Binary Addition: 11 + 11 - What's the Rule?

[kolleamm]

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.

 

[FactChecker]

Yes, it happens all the time. You carry the 1 to the higher position as you say and then you have 1+1+1 = 11_b in that position. So the result is 11_b+11_b=110_b.

 

[Ibix]

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.

 

[PeroK]

And, of course, you can always convert to and from base 10 to check your answer!

 

[Mark44]

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.)

 

[Svein]

Also 11_b+11_b=11_b⋅2_D=11_b⋅10_b=11_b shift left 1.