 Relation between min and max terms(canonical form):

The compliment of the function expressed in terms of sum of min terms can be obtained by taking sum of missing min terms in the original functions

e.g.  f= ∑(4, 5, 7) = m7 + m5 + m4

Its compliment is              f’ = ∑(0, 1, 2, 3, 6) = m0 + m1 + m2 + m3 + m6

The compliment of the function expressed in terms of product of max terms can be obtained by taking product of max missing terms in the original functions

e.g. f= M4 M5 M2 M0 = π (0, 2, 4, 5)

Its compliment is              f’ = π (1, 3, 6, 7)= M7 M6 M3 M1

The compliment of the function expressed iin any of the canonical terms can be obtained by just interchanging the symbols π & ∑ and keeping the list of numbers same

e.g. f= ∑(4, 5, 7) = m7 + m5 + m4

Its compliment is              f’ = π (4, 5, 7)= M4 M5 M7

e.g. f= M4 M5 M2 M0 = π (0, 2, 4, 5)

Its compliment is              f’∑(0, 2, 4, 5) = m0 + m2 + m4 + m5

The function expressed in terms of product of max terms can be converted to sum of min terms or vice-versa can be done by interchanging π & ∑ and list the numbers which were missing from the original function.

e.g. f= ∑(4, 5, 7) = m7 + m5 + m4

then f can also be expressed as  f= ∑(4, 5, 7) = π(0, 1, 2, 3, 6)

e.g. f= π (0, 2, 4, 5)

then f can also be expressed as  f= π (0, 2, 4, 5)=∑(1, 3, 6, 7)

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