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132 CHAPTER 4 / LOGIC FUNCTION REPRESENTATION AND MINIMIZATION

The function in Eq. (4.1) is written in sum-of-products (SOP) form, meaning ORing
of ANDed terms also called p-terms (product-terms). Although there are three p-terms
in this expression, only the term ABC is called a minterm. A minterm is defined as
follows:

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

Use will be made of the symbol

m t,=mi(A,B, C,...) (4.2)
to represent the /th minterm of a function. Notice that two of the three p-terms in Eq. (4.1)
cannot be minterms by this definition.
To simplify minterm representation, a shorthand notation is used and is based on the
following minterm code:

MINTERM CODE
Complmented variables: logic 0
Uncompleted variables: logic 1

Once the logic O's and 1 's have been assigned to all variables in a given minterm, a minterm
code is established where the subscript in m, becomes the decimal equivalent of the binary
code formed by the logic state assignments. For example, the minterm in Eq. (4. 1) is repre-
sented by

ABC = m 4,
100

since the binary of 100 has a decimal value of 4. A complete minterm code table for four
variables is given in Fig. 4.1. A similar minterm code table can be constructed for any
number of variables.
A function composed completely of a logical sum of minterms is said to be in canonical
SOP form. A typical example is given by the following expressions, where use has been
made of the minterm code shorthand notation and the operator symbol £] to represent the
logical sum of minterms:

Y(A,B, O=
000 Oi l 111 100 110
= ra 0 + m 3 + m-i + ra 4 + ra 6

A reduced SOP function such as that in Eq. (4.1) can be expanded to canonical form by
applying the factoring law and the AND and OR laws given in Section 3.10. This is