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as importantly, their inabilities. Years before anyone demonstrated what a computer could
do, Turing proved what computers could never do.
Turing's original motivation in the invention of the computer was to solve a problem
formulated by German mathematician David Hilbert (1862-1943). Hilbert asked for a gen-
eral process to determine the provability of arbitrary statements in mathematical logic. The
process of finding the general process was called the Entscheidungsproblem (the Decision
Problem). Although the Entscheidungsproblem was certainly the motivation for Turing's
paper, the bulk of the paper is really about computable numbers. In Turing's definition, the
numbers can be calculated by a machine. Turing's exploration of computable numbers ac-
counts for the first 60 percent of his work, which can be read and understood without any
familiarity with Hilbert's work in mathematical logic or the Entscheidungsproblem.
Alan's machine remains a popular topic for exposition and discussion. Yet the original
idea describing the great invention is rarely read. Perhaps the neglect has something to do
with the title: “On Computable Numbers, With an Application to the Entscheidungsprob-
lem” (decision problem); it seems Turing expected his readers to have a basic knowledge
of heavy German mathematical matters. A quick glance through the paper—and its use of
a German gothic font to represent machine states—does not allay the fears. Can people
today take on an idea paper published seventy years ago in the Proceedings of the Lon-
don Mathematical Society and stay afloat long enough to glean a few insights and even
(perhaps) satisfaction. The focus on how cognitive human development had played a vital
role in the study of computer science and its practical contributions to the cognitive, social,
technological, and scientific improvement of mankind may require the use of a practical
scenario, case study, or training program relative to the theories of Maslow (1954, 1968),
Glasser (1965, 1998), and Bandura (1977, 1986, 1997).
The Logical Gates Used to Design RAM and CPU Chips
Practical example: These gates operate in the binary system, which means with only two
digits; 1 and 0. In normal function, the 1 is generally connected to be in the on state while
the 0 is on the off state.
Figure 1: The output of the not logic gate always produces the opposite of the input.
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