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Fixed Point and Floating Point Numbers

Date: 05/19/2000 at 00:36:58
From: Paul Huband
Subject: Fixed point numbers

What are "fixed point" or "fixed decimal" numbers? How do they behave 
in basic math operations? What are they used for? I have searched many 
sites, including yours, and can find nothing on fixed point numbers, 
or fixed point mathematics. Most searches return topics dealing with 
points fixed in space. I wish to know about numbers with fixed decimal 
places, as opposed to floating point or floating decimal.

Thank you.

Date: 05/19/2000 at 10:12:37
From: Doctor Rob
Subject: Re: Fixed point numbers

Thanks for writing to Ask Dr. Math, Paul.

This is not a mathematical idea, but a computer science idea, which is 
why you didn't find anything about this on our site.

There are two ways to store a decimal number in a computer. In one 
method, the decimal point is assumed to be in a particular place, such 
as at the left-most or high-order end of the computer word, and the 
exponent of a power of 10 is adjoined to give you the value in 
scientific notation. For example, 6.0235 * 10^23 (Avogadro's number) 
might be stored as +6023500000 +24, with the decimal to the left of 
the 6, and Pi as +3141592654 +01, with the decimal to the left of the 
3. The first part is the "mantissa" of the number, and the second is 
the "characteristic." This is what is meant by floating point numbers. 

Fixed point decimal numbers are stored essentially as integers, and it 
is left up to the programmer to deal with the decimal point. Thus 
Avogadro's number might be stored as +602350000000, and Pi as 
+314159256359, with no characteristic stored.

Actually the terms "fixed point" and "floating point" are misnomers: 
with floating point numbers, the decimal location is fixed (in the 
examples, at the far left), and with fixed point numbers, the decimal 
location is floating (and in fact unspecified).

- Doctor Rob, The Math Forum   
Associated Topics:
High School Number Theory

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