c
A.H.Dixon
CMPT 150: Week 1 (Jan 7  11, 2008)
1
1
ALPHABETS AND ENCODINGS
An
alphabet
is a finite set of distinct symbols often called “characters”.
Some, but not necessarily all, sequences of characters are “meaningful”.
That
is, they have been selected to represent an idea or concept.
The assignment of
meanings to a subset of sentences defined on an alphabet is called an
interpreta
tion
.
The 26 letters of the alphabet can be used to define
sequences
more commonly
called “words”. Some words are meaningful, others are just garbled sequences of
letters.
The 10 digits, “0” through “9” define sequences called the nonnegative integers.
In this case every sentence is meaningful since each defines some integer.
By adding the character “” to the alphabet of digits, we can construct sentences
that correspond to the full set of integers, both positive and negative.
An
encoding
is the assignment of a unique sequence of symbols from one alphabet
to represent each symbol of the second alphabet. When a symbol (or sequence of
symbols) in one alphabet has been assigned a unique sequence of characters from
the second alphabet, that sequence is called a “codeword” for the original symbol
or sequence.
In the design of electrical circuits an encoding is defined to represent an alphabet
of symbols using different voltage levels.
It is desirable to use an alphabet of
only two symbols to maximize the voltage level interval that can be associated
with each symbol in an encoding of characters by voltage levels. Although more
symbols could be used, an alphabet of only two symbols simplifies the design of
circuits and reduces the chance of error from voltage fluctuations.
However, a binary alphabet does not lend itself to human interpretation readily,
and so encodings must be defined for “userfriendly” alphabets using the binary
alphabet. Some of the ways of encoding larger alphabets using the binary alphabet
are:
1.
Natural binary encoding
: Each unsigned integer is represented by its base2
value. The arithmetic techniques for converting between base2 and base10
provide the tools for transforming sentences in one alphabet to sentences
in the other.
Techniques for converting from decimal to binary and from
binary to decimal are described in the textbook by Mano and Kime, pages
13  15.
2.
Binary Coded Decimal (BCD)
: Rather than encode every integer into its
base2 equivalent, only the symbols “0” through “9” are represented by
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c
A.H.Dixon
CMPT 150: Week 1 (Jan 7  11, 2008)
2
their corresponding 4bit base2 equivalents.
The BCD representation of
an unsigned integer is obtained by concatenating the corresponding binary
codes together.
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 Spring '08
 Dr.AnthonyDixon
 Boolean Algebra, Binary numeral system, Decimal

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