Study the logic circuit below with three inputs A, B, and C. Input C passes through a NOT gate before entering the AND gate. Inputs A and B pass through an ...
Question 1 Report
Study the logic circuit below with three inputs A, B, and C.
Input C passes through a NOT gate before entering the AND gate. Inputs A and B pass through an OR gate, and the output of the OR gate feeds into the AND gate along with NOT C.
(a) Write the Boolean expression for X. [2]
Answer Details
(a) Boolean expression for the logic circuit: [2]
X = (A OR B) AND (NOT C)
[1] for (A OR B), [1] for AND NOT C.
The circuit processes the inputs in two stages. First, inputs A and B pass through an OR gate, producing an intermediate result that is 1 whenever at least one of A or B is 1. Separately, input C passes through a NOT gate, inverting its value. Finally, an AND gate combines the OR output with NOT C. The overall output X is 1 only when (A or B is 1) AND (C is 0).
For example: A=1, B=0, C=0 gives (1 OR 0) AND (NOT 0) = 1 AND 1 = 1. But A=1, B=0, C=1 gives (1 OR 0) AND (NOT 1) = 1 AND 0 = 0.
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