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Base 2 trouble

  1. Feb 24, 2012 #1
    I'm a little embarrassed by this and having a total brain fart.
    I understand:
    (6 * 10^3) + (3 * 10^2) + (5 * 10^1) + (7 * 10^0) = 6000 + 300 + 50 + 7 = 6357

    But for some reason I can't get this:
    (1 * 2^3) is equal to 8.

    (1 * 2^3) + (0 * 2^2) + (1 * 2^1) + (1 * 2^0) = 8 + 0 + 2 + 1 = 11
     
  2. jcsd
  3. Feb 24, 2012 #2

    berkeman

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    Staff: Mentor

    Why do you have ones in these terms? "(1 * 2^1) + (1 * 2^0)"
     
  4. Feb 24, 2012 #3
    I copied directly from here;
    http://computer.howstuffworks.com/bytes1.htm

    Its a page I came across while searching for more information. I did know how to work it out but have forgotten.
     
  5. Feb 24, 2012 #4

    DaveC426913

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    Gold Member

    Yes, but that adds up to 11, not 8. 1011.

    What you started with was 2^3 which is 1000 which is 8


    Hey lookit that. I can look down and see Berkeman slooooooowly tyyyyping away..... :biggrin:
     
    Last edited: Feb 24, 2012
  6. Feb 24, 2012 #5

    berkeman

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    The thing you copied shows how 0b1011 = 11. (binary 1011 = 11 decimal)

    Below that do you see "8 = 1000" listed?
     
  7. Feb 24, 2012 #6

    berkeman

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    Dagnabit! Beaten by Dave again :biggrin:
     
  8. Feb 24, 2012 #7
    OK, thank you guys I understood :).
     
  9. Feb 24, 2012 #8

    HallsofIvy

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    Staff Emeritus
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    So this is what you are reall9y asking about- why 1*2^3= 8?

    1*2^3= 1*(2*2*2)= 1*(2*(2*2)). 2*2= 4 so that becomes 1*(2*4). 2*4= 8 so that becomes 1*8= 8.

    Yes 10112 is 1*8+ 0*4+ 1*2+ 1= 11 base 10.
     
  10. Feb 24, 2012 #9

    I was having trouble working out why 2^3=8. As simple as it seems. I haven't done any sort of to the power maths in years and it skipped my mind.
    But yes, you had answered my question, thank you.

    But ignoring the 1 in 1 * 2^3 as it was simply telling what binary digit 2^3 was representing.
     
  11. Feb 24, 2012 #10
    There are 10 kinds of people in the world. Those who read binary and those who don't.
     
  12. Feb 25, 2012 #11

    Mark44

    Staff: Mentor

    Or, there are 3 kinds of people in the world: those who understand mathematics, and those who don't. :tongue:
     
  13. Feb 25, 2012 #12
    I don't :rolleyes:
     
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