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Homework Help: Binary to decimal.

  1. Oct 1, 2013 #1
    1. The problem statement, all variables and given/known data
    Not so much a problem as a general wondering. I know how to convert from decimal to binary and binary to decimal apart from when there's a recurring pattern involved. One which I really can't figure out it 0.1001 (repeating). How do you go about converting that to decimal?

    2. Relevant equations
    None really.

    3. The attempt at a solution
    I really don't have any attempt as I can't find much about it on the internet. It features in a worked example in our notes and it's never explained. The answer is 0.6 apparently. (Not sure if this would be considered a computing problem or a mathematical one)
  2. jcsd
  3. Oct 1, 2013 #2


    Staff: Mentor

    The trick here is similar to what you do to convert a repeating decimal fraction to a rational number. For example, if you need to convert .35353535... to a fraction, you multiply by a power of 10 large enough to move the part that repeats to the other side of the decimal point, which in this case would be 102. If we write x = .353535..., then 100x = 35.353535...

    Subtracting the equation with x from the equation with 100x, we get
    99x = 35 ==> x = 35/99

    For your binary fraction, write an equation x = .10011001...2. Get a new equation that you can subtract this one from by multiplying by 24 (or 16).
  4. Oct 1, 2013 #3
    Won't you then end up with 15x = 1001, and that equals 66.733... and not 3/5 as it says in my notes. Is there a mistake in the notes or am I misunderstanding you?
  5. Oct 1, 2013 #4


    Staff: Mentor

    No, you won't. In my work I was careful to note that the fraction was in base-2 (something you neglected to do). You should have gotten 15x = 10012.

    This is a bit ungainly, having a decimal number on one side, and a binary number on the other, but at least it's marked to indicate that different bases are being used.
  6. Oct 1, 2013 #5
    Got it! Thanks a million.
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