Project ForgeConsider the minterm list form of a Boolean function F given below.
F(P,Q,R,S) = Σm(0,2,5,7,9,11) + d(3,8,10,12,14)
Here, m denotes a minterm and d denotes a don't-care term. The number of essential prime implicants of the function F is ____.
Explanation
K-map grouping (using don't-cares to maximize group size) yields exactly 3 essential prime implicants that together cover all 6 onset minterms: Q'S' (covering m0,m2, using dc m8,m10 — the unique maximal group containing m0), P'QS (covering m5,m7 — the unique group containing m5, no adjacent don't-cares available), and PQ' (the full row covering m8,m9,m10,m11 — the unique maximal group containing m9 and m11). Each is essential since it is the only prime implicant covering at least one required onset minterm.
Source: GATE CS 2018 (2018)
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