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October 26th, 2013, 07:24 AM   #1
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0.1 binary

Hello!
Please, as far as there are no problems to turn decimal numbers to binary, I just stuck at turning 0.1 to binary system.

0.1 : 2 = 0. rest
0.05 :2 = 0 rest
0.025 : 2 = o rest

...

and the result should be infinite number containing 1s too:

0.00011001100110011

How do they get these 1s at all cause you can all the rational numbers divide with 2...


Please, can someone help?
Many thanks!
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October 26th, 2013, 08:13 AM   #2
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Re: 0.1 binary

Hello, ungeheuer!

Quote:



Here is one way . . .

Assume that 0.1 (base ten) equals some decimal in base two.

[color=beige]. . [/color]






















And we see that we have a repeating pattern.
[color=beige]. . [/color]

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October 26th, 2013, 08:14 AM   #3
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Re: 0.1 binary



In binary this is:



Dividing by 2 moves the decimal point to the left one place, thus:

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October 26th, 2013, 08:33 AM   #4
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Or use long division...

Code:
      0.000110011
__________________
1010 |1.0000000000
        1010
        ----
         1100
         1010
         ----
           10000
            1010
            ----
             1100
             1010
             ----

etc.
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