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Consider the annoying problem that arises when trying to store the value 25⁄8 on a 1-byte floating-point system. First, write 25⁄8 in binary. This will give you 10.101. But if you copy it to a mantissa There is not enough space and the rightmost 1 (representing the last 1⁄8) is lost (Figure 40). If you ignore it There is a problem so far, if you enter the exponent field and the sign bit and continue, you will get a bit pattern that Represents 21⁄2 instead of What happened is called a truncation error or a rounding error-that is, The mantissa field is not large enough that the stored value is lost.
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The magnitude of these errors can be reduced by using longer mantissa fields. In fact, most computers Today’s productions use at least 32 bits to store values in floating-point symbols instead of 8 bits. You can also use it here to create longer power fields at the same time. Even longer, However, there may be times when higher accuracy is required. Another cause of shortening errors This is a phenomenon you are already accustomed to with the 10th year symbol: a never-ending problem.
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Development as seen when trying to express 1⁄3 in decimal. Some values cannot be It is written accurately no matter how many digits are used. The difference between our traditional base 10 Notation and binary notation is that more values have non-terminal representations in binary rather than decimal notation. For example, the value is unterminated when expressed in binary form. Imagine the problems it could cause the careless person using Floating-point notation for storing and manipulating dollars and cents.
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Especially when the dollar is used as a Unit of measurement, the value of one cent could not be saved exactly. MGMT631 Handouts PDF A solution, in this case, is to manipulate data in units of cents, so all values are whole numbers that can be stored accurately using a method like this: to 1/8 we end up with 25/8 which is 10.101 which cannot be stored in the.
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