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Scientific notation
An
alternative floatingpoint
representation
Table 3.1
Values in decimal notation and floatingpoint notation
(five digits)
Real Value
FloatingPoint Value
12001.00
–120.01
0.12000
–123.1
1555555555
12001*
–12001*
1200*
–12310*
15555*
10
0
10
3
10
2
10
–5
10
–2
62
Chapter 3
Data Representation
positive exponent shifts the decimal point to the right, and a negative
exponent shifts the decimal point to the left.
Let’s look at how to convert a real number expressed in our usual
decimal notation into floating point. For example, consider the number
148.69. The sign is positive, and there are two digits to the right of the
decimal point. Thus, the exponent is
±
2, giving us 14869 * 10
±
2
. Table
3.1 shows other examples. For the sake of this discussion, we assume that
only five digits can be represented.
How do we convert a value in floatingpoint form back into decimal
notation? The exponent on the base tells us how many positions to move
the radix point. If the exponent is negative, we move the radix point to the
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This note was uploaded on 01/13/2011 for the course CSE 1550 taught by Professor Marianakant during the Fall '10 term at York University.
 Fall '10
 MARIANAKANT

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