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Math Help - Range and Precision in Fixed Point number systems.

  1. #1
    elg009
    Guest

    Range and Precision in Fixed Point number systems.

    Hi everybody, i have a question that relates to fixed point number systems. In a Computer Architecture book it says that: A fixed point representation can be characterized by the range of expressible numbers (that is, the distance between the largest and smallest numbers) and the precision (the disctance between two adjacent numbers on a number line).For example, using three digits and the decimal point placed two digits from the right, the range is from 0.00 to 9.99 and the precision is .01; So far so good, i can understand that, what i can not understand and i need some help is: the error is 1/2 of the difference betwen two adjoining numbers such as 5.01 and 5.02 which have a difference of .01 The error is .01/2=.005. That is we can represent any number within the range 0.00 to 9.99 to within .005 of its true or precise value.
    If someone can help please reply
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  2. #2
    MHF Contributor
    Joined
    Apr 2005
    Posts
    1,631
    I don't know the subject (branch of Math) of your topic here, so I will comment by "common sense" or by any reasoning.

    Precision is 0.01
    Cannot go less or beyond that.
    So if a number falls between 5.01 and 5.02, how will you call/write it?

    say, 5.012345?
    You will call it 5.01

    5.014?
    Call it 5.01

    5.0179?
    Call it 5.02

    5.015?
    By convention, call it 5.02

    5.0149999999999999999999999999999999999?
    Call it 5.01

    Meaning, between 5.01 and 5.02, you have 0.05 of play before you write 5.02. You have exactly halfway between 5.01 and 5.02 before 5.01 becomes 5.02. You are allowed an error up to 0.05 and you are still precise.

    Meaning, 5.01 is from 5.005 up to 5.0149999999999999999999999999999999. You have 0.05 alowance either side of 5.01 and you are still precisely 5.01.
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