Page 107 - Bebop to The Boolean Boogie An Unconventional Guide to Electronics Fundamentals, Components, and Processes

88 ChapterNine

The First Distributive Rule
In standard arithmetic, the multiplication operator will distribute over the
addition operator because it has a higher precedence; for example:

6 x (5 + 2) (6 x 5) + (6 x 2)

Similarly, in Boolean Algebra, the & (AND) operator will distribute over
an I (OR) operator because it has a higher precedence; this is known as the
first distributive rule (Figure 9-8).

-* y = (a & b) I (a & G)
y=a&(b I G)

AND

a b c abG (a&b) (a 4 Y

000 000 0 0 0
001 001 0 0 0
010 010 0 0 0
011 011 0 0 0
100 100 0 0 0
101 101 0 1 1
110 110 1 0 1
1 1 1 1 1 1 1 1 1
t t

I Output columns are identical I

Figure 9-8. The first distributive rule