Construct a Turing Machine which multiplies two binary numbers.

Initial condition

The two numbers are given in binary representation. The position of the numbers within the world can be choosen freely.

Hint

The two numbers can be multiplied using the "gipsy multiplication" algorithm. The gipsy multiplication divides one number by two while doubling the other one. If the number that has to be divided by two is odd, the one to be doubled is added to the result (rows marked yellow).

Example 9 * 5:
1. Number
(half)		 2. Number
(double)		 Result
        0 [0]
9 [1001] 5 [101] 5 [101]
4 [100] 10 [1010] 5 [101]
2 [10] 20 [10100] 5 [101]
1 [1] 40 [101000] 45 [101101]

To double a binary number, the bits can be shifted to the left. Dividing a binary number by two can be done by shifting it to the right, erasing the least significant bit.