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) = m_{7} + m_{5} + m_{4}
Its compliment is f’ = ∑(0, 1, 2, 3, 6) = m_{0} + m_{1} + m_{2} + m_{3} + m_{6}
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= M_{4} M_{5} M_{2} M_{0} = π (0, 2, 4, 5)
Its compliment is f’ = π (1, 3, 6, 7)= M_{7} M_{6} M_{3} M_{1}
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) = m_{7} + m_{5} + m_{4}
Its compliment is f’ = π (4, 5, 7)= M_{4} M_{5} M_{7}
e.g. f= M_{4} M_{5} M_{2} M_{0} = π (0, 2, 4, 5)
Its compliment is f’∑(0, 2, 4, 5) = m_{0} + m_{2} + m_{4} + m_{5}
The function expressed in terms of product of max terms can be converted to sum of min terms or viceversa can be done by interchanging π & ∑ and list the numbers which were missing from the original function.
e.g. f= ∑(4, 5, 7) = m_{7} + m_{5} + m_{4}
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)
