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In addition to specifying the results of operations on numeric data, the IEEE standard also specifies the precise behavior on undefined operations such as dividing by zero. These results are indicated using several special values. These values are bit patterns that are stored in variables that are checked before operations are performed. The IEEE operations are all defined on these special values in addition to the normal numeric values. [link] summarizes the special values for a 32-bit IEEE floating-point number.

Special values for an ieee 32-bit number
Special Value Exponent Significand
+ or – 0 00000000 0
Denormalized number 00000000 nonzero
NaN (Not a Number) 11111111 nonzero
+ or – Infinity 11111111 0

The value of the exponent and significand determines which type of special value this particular floating-point number represents. Zero is designed such that integer zero and floating-point zero are the same bit pattern.

Denormalized numbers can occur at some point as a number continues to get smaller, and the exponent has reached the minimum value. We could declare that minimum to be the smallest representable value. However, with denormalized values, we can continue by setting the exponent bits to zero and shifting the significand bits to the right, first adding the leading “1” that was dropped, then continuing to add leading zeros to indicate even smaller values. At some point the last nonzero digit is shifted off to the right, and the value becomes zero. This approach is called gradual underflow where the value keeps approaching zero and then eventually becomes zero. Not all implementations support denormalized numbers in hardware; they might trap to a software routine to handle these numbers at a significant performance cost.

At the top end of the biased exponent value, an exponent of all 1s can represent the Not a Number (NaN) value or infinity. Infinity occurs in computations roughly according to the principles of mathematics. If you continue to increase the magnitude of a number beyond the range of the floating-point format, once the range has been exceeded, the value becomes infinity. Once a value is infinity, further additions won’t increase it, and subtractions won’t decrease it. You can also produce the value infinity by dividing a nonzero value by zero. If you divide a nonzero value by infinity, you get zero as a result.

The NaN value indicates a number that is not mathematically defined. You can generate a NaN by dividing zero by zero, dividing infinity by infinity, or taking the square root of -1. The difference between infinity and NaN is that the NaN value has a nonzero significand. The NaN value is very sticky. Any operation that has a NaN as one of its inputs always produces a NaN result.

Questions & Answers

what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Cómputo de alto rendimiento. OpenStax CNX. Sep 02, 2011 Download for free at http://cnx.org/content/col11356/1.2
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