Three-input OR expression: Choose the correct Boolean expression for a 3-input OR gate with inputs A, B, C and output X.
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AX = A + B
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BX = A + B + C
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CX = ABC
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DX = A + BC
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EX = (A + B)C
Answer
Correct Answer: X = A + B + C
Explanation
Introduction / Context:Boolean notation links directly to gate symbols and truth tables. The OR operator is denoted by a plus sign and produces a HIGH output if any input is HIGH.
Given Data / Assumptions:
- Inputs: A, B, C.
- Standard operators: “+” for OR, “·” for AND.
Concept / Approach:A 3-input OR gate is written as the sum of the three input literals: X = A + B + C.
Step-by-Step Solution:Identify the intended function → OR across three signals.Write directly → X = A + B + C.
Verification / Alternative check:Construct a truth table and verify that whenever any input is 1, X is 1; only A = B = C = 0 yields 0.
Why Other Options Are Wrong:X = A + B: ignores C.X = ABC: AND of three inputs.X = A + BC or (A + B)C: mixed expressions not equivalent to a plain 3-input OR.
Common Pitfalls:Confusing OR with mixed sum-of-products structures.
Final Answer:X = A + B + C