Page 108 - Bebop to The Boolean Boogie An Unconventional Guide to Electronics Fundamentals, Components, and Processes

BooleanAlgebra 89

The Second Distributive Rule
In standard arithmetic, the addition operator will not distribute over the
multiplication operator because it has a lower pre~edence:~

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

However, Boolean Algebra is special in this case. Even though the I (OR)
operator has lower precedence than the &a (AND) operator, it will still
distribute over the &a operator; this is known as the second distributive rule
(Figure 9-9).

y=a 1 (b&c) y = (a I b) & (a I G)

S’

OR
G
&
AND c/I/
OR

a b c (b&c) Y a b c (aIb) (a I Y
000 0 0 000 0 0 0
0 0 1 0 0 0 0 1 0 1 0
0 1 0 0 0 0 1 0 1 0 0
0 1 1 1 1 0 1 1 1 1 1
1 0 0 0 1 1 0 0 1 1 1
1 0 1 0 1 1 0 1 1 1 1
1 1 0 0 1 1 1 0 1 1 1
1 1 1 1 1 1 1 1 1 1 1
f

Figure 9-9. The second distributive rule

4 Note that the symbol z shown in the equation indicates “is not equal to.”