Question
Asked Apr 26, 2019
80 views

Design a Turing machine that computes the function

f(w)

=

1 if w is even

 

=

0 if w is odd.

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Expert Answer

Step 1

To discover whether a string is even or odd, just examine the LSB (least significant bit).

  • If LSB is 1 => odd ,
  • If LSB is 0 => even.

For instance,

  • String “1001” is odd and
  • String “1000” is even.

 

Step 2
  • Three states are needed only.
  • Move right until a # (end of the string) is encountered.
  • When encountered a #, then move left.
  • Check the bit:
    1. If bit is 1 => Numberw&rdqu...

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