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
The truth table for the half adder, with a column showing the minterm, is as follows:
If we were only interested in the sum output
S then we see that both minterms m1 and m2
give an output of
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 = 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.
Copyright © 2014 Barry Watson. All rights reserved.