The scientific notation has a single digit to the left of the decimal point. A number in scientific notation that has no leading 0s is called a normalized number, which is the usual way to write it.

**FLOATING POINT OPERATIONS **

The scientific notation has a single digit to the left of the decimal point. A number in scientific notation that has no leading 0s is called a normalized number, which is the usual way to write it. Foating point - Computer arithmetic that represents numbers in which the binary point is not fixed. Floating-point numbers are usually a multiple of the size of a word.

The representation of a MIPS
floating-point number is shown below, where s is the sign of the floating-point
number (1 meaning negative), exponent is the value of the 8-bit exponent field
(including the sign of the exponent), and fraction is the 23-bit number. This
representation is called sign and magnitude, since the sign has a separate bit
from the rest of the number.

A standard scientific notation for
reals in normalized form offers three advantages. · It simplifies exchange of data that includes
floating-point
numbers; It simplifies the floating-point
arithmetic algorithms to know that numbers will always be in this form;

·
It increases the accuracy of the numbers that can
be stored in a word, since the unnecessary leading 0s are replaced by real
digits to the right of the binary point.

**Fig. 2.14
Scientific notation**

**Floating point addition**

Step 1. To be able to add these
numbers properly, align the decimal point of the number that has the smaller
exponent. Hence, we need a form of the smaller number, 1.610ten x10–1, that
matches the larger exponent. We obtain this by observing that there are
multiple representations of an unnormalized floating-point number in scientific
notation:

Step 1.1.610ten x10^{–}^{1} =
0.1610ten x100 = 0.01610ten x10^{1}

Step 2. Next comes the addition
of the significands: 9.999ten+ 0.016ten The sum is 10.015ten x10^{1}.

Step 3. This sum is not in
normalized scientific notation, so we need to adjust it: 10.015ten x10^{1}
= 1.0015ten x10^{2}

Thus, after the addition we may
have to shift the sum to put it into normalized form, adjusting the exponent
appropriately.

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Computer Architecture : Arithmetic Operations : Floating Point Operations |

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