SOLUTION: perform the operation (a)1010two x 101two

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Question 352909: perform the operation
(a)1010two x 101two

Answer by jsmallt9(3759) About Me  (Show Source):
You can put this solution on YOUR website!
The multiplication part of multiplication in base two is extremely easy because you have nothing but 1's and 0's and these are the easiest two numbers to multiply. As we will see, the additiion part of multiplication is the harder part.

The multiplication part:
   1010
x   101
 ------
   1010
 1010
 ------

Now the harder part, the addition. 0 + 0 = 0 and 1 + 0 = 1 even in base two. And 1 + 1 is still two but a two in base two is 10! So as we add and when get to the 4th column from the right (where we have two 1's to add), we will have to write a zero for that column and carry 1 over to the next column. So now the complete multiplication:
   1010
x   101
 ------
   1010
 1010
 ------
 110010