Although there might be some amazing trick to this, the easiest to do is to convert the numbers to base 10, do the operation, then convert the solution back if necissary.
Ex. 10100101₂ times 101₂?
10100101₂ is 165
101₂ is 5
165 * 5 is 825.
Convert it to whatever base the answer is in and voila, you have completed the first problem.
-Josh
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