Which single logic gate can be used to implement the Boolean equation Y = A + B in a digital circuit?
OR gate
To implement the Boolean equation \( Y = A + B \) in a digital circuit, the most suitable logic gate is the OR gate. Here's why:
1. Understanding the Boolean Equation:
- The equation \( Y = A + B \) is a logical OR operation. This expression signifies that the output \( Y \) will be true (or '1') if either input \( A \) is true, or input \( B \) is true, or both are true.
2. Logic Gate Options:
- OR Gate: The OR gate is specifically designed to perform this exact operation. It outputs true if any one or more of its inputs are true.
- AND Gate: Performs a logical AND operation, outputting true only if all of its inputs are true. This gate cannot replace the OR operation.
- NAND Gate: This gate is a combination of an AND gate followed by a NOT gate. It outputs the inverse of an AND operation and is not suitable for directly implementing an OR operation without additional circuitry.
- NOT Gate: This gate inverts the input signal (i.e., if the input is true, it outputs false and vice versa). It cannot implement the OR operation by itself.
3. Conclusion:
- To achieve the function \( Y = A + B \), the most direct and appropriate choice is the OR gate.
Therefore, the correct answer is the OR gate.
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