How to write own multiplication of big numbers?

For my homework, I have to deal with multiplication of big numbers ( greater then java.long ) stared in my own BigNumber class as int[]. Basically I need to implement something like this :

    157 x
    121 y
   ----
    157 result1
   314  + result2
  157   + result3
 ------
 18997  finalResult

But how do I implement it?

I thought about expanding result2,3 with zeros (3140, 15700) and adding them. But first I somehow need to navigate between each digit of y and multiply it by each digit of x.

Solution

Use the diagonal approach. Make an array, and multiply each digit by each other digit and fill in the numbers in each cell.

36 x 92

       3     6
    +-----+-----+
    | 2 / | 5 / |
9   |  /  |  /  |
    | / 7 | / 4 |
    +-----+-----+
    | 0 / | 1 / |
2   |  /  |  /  |
    | / 6 | / 2 |
    +-----+-----+

Add the numbers on each diagonal. Move from the least-significant digit (at the lower right) to the most (upper left).

2                                                                    2 (least-significant)
(6 + 1 + 4) = 11 (make this 1, and carry the 1 to the next digit)    1
(5 + 7 + 0 + 1(carried)) = 13 (make this 3, and carry the 1)         3
2 + 1(carried) = 3                                                   3 (most-significant)

The answer's 3312.

Make a two-dimensional array of your digits. Fill the array with the multiplications of the single digits together.

Write some logic to scrape the diagonals as I did above.

This should work for arbitrarily large numbers (as long as you still have memory left).