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FixedPoint Numbers
All computer instructions and data are represented and stored in binary (base 2) form. In the
representation of
fxedpoint
numbers, the value of each digit in the number depends on its position
relative to the Fxed decimal point. ±or example the integer value 53 in base 10 is represented by
the binary or base 2 value 00110101, denoted by
53
10
= 00110101
2
In base 10, this means
53
10
=5
×
10
1
+3
×
10
0
Similarly,
00110101
2
=0
×
2
7
+0
×
2
6
+1
×
2
5
+1
×
2
4
+0
×
2
3
+1
×
2
2
+0
×
2
1
+1
×
2
0
=3
2
10
+16
10
+4
10
+1
10
Thus, each bit position represents an increasing power of 2, beginning with 2
0
on the right.
FloatingPoint Numbers
To represent noninteger numbers, a number representation known as
ﬂoatingpoint
must be
deFned. ±loatingpoint numbers are used on computers to approximate a subset of the real numbers.
While there are many possible ﬂoatingpoint number systems, all such systems consist of zero, a
set of positive numbers, and the corresponding set of negative numbers.
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This note was uploaded on 03/07/2010 for the course ENG 101 taught by Professor Chang during the Summer '09 term at 東京国際大学.
 Summer '09
 CHANG
 English

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