Four-input OR expression: Select the correct Boolean expression for a 4-input OR gate with inputs A, B, C, and D and output Y.
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AY = A + B + C + D
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BY = A· B · C · D
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CY = A – B – C – D
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DY = A $ B $ C $ D
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EY = (A + B)(C + D)
Answer
Correct Answer: Y = A + B + C + D
Explanation
Introduction / Context:Recognizing canonical Boolean forms is indispensable for design and verification. The OR function outputs HIGH if any input is HIGH.
Given Data / Assumptions:
- Inputs: A, B, C, D.
- Operator “+” denotes OR; “·” denotes AND.
Concept / Approach:A 4-input OR gate is written as the sum of all inputs: Y = A + B + C + D.
Step-by-Step Solution:Map function → OR.Write as sum of literals → A + B + C + D.Thus Y = A + B + C + D.
Verification / Alternative check:Truth table shows output HIGH for any case with at least one input HIGH, matching the sum form.
Why Other Options Are Wrong:A·B·C·D: AND of all four inputs, not OR.Minus sign and dollar sign are not standard Boolean OR operators.(A + B)(C + D): equals AC + AD + BC + BD, which is not a simple 4-input OR.
Common Pitfalls:Mixing arithmetic and Boolean operators or expanding incorrectly.
Final Answer:Y = A + B + C + D