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The Silicon Web: Physics for the Internet Age
to some well-def
ned instructions. Such a process is called
logic
. It is similar to the
human activity oF reasoning. A simple example occurs in a calculator when you
press the “add” or “
+
” button. The
input
data are the two numbers you want to add
(18, 5). The calculator carries out several logical operations to produce the resulting sum
(18
+
5
=
23), which is the
output
data. BeFore we consider the actual electronic circuits
that perForm the operations, we will discuss the principles behind logic.
English mathematician George Boole (1815–1864) was one oF the Founders oF the
principles oF logic. In his honor, the methods used are called
Boolean logic
. In the
context oF modern computing, Claude Shannon was the most in±
uential scientist who
contributed to the theory oF logic. In 1938, as a graduate student at Massachusetts
Institute oF Technology, he submitted his master’s thesis that showed how electronic
circuits could be used to perForm logic. Ten years later Shannon published the paper,
“A Mathematical Theory oF Communication,” which revolutionized scientists’ under-
standing oF the concept oF inFormation.
6.2
CONCEPTS OF LOGIC
What is logic? In everyday liFe, it means to take in some inFormation, apply certain
rules oF reasoning, and produce a decision. ²or example, you might reason that “iF
the sky is blue then I will take a walk without an umbrella, but iF the sky is cloudy
then I will take my umbrella.” The color oF the sky is the input data
and the umbrella
decision is the output data. We can make a table
showing our logic about the sky and
umbrellas:
Input:
Sky blue?
Output:
Umbrella?
No
Yes
Yes
No
The rules we use to process data or inFormation are called
logic operations
.
A
logic operation
is an elementary rule For arriving at a logical outcome. Three basic opera-
tions that can serve as building blocks For all logic operations are NOT, AND, and OR.
In considering complex situations, a diagram is useFul to help visualize the logic
process. Think oF this as a ±
ow chart For making a decision. IF you Face a complicated
decision, such as which college to attend, there might be many Factors to consider. Let us
say that college B is a better school academically. Your rules For making a decision are:
IF college B oFFers you a scholarship, or iF college B’s dorms have DSL lines (high-speed
Internet connections), then you would attend B. However, iF college A oFFers you a schol-
arship, but not college B, and iF college B’s dorms do not have DSL, then you would
attend A. IF neither A nor B oFFers a scholarship or DSL, then you would choose neither.
A ±
ow chart For this decision is shown below in
Figure 6.1
. The particular case illus-
trated is indicated by the circled data.