A minterm is the Boolean algebra expression formed by taking a row of a truth table and forming an and function where the inputs are the input variables of the row. Each minterm variable will be negated if the same variable takes 0 in the row, otherwise the variable is unnegated. The minterms are often numbered, one for each row, and named mi for row i. We can form an expression as a sum of products which is equivalent to the function of the truth table by applying the or function to all the minterms whose function result is 1.


The truth table for the half adder, with a column showing the minterm, is as follows:

 A  B  S  C minterm

If we were only interested in the sum output S then we see that both minterms m1 and m2 give an output of 1 for S and this gives the sum of products equivalent of (not(A) and B) or (A and not(B)). We know that the equation for S is S = A xor B, so our sum of products result is correct.


Mano, M. Morris, and Kime, Charles R. Logic and Computer Design Fundamentals. 2nd Edition. Prentice Hall, 2000.