设计一个图灵机来计算二进制数的奇偶校验

Question

so I have this problem given to me at my university, and I'm really lost about it, I don't know if you can help me cause this is not strictly code, I think I have to doit with digrams and tables by hand.

So, the problem is to design a Turing machine that calculates the parity of a binary number. If the number of 1's is pair add a 0 at the end, if it is unpair add a 1 at the end.

Example

a) 001001 -> 0010010

b) 101010 -> 1010101

Hoping you can help me, thanks

Answer 1

Input: a string x of binary digits

Output: xd where d id 0 if #1(x) is even and 1 if #1(x) is odd, where #1(x) is the number of instances of 1 in x .

Design: we will scan the string from left to right, keeping track of the parity of the number of instances of 1 seen so far. When we run out of input, we will see which state we are in, write the corresponding final digits, and then halt-accept.

Implementation:

q    t    q'   t'   d      comment

q0   0    q0   0    right  see a zero, stay in state and keep looking
q0   1    q1   1    right  see a one, now we've seen odd number, keep looking
q0   B    ha   0    same   ran out after seeing even number

q1   0    q1   0    right  see a zero, stay in state and keep looking
q1   1    q0   1    right  see a one, now we've seen an even number, keep looking
q1   B    hA   1    same   ran out after seeing odd number