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Engineering Digital Design
book

Engineering Digital Design

by Richard F. Tinder
January 2000
Intermediate to advanced content levelIntermediate to advanced
884 pages
29h 39m
English
Academic Press
Content preview from Engineering Digital Design
42 CHAPTER 2 / NUMBER SYSTEMS, BINARY ARITHMETIC, AND CODES
Terminating a fraction conversion at n digits (to the right of the radix point) results in an
error or uncertainty. This error is given by
ε = a
n
r
n
+ a
(n+1)
r
(n+1)
+ a
(n+2)
r
(n+2)
+···
=r
n
a
n
+
i=1
a
(n+i)
r
(n+i)
r
,
where the quantity in brackets is less than (a
n
+ 1). Therefore, terminating a fraction
conversion at n digits from the radix point results in an error with bounds
0 r
n
(a
n
+ 1). (2.9)
Equation (2.9) is useful in deciding when to terminate a fraction conversion.
Often, it is desirable to terminate a fraction conversion at n +1 digits and then round off
to n from the radix point. ...
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Publisher Resources

ISBN: 9780126912951