Results 1 to 3 of 3

Math Help - IEEE 754 Single Precision Floating Point System:

  1. #1
    Newbie
    Joined
    Jan 2010
    Posts
    18

    IEEE 754 Single Precision Floating Point System:

    Determine the smallest floating point number x greater than 1 that can be
    represented exactly in a binary single precision floating point system.
    Determine the quantity ε = x - 1 (This is called machine epsilon).

    Info on floating point number system: Floating point - Wikipedia, the free encyclopedia
    32 bits.
    1 bit sign
    8 bits for exponent
    23 bits for significand


    I'm thinking something like -

    0|01111111|00000000000000000000001

    Which equals 1.0000001
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by Celcius View Post
    Determine the smallest floating point number x greater than 1 that can be
    represented exactly in a binary single precision floating point system.
    Determine the quantity ε = x - 1 (This is called machine epsilon).

    Info on floating point number system: Floating point - Wikipedia, the free encyclopedia
    32 bits.
    1 bit sign
    8 bits for exponent
    23 bits for significand


    I'm thinking something like -

    0|01111111|00000000000000000000001

    Which equals 1.0000001
    I would leave it as 1+2^{-23}.

    I would also in passing mention normalisation (the assumed most significant bit is 1 so it is not held in the mantissa).

    CB
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,412
    Thanks
    1328
    Note that Captain Black's suggested answer is exact while yours is not!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. help with floating point error
    Posted in the Math Topics Forum
    Replies: 0
    Last Post: October 17th 2011, 08:27 PM
  2. Largest Factorial Represented Exactly In Floating Point System
    Posted in the Advanced Applied Math Forum
    Replies: 1
    Last Post: September 12th 2011, 11:44 AM
  3. Floating Point Representation
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: March 29th 2010, 02:40 AM
  4. Floating point operations
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: February 24th 2010, 12:32 PM
  5. IEEE floating point arithmetic
    Posted in the Math Software Forum
    Replies: 1
    Last Post: March 13th 2009, 02:18 PM

Search Tags


/mathhelpforum @mathhelpforum