Section 4.5
99
(b) Here is a valid number:
~1
g498661329.
Changing the 3 and 2 in positions one and three to 8
and
7
respectively produces the number
§.1
Z
498661329
which is also valid.
13. (a) The test will not identify the digit that is wrong:
An
error of the same magnitude in two even or
two odd digits will yield the same
3a
+
b.
For example, if a universal product number begins 1234,
either incorrect number 3234 or 1254 will yield the same
3a
+
b.
(b) The test will not even identify whether the error is in an odd position or in an even position since,
for example, a difference of 1 in an odd position will yield the same
3a
+
b
as a difference of 3 in
an even position. For example, if a universal product number begins 1234, the number
3a
+
b
is
the same for the incorrect numbers 2234 and 1534.
14. (a)
[BB]
123586987326;
(b)
[BB] ]
123006987326.
15. Suppose that
ala2a3a4a5a6a7aSa9alOallX
is a valid universal product code. Thus,
A
=
3(al
+
a3
+
a5
+
a7
+
ag
+
all)
+
(a2
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This note was uploaded on 11/08/2010 for the course MATH discrete m taught by Professor Any during the Summer '10 term at FSU.
 Summer '10
 any
 Graph Theory

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