Page 115 - Bebop to The Boolean Boogie An Unconventional Guide to Electronics Fundamentals, Components, and Processes

96 ChapterNine

Once an equation has been obtained in the required form, the designer
would typically make use of the appropriate simplification rules to minimize the
number of logic gates required to implement the function. However, neglecting
any potential minimization, the equations above could be translated directly
into their logic gate equivalents (Figure 9-16).

Y

4t-

I I I

5 urn -of-Prod ucts Prod uct-of-5 u rn5

Figure 9-1 6. Sum-of-products versus product-of-sums implementations

Canonical Forms
In a mathematical context, the term cunonicul form is taken to mean a
generic or basic representation. Canonical forms provide the means to compare

two expressions without falling into the trap of trying to compare “apples” with
“oranges.” The sum-of-products and product-of-sums representations are different
canonical forms. Thus, to compare two Boolean equations, both must first be
coerced into the same canonical form; either sum-of-products or product-of-sums.