Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor
    Gold Member
    2017 Award

    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


    User Avatar
    Science Advisor

    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


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

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


    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


    User Avatar
    Science Advisor

    Also 11b+11b=11b⋅2D=11b⋅10b=11b shift left 1.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted