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Assume that you multiply the two two-digit numbers 36 and 52 using the method that does only three atomic multiplies. Show that steps of the algorithm on this example.

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  1. 25 November, 07:46
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    We can use Karatsuba algorithm to achieve the required goal as follows:

    let the two numbers be X = 36 and Y = 52,

    let X = X0X1 and Y = Y0Y1 (for given example)

    so, X0 = 3, X1 = 6 and Y0 = 5, Y1 = 2

    Now, product of two numbers be:-

    X * Y = X0X1 * Y0Y1

    = 100 (X0*Y0) + 10 (X0 * Y1 + X1 * Y0) + X1 * Y1

    36 * 52 = 100 (3 * 5) + 10 (3 * 2 + 6 * 5) + (6 * 2)

    = 1500 + 360 + 12

    = 1872

    by doing this we only need 3 atomic multiplications to multiply two 2-digit numbers.
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