(SHOW ALL YOUR WORK, not just the answers) When you multiply: 21 x 68 you most l

Question

(SHOW ALL YOUR WORK, not just the answers) When you multiply: 21 x 68 you most likely do: 8x1 + 8x20 + 60x1 + 60x20 = 1, 428 So, there are 4 multiplications and then 3 additions. How long would it take a computer to do this if each multiplication or addition took 1 microsecond (1 x 10^-6 second)? How many operations (multiplications and additions) are there if each number has N digits? If each multiplication or addition takes 1 microsecond, how long would it take to do each of the following. (Express your answers in the most meaningful unit. How long would it take that computer to multiple two numbers that each had 100 digits? How long would it take that computer to multiple two numbers that each had a million digits? How long would it take that computer to multiple two numbers, that each had 22, 338, 618 digits, which are the number of digits in the largest known prime number. For VERY LARGE numbers this seems pretty slow, are there FASTER ways to multiple two VERY LARGE numbers, look on the internet, see what you find.

Explanation / Answer

2(a) to multiply 21 with 68 we have total 7 seven basic operations(4 multiplication and 3 addition). each operation takes 1 microsecond. so 7*1 =7 microseconds.

2(b) To multiply two number having N DIGIT in each number, it takes N^2 multiply and N^2-1 addition

so total is 2N^2-1 operations

2(d) To multiply two number having 100 DIGIT in each number, it takes 100^2(10000) multiply and 100^2-1(9999) addition

so total is 19999 operations and total 19999 microseconds (0.019999 seconds)

2(c)To multiply two number having million DIGIT(1000000) in each number, it takes 1000000^2(1000000000000) multiply and 1000000^2-1(99999999999) addition

so total is 199999999999 operations and total 199999999999 microseconds (0.330 week or 2.31 day or 55.55Hour or 3333.33minutes )

2(e) To multiply two number having 22338618 DIGITin each number, it takes 22338618^2 multiply and 22338618^2-1 addition

so total is 2.22338618^2-1 microsecond.

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