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11 + 11 in binary

  1. Jan 28, 2017 #1
    This one confused me a little bit. You have to carry the one and put it into the next 1 + 1, what would be the rule in this situation?

    Not sure if this ever happens in decimal addition.
     
  2. jcsd
  3. Jan 28, 2017 #2

    FactChecker

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    Yes, it happens all the time. You carry the 1 to the higher position as you say and then you have 1+1+1 = 11b in that position. So the result is 11b+11b=110b.
     
  4. Jan 29, 2017 #3

    Ibix

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    In decimal, what's 55+55? 5+5=10, so write zero and carry the one. 5+5+1=11, so write one and carry the 1.

    Same in binary, except 1+1=10. So to do 11+11 note that 1+1=10 so write zero and carry the one. 1+1+1=11, so write one and carry the one.

    I find it helpful when working with bases other than ten to explicitly write out long addition/multiplication/division like I'm back in primary school. The same mindless drills work (we call them algorithms because it sounds better), just with different representations of the numbers.
     
  5. Jan 29, 2017 #4

    PeroK

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    And, of course, you can always convert to and from base 10 to check your answer!
     
  6. Jan 29, 2017 #5

    Mark44

    Staff: Mentor

    The addition "facts" in binary addition are pretty simple, as there are only two digits.
    0 + 0 = 0 - no carry
    0 + 1 = 1 - no carry
    1 + 0 = 1 - no carry
    1 + 1 = 10 - carry to the next position on the left
    (All numbers shown are binary (base-2) numbers.)
     
  7. Jan 29, 2017 #6

    Svein

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    Also 11b+11b=11b⋅2D=11b⋅10b=11b shift left 1.
     
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