Three inputs, A, B and C, are given to a digital circuit as shown below and Y is the output. Which one is the correct output Y of the digital circuit ?
A.B.C + A.C
Trace each gate in the figure. The circuit has two AND gates whose outputs feed a single OR gate that gives Y.
Upper AND gate: its two inputs are the A line and the C line, so its output is A.C.
Lower AND gate: it has three inputs – B directly, plus branches taken from the C line and from the A line – so its output is A.B.C.
OR gate: it adds (logical OR) the two AND outputs, giving Y = A.B.C + A.C.
(By the absorption law this also reduces to A.C, but the expression read directly from the circuit is the sum of the two AND terms.) Expressions containing B or C alone as OR terms do not appear, since no input reaches the OR gate without passing through an AND gate.
Hence, the answer is A.B.C + A.C.
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