Multiplying in binary follows the same method as multiplying in decimal,
shift and add.

When you do 123 x 45 you would do:
  123 times 5 gives 615
  shift the 45 right one place, shift the 123 left one place
  1230 times 4 is 4920
  add to the running total
  shift the 45 right again, no more digits left, all done

Binary is the same, with the added advantage that everything is either times
zero or times one, so you're just adding or not adding

When you do 10101 times 101 you would do:
  10101 times 1 - just copy the 10101, add to running total
  shift the 101 right one place, shift the 10101 left one place
  101010 times 0 - zero, nothing to add
  shift the 101 right one place, shift the 101010 left one place
  1010100 times 1 - just copy the 1010100, add to running total
  shift the 101 right one place, shift the 1010100 left one place
  the 101 has now become zero, so BEQ out of the loop

You will now have added:
  ..10101 * 1 = ..10101
  .101010 * 0 = .000000
  1010100 * 1 = 1010100
  total:
  ..............1101001
(dots added for formatting)

which is 105 which is indeed %10101 x %101 which is 21 x 5.