How can you sum three binary numbers?

Answer 1

I think the best way is with an example.

Let us add three binary numbers

10

111

1010

remember that 10 is 1 two and 0 ones. so it is the number 2 in base 10

111 is 1 one, 1 two and one 2^2 or 4 so 111=1+2+4=7 in base 10

and 1010 is zero 1 and one 2 and zero 4 and one 2^3 or eight.

So 1010 is 2+8=10

Now we know that 2+7+10=19 in base 10 so whatever we get in base 2, or binary, we need to then check that it is 19. No need to do this all the time, but if we do it once, we can see our answer is correct.

So we add the columns just as we do in base 10 addition.

the column to the right is the ones since that is 20 =1

We have only 1 of them.

Next columns give 1+1+1. note that 1+1=2 which moves we can move to the next column, the same way we do with 9+1 in base 10.

so we can leave 1 one in the second column and carry a 1 to the third column.

so far we have 11 with a 1 carried

The third column has only a 1 so we add that to the 1 we carried and we have to carry again since we have 2 which is not allowed in binary. Now we have used up both the 1s in that column so only a zero left.

We add the 1 to the fourth column where is there is already a 1.

That is 0 with a 1 in the 5 column

So we have 10011=19 in base 10

Here it is in column form. The explanation is just to see what is going on I am going to put some zero's in front of number to help you keep track of the columns at first. They don't change the values and once you see what's going on, no need for them.

0010

0111

1010

---- ---- 10011

remember 10011 is 1x20 +1x2+0x22 +0x23 +1x24 =1+2+16=19