Question

difference between Cardinal form and
Canonical form

Answer 1

Logical functions are generally expressed in terms of different combinations of logical variables
with their true forms as well as the complement forms. Binary logic values obtained by the
logical functions and logic variables are in binary form. An arbitrary logic function can be
expressed in the following forms.
(i) Sum of the Products (SOP)
(ii) Product of the Sums (POS)
Product Term. In Boolean algebra, the logical product of several variables on which a
function depends is considered to be a product term. In other words, the AND function is
referred to as a product term or standard product. The variables in a product term can be either in
true form or in complemented form. For example, ABC′ is a product term.
Sum Term. An OR function is referred to as a sum term. The logical sum of several variables on
which a function depends is considered to be a sum term. Variables in a sum term can also be
either in true form or in complemented form. For example, A + B + C′ is a sum term.
Sum of Products (SOP). The logical sum of two or more logical product terms is referred to as a
sum of products expression. It is basically an OR operation on AND operated variables. For
example, Y = AB + BC + AC or Y = A′B + BC + AC′ are sum of products expressions.
Product of Sums (POS). Similarly, the logical product of two or more logical sum terms is called
a product of sums expression. It is an AND operation on OR operated variables. For example, Y
= (A + B + C)(A + B′ + C)(A + B + C′) or Y = (A + B + C)(A′ + B′ + C′) are product of sums
expressions.
Standard form. The standard form of the Boolean function is when it is expressed in sum of the
products or product of the sums fashion. The examples stated above, like Y =AB + BC + AC or
Y = (A + B + C)(A + B′ + C)(A + B + C′) are the standard forms.
However, Boolean functions are also sometimes expressed in nonstandard forms like F = (AB +
CD)(A′B′ + C′D′), which is neither a sum of products form nor a product of sums form.
However, the same expression can be converted to a standard form with help of various Boolean
properties, as:
F = (AB + CD)(A′B′ + C′D′) = A′B′CD + ABC′D′