QUESTIONS Q1. Design a Turing Machine that calculates the following function: f(n,m)= ((n+m)/2 ) where [] means ceiling/the next integer above the result (for example, if the real result of division is 3.3 or 3.5 or 3.8 and such, the output of the function is 4). nl and m1 is also given. Initial configuration: 0000...0011111....111AA..... n zeros m ones Final configuration: XXXX...XXXXXXX...XXX2222..2AA... n+m X's fn,m) a) Explain how your machine works. b) Draw the state transition diagram of your machine. c) Give the execution chain for f(3,4)