \hline 1 & 0 & 0 \\ \hline 1 & 1 & 1 \\ \hline \end{array} \][/tex]
We'll check each entry of the table against the definitions of common logic gates:
### 1. OR Gate
- Definition: The output is 1 if at least one input is 1.
- Truth Table:
[tex]\[ \begin{array}{|c|c|c|} \hline A & B & \text{Output} \\ \hline 0 & 0 & 0 \\ \hline 0 & 1 & 1 \\ \hline 1 & 0 & 1 \\ \hline 1 & 1 & 1 \\ \hline \end{array} \][/tex]
This does not match our given table. The entry (0, 1) in the OR gate has an output of 1, but in our table, it is 0.
### 2. XOR Gate
- Definition: The output is 1 if exactly one input is 1.
- Truth Table:
[tex]\[ \begin{array}{|c|c|c|} \hline A & B & \text{Output} \\ \hline 0 & 0 & 0 \\ \hline 0 & 1 & 1 \\ \hline 1 & 0 & 1 \\ \hline 1 & 1 & 0 \\ \hline \end{array} \][/tex]
This also does not match our given table. The entry for (0, 1) and (1, 0) in the XOR gate has an output of 1, but in our table, both are 0.
### 3. AND Gate
- Definition: The output is 1 if both inputs are 1.
- Truth Table:
[tex]\[ \begin{array}{|c|c|c|} \hline A & B & \text{Output} \\ \hline 0 & 0 & 0 \\ \hline 0 & 1 & 0 \\ \hline 1 & 0 & 0 \\ \hline 1 & 1 & 1 \\ \hline \end{array} \][/tex]
This matches exactly with our given table.
### 4. NAND Gate
- Definition: The output is 1 if at least one input is 0 (the negation of the AND gate).
- Truth Table:
[tex]\[ \begin{array}{|c|c|c|} \hline A & B & \text{Output} \\ \hline 0 & 0 & 1 \\ \hline 0 & 1 & 1 \\ \hline 1 & 0 & 1 \\ \hline 1 & 1 & 0 \\ \hline \end{array} \][/tex]
This does not match our given table. The entries for (0, 0), (0, 1), and (1, 0) are 1 in the NAND gate, but in our table, all these entries are 0.
### 5. NOR Gate
- Definition: The output is 1 if both inputs are 0 (the negation of the OR gate).
- Truth Table:
[tex]\[ \begin{array}{|c|c|c|} \hline A & B & \text{Output} \\ \hline 0 & 0 & 1 \\ \hline 0 & 1 & 0 \\ \hline 1 & 0 & 0 \\ \hline 1 & 1 & 0 \\ \hline \end{array} \][/tex]
This does not match our given table. The entry for (0, 0) is 1 in the NOR gate, but in our table, it is 0.
### 6. NOT Gate
- Definition: A single input gate where the output is the negation of the input.
- Truth Table:
[tex]\[ \begin{array}{|c|c|} \hline \text{Input} & \text{Output} \\ \hline 0 & 1 \\ \hline 1 & 0 \\ \hline \end{array} \][/tex]
This is not applicable since our given table has two inputs.
From this analysis, the truth table given matches exactly with the truth table of the AND gate. Therefore, the correct answer is:
AND.
[tex]\[ \begin{array}{|c|c|c|} \hline A & B & \text{Output} \\ \hline 0 & 0 & 0 \\ \hline 0 & 1 & 0 \\ \hline 1 & 0 & 0 \\ \hline 1 & 1 & 1 \\ \hline \end{array} \][/tex]
We'll check each entry of the table against the definitions of common logic gates:
### 1. OR Gate
- Definition: The output is 1 if at least one input is 1.
- Truth Table:
[tex]\[ \begin{array}{|c|c|c|} \hline A & B & \text{Output} \\ \hline 0 & 0 & 0 \\ \hline 0 & 1 & 1 \\ \hline 1 & 0 & 1 \\ \hline 1 & 1 & 1 \\ \hline \end{array} \][/tex]
This does not match our given table. The entry (0, 1) in the OR gate has an output of 1, but in our table, it is 0.
### 2. XOR Gate
- Definition: The output is 1 if exactly one input is 1.
- Truth Table:
[tex]\[ \begin{array}{|c|c|c|} \hline A & B & \text{Output} \\ \hline 0 & 0 & 0 \\ \hline 0 & 1 & 1 \\ \hline 1 & 0 & 1 \\ \hline 1 & 1 & 0 \\ \hline \end{array} \][/tex]
This also does not match our given table. The entry for (0, 1) and (1, 0) in the XOR gate has an output of 1, but in our table, both are 0.
### 3. AND Gate
- Definition: The output is 1 if both inputs are 1.
- Truth Table:
[tex]\[ \begin{array}{|c|c|c|} \hline A & B & \text{Output} \\ \hline 0 & 0 & 0 \\ \hline 0 & 1 & 0 \\ \hline 1 & 0 & 0 \\ \hline 1 & 1 & 1 \\ \hline \end{array} \][/tex]
This matches exactly with our given table.
### 4. NAND Gate
- Definition: The output is 1 if at least one input is 0 (the negation of the AND gate).
- Truth Table:
[tex]\[ \begin{array}{|c|c|c|} \hline A & B & \text{Output} \\ \hline 0 & 0 & 1 \\ \hline 0 & 1 & 1 \\ \hline 1 & 0 & 1 \\ \hline 1 & 1 & 0 \\ \hline \end{array} \][/tex]
This does not match our given table. The entries for (0, 0), (0, 1), and (1, 0) are 1 in the NAND gate, but in our table, all these entries are 0.
### 5. NOR Gate
- Definition: The output is 1 if both inputs are 0 (the negation of the OR gate).
- Truth Table:
[tex]\[ \begin{array}{|c|c|c|} \hline A & B & \text{Output} \\ \hline 0 & 0 & 1 \\ \hline 0 & 1 & 0 \\ \hline 1 & 0 & 0 \\ \hline 1 & 1 & 0 \\ \hline \end{array} \][/tex]
This does not match our given table. The entry for (0, 0) is 1 in the NOR gate, but in our table, it is 0.
### 6. NOT Gate
- Definition: A single input gate where the output is the negation of the input.
- Truth Table:
[tex]\[ \begin{array}{|c|c|} \hline \text{Input} & \text{Output} \\ \hline 0 & 1 \\ \hline 1 & 0 \\ \hline \end{array} \][/tex]
This is not applicable since our given table has two inputs.
From this analysis, the truth table given matches exactly with the truth table of the AND gate. Therefore, the correct answer is:
AND.
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