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134 CHAPTER 4/LOGIC FUNCTION REPRESENTATION AND MINIMIZATION

of the truth table from a reduced form permits a simple means of obtaining the canonical
representation without having to use the Boolean manipulation given by Eqs. (4.3).

4.2.2 The POS Representation
An alternative means of representing a logic expression is to cast it in product-of-sums
(POS) form, meaning the ANDing of ORed terms, also called s-terms (sum-terms). An
example of POS representation is given by the function

f(A, B, C, D) = (A + B)(A + B + C + D)(B + C + D) (4.4)
Maxterm
where, of the three s-terms, only the term (A + B + C + D) is called a maxterm.
A maxterm is defined as follows:

Maxterm: Any ORed term containing all the variables of a function in complemented
or uncomplemented form.

The symbol

Mi = Mi(A,B, C,...) (4.5)
will be used to represent the /th maxterm of a function.
Maxterm representation can be simplified considerably by using the maxterm code:

MAXTERM CODE
Complemented variable: logic 1
Uncomplemented variable: logic 0

The assignment of the logic I's and O's in this manner to all variables in each maxterm
establishes the maxterm code, where the subscript in Af, is the decimal equivalent of the
binary number formed by the logic state assignments. The maxterm code table for four
variables is given in Fig. 4.3. Use of this table is illustrated by maxterm in Eq. (4.4),

110 1

where 11012 = 13 IQ.
A comparison of the minterm and maxterm code tables in Figs. 4. 1 and 4.3 indicates that

Mi = mi
and (4.6)

m, = MJ,