Question

Turing Machine for Two's Complement [40\%] Design and implement a Turing Machine to perform the conversion of a binary number to Two's Complement, using the 'fast' method described in the class notes. Recall that the fast method starts at the LSB (to the right), leaves all 0 's and the first 1 alone, then flips all the remaining bits. The tape will initially consist of the number to convert, a blank space, and then a 'sign indicator' bit ( 0 for positive, 1 for negative).

Answer 1

To convert a binary number to Two's Complement using the 'fast' method, follow these steps: start at the LSB, leave all 0s and the first 1 alone, flip all remaining bits, and add a sign indicator (0 for positive, 1 for negative).

Step-by-step explanation:

To design and implement a Turing Machine to convert a binary number to Two's Complement using the 'fast' method, you need to follow these steps:

1. Start at the least significant bit (LSB) and move to the left.
2. Leave all 0s and the first 1 untouched.
3. Flip all the remaining bits after encountering the first 1.
4. After reaching the end of the binary number, write a blank space and a sign indicator bit (0 for positive, 1 for negative) on the tape.

For example, let's consider the binary number 10110. After applying the 'fast' method, the Two's Complement representation would be 01010, with the sign indicator as 0 for positive. The tape would look like this: 01010_0.