Well, sure, but the question is how you do "123 * 456". In binary you have the multiplication 111001000 x 1111011 and the traditional grade-school algor

Well, sure, but the question is how you do "123 * 456". In binary you have the multiplication 111001000 x 1111011 and the traditional grade-school algorithm looks something like this 111001000 1110010000 00000000000 111001000000 1110010000000 11100100000000 111001000000000 --------------- 1101101100011000 122222221 so the answer is 1101101100011000, or 56088 in decimal. This method takes O(n^2) bitwise multiplications, where n is the number of bits in the larger of the two integers. Clearly if you're multiplying very large integers (say you're doing cryptography - the kind of computation that computers do millions of times every day) then there's clearly an interest in having faster algorithms for multiplication.