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Minterm and maxterm in Digital logic design - Computer Science fundamentals tutorial


Minterm and Maxterm
First thing to know before we proceed  towards  what is ‘minterm’ and ‘maxterm’ we have to know the sum of product and product of sum.

Sum of product: - The logical sum of two or more logical product term is called sum of products expression. It is basically an OR operation of AND operated variables such as
Y = AB+BC+ABC

Product of Sum: - The logical product of two or more logical sum term is called product of sums expressions. It is basically an AND operation of OR operated variables such as
Y = (A+B).(B+C).(A+B+C)

Minterm: -Product term containing all the k variables of the functions is either complimented or uncomplimented form is Minterm.


Canonical form of sum of product: - It is defined as the logical sum of all the minterms derived from the rows of a truth table for which value of the function is 1. It is called a minterm canonical form. The canonical sum of product expression can be given in a compact form by listing the decimal code in correspondence with the minterm containing the function value 1.
                   If any sums of products expressions are not in canonical form then we can use the following procedure to obtain canonical sum of products.
   1. Examine each term in given logic function retain it. If it is a minterm continue to examine the term in the same manner.
   2.   Check for variables that are missing each product which is not a minterm. Multiply product by (X+=1) for each variable X that is missing.
   3.   Multiply all the products omit redounded terms.
Example of Minterm
Obtain the canonical sum of product from of the function


Maxterm: -
A sum term containing all the k variable of the function in either complimented or uncomplimented form is called maxterm. Each maxterm can obtain by OR operation of all the variables of the function in a maxterm variable appears either in uncomplimented form if it possess the value 0 in corresponding combination or complimented form if it possess the value of 1

Canonical form of Canonical form of sum of product: -
This is defined as the logical product of all the maxterm derived from the rows of truth table for which the value of function is ‘0’. It is also known as maxterm canonical form. The canonical product of sum expression can be given in a form by listing decimal code corresponding to the maxterm containing function value of ‘0’. If any product of sum expression are not in canonical form of product of sum expression by using following procedure:-
1.Examine each term in the given logical function retain it. If its maxterm continue to examine the next term in the same manner.
     2.  Check for variables that are missing in each sum which is not a maxterm.ADD(X.=0) to the sum term for each variable X that is missing.
     3. Expand the expression using the distribute property and eliminate the redounded term.
Example of maxterm: -


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