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October 21st, 2012, 03:45 AM  #1 
Newbie Joined: Oct 2012 Posts: 2 Thanks: 0  exercise problem IEEE 754 floating point
Hi Everyone, I need some help on how to convert decimal numbers in to IEEE 754 (single) floating point notation. For example, given a number 1995,5, then I do: 1995 to binary is 111 1100 1011 0,5 to binary is 0,1 Together we have: 111 1100 1011,1 After standardising, we have 1,11110010111 x 2^10(dec) and and then it's clear on howto convert it to IEEE 754. But now I have an excercise like 0,000000012. How do you solve this kind of exercise manually. We may not use a calculator. I'm especially interested on how to standardize this number? For hours I've been searching for the answer with no result... Any help would be great. Best regards! 
October 21st, 2012, 11:15 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 933 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: exercise problem IEEE 754 floating point
Exactly the same, but flip the sign bit.

October 22nd, 2012, 05:13 AM  #3  
Newbie Joined: Oct 2012 Posts: 2 Thanks: 0  Re: exercise problem IEEE 754 floating point Quote:
0,000000012 x 2 = 0,000000024 0,000000012 x 2 = 0,000000048 0,000000012 x 2 = 0,000000072 0,000000012 x 2 = 0,000000144 0,000000012 x 2 = 0,000000288 0,000000012 x 2 = 0,000000576 0,000000012 x 2 = 0,000001152 0,000000012 x 2 = 0,000002304 ... You see, it's not the most pretty and quickest method. I would like to write 0,000000012 as a power of two, like 1,... x 2^n. (Preferably without using a calculator.) Someone (else) ?  
October 22nd, 2012, 05:28 AM  #4 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 933 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: exercise problem IEEE 754 floating point
If you know your powers of two, this is just the sum of adjacent powers of two (shifted appropriately). So you shouldn't need more than a single addition to see how far to shift it (and possibly a second if that was the wrong amount, to get the significand).

June 14th, 2017, 12:30 AM  #5 
Newbie Joined: Jun 2017 From: Vietnam Posts: 1 Thanks: 0 
10110010000110011001100110011001


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