Question

(1 point) This question is required to receive an A+ in the course. This question contains two problems: one focussed on Computer Science, and one focussed on Mathematics. You only need to do ONE of the problems. If you choose to do both, then the best answer will be used for assessment. You do not need to do the problem corresponding to the course number you're registered in. For instance, if you are registered in MATH 2112, you may do the Computer Science problem instead of the Mathematics problem. [10 Marks] Problem a) Computer Science Focus: Let B – {0,1} and B" BBX...B. We provide four functions: and : BB → B. or: BB B, xor : B x B → B, and not: BB which corresponds to the boolean conjunction, disjunction, exclusive-or and negation operations. Define an n-bit addition in > 0) function f that takes 3 inputs such that it adds n- bits together, i.e. f(n, ay, Core 1...21, bubre 1...b) = $.$r 1. . . $1 such that any 1...01, br br 1...b1,5$ r1. . . $ 13", and SS 1... $1 is the binary addition of a,an-1...a and bubn-1...b. For example, f(3,001, 100) should return 101, and f(4,0111, 0001) should return 1000. Note that f takes 3 inputs; the first input is indicating the length of the bit addition. You can only use the four boolean functions and recursion to define f and auxiliary functions. Problem b) Mathematics Focus: Consider the integers 273, 110, 100, and 103. Using the pigeonhole principle, show that there exists an integer a such that x = 273p + 100 and x = 110q+ 103 for some integers p and q.

Answer 1