Now, I have assumed the unary number to be 1. and my doubts are
- Do you design this machine similar to normal unary multiplication assuming that the constant 2 (11) is always present in the input tape? Or
- Is there only one unary number present in the tape?
This confusion may be because of my poor understanding of the question. But, I tried solving it assuming that the tape has only one unary number.
What I thought is
i. Any unary number multiplied by 2 is the number concatenated to itself. Eg. 111 times 2(11) is 111111
ii. I took a tape with the number and a separator 0.
iii. Then convert a 1 to 'x' and a blank symbol after the separator to 1.
iv. now after every 1 before the separator is turned x and the same number of blanks after the separator has been turned into 1, change the separator to 1, turn all x back to 1, and change terminal 1 to blank.
v. That way the number was concatenated after itself (multiplied by 2)
Would it be correct to solve this using the approach in point 1 or the way I did it?