OR Gate Evaluation — Substituting Concrete Inputs A 4-input OR gate receives A = 1, B = 1, C = 0, and D = 0. Which equation correctly evaluates the OR operation for these inputs and shows the correct result?

Introduction / Context:
The OR operation outputs 1 if at least one input is 1. Evaluating a concrete input set helps reinforce the rule and avoid common mistakes such as thinking that “1 + 1” might produce a multi-bit sum in Boolean algebra. In logic, the plus symbol represents OR, not arithmetic addition.

Given Data / Assumptions:

• Inputs: A = 1, B = 1, C = 0, D = 0.
• Operator “+” denotes logical OR, not numeric addition.
• Binary logic levels 1 (true/HIGH) and 0 (false/LOW).

Concept / Approach:
In Boolean algebra, X + Y = 1 if X = 1 or Y = 1 (or both). For multiple inputs, OR evaluates to 1 as soon as any single input is 1. Therefore, with at least one 1 among the inputs, the final result must be 1.

Step-by-Step Solution:
1) Evaluate A + B: 1 + 1 = 1 (in Boolean logic, not arithmetic).2) Include C: 1 + 0 = 1.3) Include D: 1 + 0 = 1.4) Final expression: 1 + 1 + 0 + 0 = 1.

Verification / Alternative check:
Truth table of OR confirms that any row with at least one 1 yields an output of 1. Here there are two ones, so the output is definitely 1.

Why Other Options Are Wrong:

• “= 01” or “= 00”: Suggests multi-bit arithmetic notation, not Boolean OR.
• “= 0”: Incorrect because OR of at least one 1 cannot be 0.

Common Pitfalls:
Mixing arithmetic with Boolean algebra; in Boolean algebra, 1 + 1 remains 1 (idempotent law), not 2.

Final Answer:
1 + 1 + 0 + 0 = 1