Given the following two binary numbers: 111111002 and 011100002. a) Which of these two numbers is the larger unsigned binary number? b) Which of these two is the larger when it is being interpreted on a computer using signed-two's complement representation? c) Which of these two is the smaller when it is being interpreted on a computer using signed-magnitude representation?

You have to run Prim's algorithm for the problem defined by adjacency matrix: 1 2 3 4 5 6 7 8 9 1 0 10 9 999 999 17 999 999 999 2 3 69 10 0 14 4 2 999 999 13 999 14 0 7 999 999 999 999 999 4 999 4 7 0 999 2 8 999 999 5 999 2 999 999 0 6 999 1 999 6 17 999 999 2 6 0 999 7 999 7 999 999 999 8 999 999 0 11 4 8 999 13 999 999 1 7 11 9 999 999 999 999 999 999 4 80 8 0 1. We started from the vertex vl, so initially we have Y = {v1}: initial 1 2 3 4 5 6 7 8 9 nearest 1 1 1 1 1 1 1 1 1 distance -1 10 9 999 999 17 999 999 999 Print out the values stored in the nearest and distance arrays after first iteration of Prim's algorithm. Specify the value of vnear and the next vertex that has to be added to Y Hint: use (copy) the table above to record your answer.

Given 5 rocks of different weight and lever scales, in 7 tests sort the rocks by weight.

Find the maximum value of the following function F(x)=2x3 , using the genetic algorithm, performing two iterations.

suppose a,b, and c are odd integers. Prove that a+b+c is odd

5. Let a, b CZ so that 4a + 56 is a multiple of 13. Prove that 13 divides 9a +-8b.