Information Technology Reference
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Fig. 2.7. This photograph shows the binary message that was sent out to space by the Arecibo radio
telescope in November 1974. Using numbers to represent information is expected to be a univer-
sally understandable way to communicate with alien civilizations. The message shown here contains
1,679 binary digits arranged in seventy-three rows and twenty-three columns. The first ten rows
represent numbers from 1 to 10 in binary format. The following rows are numbers that represent
our genetic basis: the atomic numbers of chemical elements that form DNA, followed by the chem-
ical formulas of the bases in DNA, the shape of the double helix, and the number of nucleotides in
DNA. These are followed by the figure and height of an average man, the population of Earth, the
position of the planet in our solar system, and the dimensions of the radio antenna broadcasting this
message.
gates can be written as in
Figure 2.9
, where we also show the usual pictorial
symbol for an OR gate. For the output of the OR gate to be 1, either or both of
the inputs A and B have to be 1.
For a complete set of logic gates from which we can build any logical oper-
ation, it turns out that we need to supplement these AND and OR gates by
another, very simple gate, the NOT, or invert, operation (see
Fig. 2.10
). This is a
black box that inverts the input signal. If the input is 1, the NOT gate outputs
a 0; if the input is a 0, NOT outputs a 1. The truth table for the NOT gate is
shown in with the usual symbol for NOT. De Morgan's theorem allows one to
play around with these operators and find complicated equivalences between
combinations of operators, such as writing an OR gate in terms of AND and
NOT gates. Another example is joining the OR and NOT gates to construct a
NOR gate (see
Fig. 2.11
).
Functional abstraction allows us to implement these logic building blocks
in a range of technologies - from electromagnetic relays to vacuum tubes to
transistors. Of course, different types of gates may be easier or harder to make
in any given technology. The set of AND, OR, and NOT gates are sufficient to
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