Electrical Engineering ⇒ Topic : Minterms and Maxterms
Minterms and Maxterms
Minterms and Maxterms are the each individual term of SOP and POS form respectively. We can introduce a very convenient method of shorthand notations to express logical functions with the help of the minterms and maxterms. The minterms and maxterms for three literals have been given in Table (1).
Table (1) Minterms and maxterms
Each Minterm is represented by mi and each Maxterm is represented by M. The subscript i is the decimal number. The logical function can be represented with the help of these shorthand notations as follows:
Table (2) gives the logical expression in the truth table form. We can also write logic expression in standard SOP and POS form corresponding to the given truth table. To write the logic expression in standard SOP form, one product term for each input combination that produces an output of 1 will be taken only. Let us consider the truth table given in Table (2) below.
Table (2) Minterms
Y = 1 when A = 0, B = 0 and C = 1. Or, ABC will make Y = 1 only. Similarly, Y = 1 for ABC and ABC.
Thus, the standard SOP form becomes
To write the logic expression corresponding to a truth table in standard POS form, one sum term for each output 0 will be taken. Let us consider another truth table given in Table (3).
Table (3) Maxterms
From Table (3), Y = 0 when A = 0, B = 0 and C = 1. Therefore, A + B + C gives Y = O.Similarly, A + B + C gives Y = O. Thus, the standard product of sum form is
We can show that a product of sums form derived from a truth table is logically equivalent to a sum of products form derived from the same truth table. From Table (3), we get
Hence, a complementary relationship exists between a function expressed in Minterms and Maxterms. Therefore, we can find logical expression in Minterms if the function's Maxterms are known, and vice versa
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