1. (a) an algorithm to convert base 2 number string b4b3b2b1.d1d2 (Please note the numbers d1 and d2 are the numbers after the point in the string.) into decimal.

(b) trace table of the algorithm for the binary number 1011.012.

c) Let x be any one of the four students in a college. Tam attended only Lecture 1. Ramie attended both Lecture 1 and Lecture 2. Vim attended only Lecture 2. Sam attended neither of the Lectures. Let F(x) be "x attended Lecture 1" and B(x) be "x attended Lecture 2", where x denotes one of the above students. Rewrite the following statements in simple English sentence and use above information to determine its truth values. (a) x such that F(x) B(x). (b) x, F(x) B(x) (c) x such that (F(x) B(x))

d) Prove that if x2+2 is even then x is even.