Since a binary digit has only two possible values, each digit bears less information than in decimal, where each digit can have ten different values.
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For the simple reason that the 'places' in a binary number represent multiples of 2, rather than 10. Therefore, a binary '10' = a decimal '2.'
Good grief! We can't even write out a googolplex in decimal! How are you going to write it out in binary?
A product is a binary operation: you need 2 (or more) numbers in order for there to be a product.