<p>Given f<sub>1</sub> , f<sub>3</sub> and f in canonical sum of products form (in decimal) for the circuit</p> <p><img alt="" src="https://firebasestorage.googleapis.com/v0/b/mcaprep-d6081.appspot.com/o/66408a3e8f5fa0df2bcec971.png?alt=media&token=7dc81c34-08fe-499e-950d-a8d006838c1e" style="width: 184px; height: 73px;" /></p> <p>f<sub>1</sub> Σm (4, 5, 6, 7, 8), f<sub>3</sub> Σm (1, 6, 15) and f Σm (1, 6, 8, 15) then f<sub>2</sub> is</p>
In this circuit (GATE CS 2008), \(f = f_1 \cdot f_2 + f_3\).
\(f_3\) already gives the minterms 1, 6 and 15 of \(f = \Sigma(1, 6, 8, 15)\). The term \(f_1 \cdot f_2\) must give minterm 8, and must not add any minterm outside \(f\).
Among the options, only \(\Sigma(6, 8)\) satisfies all these.
Answer: (C) ฮฃ(6, 8)
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