J. Dichter Random Generator Program CS 501X Universit

J. Dichter Random Generator Program CS 501X University of Bridgeport Instructions: You will write a program to generate a series of pseudo random numbers, using a linear feedback shift register method. You will start with an arbitrary number (not zero) x with a representation in n bits. If x = 15 and n = 4, then x = 1111. Then you will select a pair of bits, say bits 0 and 1, take their “xor” producing a new bit -in this case a 0. The number x will then shift to the right, with the new bit becoming the new high bit -in this case 0111. The process continues in this manner to produce a random set of bits. With four bits, we can only have up to 15 unique transitions before repetitions begin, or 2n -1. With n = 32, the number of random bits has a much greater potential. The numbers actually produced by the “shifting” cannot be considered “random”, since all but one of the bits overlap from each succeeding number. However, if we want to produce, say 100 6-bit numbers, then we need to shift the bits into an 6-bit register. We can then save its “value” in an array of 100 integers. Then we should produce the output which will display the distribution. Random numbers should follow a uniform distribution. Using a 32-bit generator does not guarantee 2n -1 random bits. For good results try using bit combinations 0/4, 0/7, 0/25, 0,26, 0/29. Example: 11001110 -> 11100111 -> 01110011 -> 10111001 -> 11011100 -> 11101110 -> 11110111 -> 01111011 -> 10111101 -> 01011110 -> etc Three random 4-bit numbers produced: 11, 13, 4, …. Try “tapping” different bit combinations, as well as the ones I suggested. To verify that the set of numbers you generated are really pseudo random, you will test them using the statistical ? 2 test. You will generate 10,000 numbers in the 0-63 range. Then N=10,000 and r=64. You will then compute ?2 by the formula If ?2 is in the range of r ± 2 r , we conclude that distribution is indeed random. Otherwise it may not be. In your progr