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Thank you. I had no idea what the "secret" was myself. What would be meant, in the original article, by the "multiplication algorithm"? I know that's a bizarr

• anonymoushn 14y ago
  The multiplication algorithm I was taught in school was something like this: for each digit in the bottom number, starting with the ones digit: begin a new line beneath the current state. write a number of trailing zeroes equal to the number of digits of the bottom number you've already processed. for each digit in the top number, starting with the ones digit: write (carry + top digit * bottom digit) % 10 to the left of the leftmost digit on the bottom line of the state. the carry for the next digit of the top number will be (carry + top digit * bottom digit) / 10 use the addition algorithm to compute the sum of all the numbers you wrote this way. If you hard code it to only handle two digit numbers, it's a bit simpler. It computes the product of two numbers 10A+B, 10C+D for one digit A,B,C,D as (D * B + 10 * D * A) + 10 * (C * B + 10 * C * A). That sounds really confusing, because it is. The visual explanation relates it to something much less confusing in an obvious way.