10/16/14
CSF 430
Homework 6
1) Classify each of the following occurrences as an incident or disaster. If an occurrence is
a disaster, determine whether or not business continuity plans would be called into play.
a. A hacker gets into the network and delet
128.5 to binary, we have 10000000.1, which is 9 bits wide. Our significand can hold
only eight. Typically, the low-order bit is dropped or rounded into the next bit. No
matter how we handle it, however, we have introduced an error into our system.
We can
2.7.3
Phase Modulation (Manchester Coding)
The coding method known commonly as phase modulation (PM), or Manchester
coding, deals with the synchronization problem head-on. PM provides a transition for each bit, whether a one or a zero. In PM, each binary
If the code word 001 is encountered, it is invalid and thus indicates an error has
occurred somewhere in the code word. For example, suppose the correct code
word to be stored in memory is 011, but an error produces 001. This error can
be detected, but it
of error would not be detected. Therefore, if we wish to create a code that guarantees detection of all single-bit errors (an error in only 1 bit), all pairs of code
words must have a Hamming distance of at least 2. If an n-bit word is not recognized as a
tion is not necessarily correct! We are assuming the minimum number of possible errors has occurred, namely 1. It is possible that the original code word was
supposed to be 10110 and was changed to 10000 when two errors occurred.
Suppose two errors really
and 12. If we write the data bits in the nonboxed blanks, and then add the parity
bits, we have the following code word as a result:
0 1 0 0
12 11 10 9
1
8
1
7
0
6
1
5
0
4
1
3
1
2
0
1
Therefore, the code word for K is 010011010110.
Lets introduce an error
s = The number of bits in a character (or symbol)
k = The number of s-bit characters comprising the data block
n = The number of bits in the code word
(n k)
RS(n, k) can correct errors in the k information bytes.
2
The popular RS(255, 223) code, theref
Unicode is the default character set used by Java and recent versions of Windows. It is likely to replace EBCDIC and ASCII as the basic method of character
representation in computer systems; however, the older codes will be with us for
the foreseeable fu
If youd prefer a rigorous and exhaustive study of error-correction theory,
Pretzels (1992) book is an excellent place to start. The text is accessible, wellwritten, and thorough.
Detailed discussions of Galois fields can be found in the (inexpensive!)
boo
9. How are complement systems like the odometer on a bicycle?
10. Do you think that double-dabble is an easier method than the other binary-to-decimal
conversion methods explained in this chapter? Why?
11. With reference to the previous question, what are
c) 151810 = _ 7
d) 440110 = _ 9
2. Perform the following base conversions using subtraction or division-remainder:
a) 58810 = _ 3
b) 225410 = _ 5
c) 65210 = _ 7
d) 310410 = _ 9
3. Convert the following decimal fractions to binary with a maximum of six pla
which implies r must be greater than or equal to 3. We choose r = 3. This means
to build a code with data words of 4 bits that should correct single bit errors, we
must add 3 check bits.
The Hamming algorithm provides a straightforward method for designin
3. Shift I to the left by one less than the number of bits in P, giving a new I =
10010110002.
4. Using I as a dividend and P as a divisor, perform the modulo 2 division (as
shown in Example 2.28). We ignore the quotient and note the remainder is
1002. Th
2.8.2
Hamming Codes
Data communications channels are simultaneously more error-prone and more
tolerant of errors than disk systems. In data communications, it is sufficient to
have only the ability to detect errors. If a communications device determines t
0
1
0
1
0
1
1
0
0
0
1
0
0
0
=
0
1
0
1
1
0
0
1
0
0
0
1
0
0
=
0
1
0
1
1
1
0
0
1
0
0
0
1
0
=
0
1
1
0
0
0
0
0
0
1
0
0
0
1
Because synonymous forms such as these are not well-suited for digital computers, a convention has been established where the leftmost bi
11.001000
+ 0.10011010
11.10111010
Renormalizing, we retain the larger exponent and truncate the low-order bit.
Thus, we have:
0
1
0
0
1
0
1
1
1
0
1
1
1
0
Multiplication and division are carried out using the same rules of exponents
applied to decimal ari
2.5.4
The IEEE-754 Floating-Point Standard
The floating-point model that we have been using in this section is designed for
simplicity and conceptual understanding. We could extend this model to include
whatever number of bits we wanted. Until the 1980s,
was derived from the Baudot code, which was invented in the 1880s. By the early
1960s, the limitations of the 5-bit codes were becoming apparent. The International Organization for Standardization (ISO) devised a 7-bit coding scheme that
it called Interna
0
NUL
16 DLE
32
48 0
64 @
80 P
96
`
112 p
1
SOH
17 DC1
33 !
49 1
65 A
81 Q
97
a
113 q
2
STX
18 DC2
34 "
50 2
66 B
82 R
98
b
114 r
3
ETX
19 DC3
35 #
51 3
67 C
83 S
99
c
115 s
4
EOT
20 DC4
36 $
52 4
68 D
84 T
100 d
116 t
5
ENQ
21 NAK
37 %
53 5
69 E
85 U
101
in 1964. One would expect that both systems will continue to be supported, owing
to the substantial amount of older software that is running on these systems.
2.6
CHARACTER CODES
We have seen how digital computers use the binary system to represent and
ma
approximately 1.05%. In BCD, the number is stored directly as 1111 0011
(we are assuming the decimal point is implied by the data format), giving no
error at all.
The digits of BCD numbers occupy only one nibble, so we can save on space
and make computati
Character
Types
Character Set
Description
Number of
Characters
Hexadecimal
Values
Alphabets
Latin, Cyrillic,
Greek, etc.
8192
0000
to
1FFF
Symbols
Dingbats,
Mathematical,
etc.
4096
2000
to
2FFF
CJK
Chinese, Japanese,
and Korean phonetic
symbols and
punctu
blurred, particularly when long strings of ones and zeros are involved. This blurring is partly attributable to timing drifts that occur between senders and
receivers. Magnetic media, such as tapes and disks, can also lose synchronization
owing to the ele
1
1
0
0
1
FIGURE 2.12
1
1
1
0
1
0
0
1
0
1
1
Frequency Modulation Coding of OK
are provided only between consecutive zeros. With MFM, then, at least one transition is supplied for every pair of bit cells, as opposed to each cell in PM or FM.
With fewer tra
a.
1
1
0
0
1
1
1
1
0
1
0
0
1
0
1
1
High
Zero
Low
b.
FIGURE 2.9
NRZ Encoding of OK as
a. Transmission Waveform
b. Magnetic Flux Pattern (The direction of the arrows
indicates the magnetic polarity.)
A little experimentation with this example will demonstra
are encoded using the shortest code word bit patterns. (In our case, we are talking about the fewest number of flux reversals.) The theory is based on the
assumption that the presence or absence of a 1 in any bit cell is an equally
likely event. From this
redundancy check (CRC) is a type of checksum used primarily in data communications that determines whether an error has occurred within a large block or
stream of information bytes. The larger the block to be checked, the larger the
checksum must be to pr