Page 106 - Bebop to The Boolean Boogie An Unconventional Guide to Electronics Fundamentals, Components, and Processes

Boolean Algebra w 87

Precedence of Operators
In standard arithmetic, the multiplication operator is said to have a
higher precedence than the addition operator. This means that, if an equation
contains both multiplication and addition operators without parenthesis, then
the multiplication is performed before the addition; for e~ample:~

6+2x4 = 6+(2x4)

Similarly, in Boolean Algebra, the & (AND) operator has a higher prece-
dence than the I (OR) operator:

a I b&c = a I (b&c)

Due to the similarities between these arithmetic and logical operators,
the & (AND) operator is known as a logical multiplication or product, while
the I (OR) operator is known as a logical addition or sum. To avoid any
confusion as to the order in which logical operations will be performed, this
book will always make use of parentheses.

h to light a small
mputer, ENIAC (Elect
merical Integrator and with computers built from
Iculator), was construc vacuum tubes was reliability:
University of Pennsylvania 90% of ENIAC’s down-time was
between 1943 and 1946. In attributed to locating and
many ways ENIAC was a m replacing burnt-out tubes.
it occupied 30 feet by 50 feet of Records from 1952 show that
floor space, weighed approxi- approximately 19,000 vacuum
mately 30 tons, and used mo tubes had to be replaced in that
than 18,000 vacuum tubes year alone; that averages out
which required 150 kilowa to about 50 tubes a day!

3 Note that the symbol shown in these equations indicates “is equivalent to” or “is the same as.”