Four-input OR evaluation: For inputs A = 1, B = 1, C = 0, and D = 0 to a 4-input OR gate, what is the correct Boolean sum and output value?

Introduction / Context:OR gates implement logical addition: the output is HIGH if any input is HIGH. Evaluating multi-input OR expressions reinforces facility with Boolean algebra and prepares learners for sum-of-products simplifications.

Given Data / Assumptions:

• Inputs: A=1, B=1, C=0, D=0.
• Definition: X = A + B + C + D.
• Boolean “+” denotes logical OR, not arithmetic addition.

Concept / Approach:For OR, the presence of at least one 1 drives the output to 1. Multiple ones do not change the result—it remains 1. No carry or multi-digit result exists in Boolean OR; the output is a single logic level (0 or 1).

Step-by-Step Solution:Evaluate A + B = 1 + 1 = 1 (Boolean OR).Then 1 + C = 1 + 0 = 1.Then 1 + D = 1 + 0 = 1.Thus, the expression simplifies to 1, and the output is HIGH.

Verification / Alternative check:Truth-table view: any case with A=1 OR B=1 yields X=1 regardless of other inputs. Here both A and B are 1, so X must be 1.

Why Other Options Are Wrong:

• Results such as “01” or “00” imply multi-bit outputs, which do not apply to a single OR gate.
• “= 0” contradicts the presence of HIGH inputs.

Common Pitfalls:

• Treating Boolean “+” as arithmetic addition; Boolean OR outputs a single logic level.
• Assuming two ones might “overflow” to something other than 1—this is not applicable in Boolean logic.

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