1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Binary help!

  1. Sep 8, 2008 #1
    The problem statement, all variables and given/known data
    Calculate the binary equivalent of 2/3 out to eight places. Then convert from binary to decimal. How close is the result to 2/3?

    The attempt at a solution

    I new to this and I am still trying to figure this stuff out so if someone could walk me through this that would be great! Here's what I came up with from some stuff I read.....

    2/3 * 2 = 1+1/3 X1=1
    1/3 * 2 = 0+2/3 X2=0
    .......and so on.....

    I did that out to 8 places and got the number 10101010 and i suppose that that is actually 0.10101010 since 2/3 is .66666667?

    Is this correct and if so how do I convert to decimal?
  2. jcsd
  3. Sep 8, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    Fractions in binary are stored as sum's of negative powers of two.
    So write the headings, 1/2 1/4 1/8 1/16 1/32 ......
    Convert the decimal to binary in almost the same way as you would for a whole number.
    eg 0.66666666 -0.5 = 0.16 , so a 1 in the half column
    0.16 is less than 0.25 so a 0 in the quarter column
    0.16 - 0.125 = 0.035 so a 1 in the 1/8 column


    If you do it this way, you have the remainder automatically as you work out thebinary.
  4. Sep 8, 2008 #3
    I don't understand why your subtracting?
  5. Sep 8, 2008 #4


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Each time you put down a 1 (representing a value of 1/2 or 1/4 of 1/8, etc.), you have less and less remainder left.

    - Warren
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook