**BINARY**

Consider the problem of computing the XOR of two binary and determining if the result is equal to a third binary number. Suppose the input tape contains three binary numbers, separated by $ symbols. Each binary number consists of one or more bits with one bit per cell. E.g.,

# 0 1 1 0 $ 0 1 0 1 $ 0 0 1 1 # #

(a) Describe a Turing Machine that accepts if the XOR of the first two binary numbers is equal to the third binary number and rejects otherwise. Note: You just need to describe how the TM would function as we have done in lectures. You do not need to specify the TM in full. Feel free to describe a multi-tape Turing Machine if that is easier.

(b) [5 marks] Describe a Random Access Machine that accepts if the XOR of the first two binary numbers is equal to the third binary number and rejects otherwise. Note: You just need to describe how the RAM would function as we have done in lectures.

Consider the problem of checking if an XOR of n binary numbers is equal to 0. The input tape contains n binary numbers, separated by $ symbols.

(a) Describe a Turing Machine that accepts if the XOR of the binary numbers is 0. Note: You just need to describe how the TM would function as we have done in lectures. You do not need to specify the TM in full. Feel free to describe a multi-tape Turing Machine if that is easier.

(b) Describe a Random Access Machine that accepts if the XOR of the binary numbers is 0 and rejects otherwise. Note: You just need to describe how the RAM would function as we have done in lectures.