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[Help] with Numbering System Digital Circuit

  1. Apr 27, 2014 #1
    [Help] with Numbering System "Digital Circuit"

    Hello Guys ..

    iam having an exam on digital circuits and i try to work on some problems about numbering systems

    and i found this problems but i couldn't solve it ..

    i said that (x-3)(x-6)=x^2-11x+22
    then i said that

    x^2-9x+18=x^2-11x+22
    so 2x=4 and x=2 but i didn't know what to do after that ..so please help me :))

    xq6IuWH.png

    Thx Guys !!
     
  2. jcsd
  3. Apr 27, 2014 #2

    berkeman

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    Staff: Mentor

    If 3 * 6 = 22, what is the base?

    And this is for a logic circuits class? Really?
     
  4. Apr 27, 2014 #3

    phinds

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    Gold Member
    2016 Award

    X=3 and X=6 are not the same solution at the same time, so saying that (x-3)(x-6)=ANYTHING is not helpful.

    The solution falls out of Berkeman's approach immediately, but if you want an algebraic (and more complicated) method, try this:

    Express the equation you are given as a function of an assumed base B and express everything in the equation as a decimal equivalent and then solve for B. It's trivial, really, whether you start with 3 or start with 6.

    And REMEMBER, expressed as a decimal number, "22-base-B" is 2*B + 2 and similarly for the 11.
     
  5. Apr 27, 2014 #4
    This was the first chapter of Digital Circuits ..an Introduction for binary and other numbering systems ...this was the first section of the course :D

    and if 3 * 6 = 22
    then 3 * 6 = 2+2x then base = 8 :))
     
  6. Apr 27, 2014 #5

    berkeman

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    Staff: Mentor

    There are 10 kinds of people in the world... :smile:
     
  7. Apr 27, 2014 #6
    Hahahah ..i think ..it depends on the base we are using , Berkeman :biggrin:
     
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