Solved Homework: Question: 2. a) A programmer wants to design a random number generator using 32-bit unsigned integer repres…

2. a) A programmer wants to design a random number generator using 32-bit unsigned integer representations. Would this give a fair distribution of pseudo-random numbers? Explain your answer.

2. a) A programmer wants to design a random number generator using 32-bit unsigned integer representations. Would this give a “fair” distribution of “pseudo-random” numbers? Explain your answer.

Expert Answer


I believe I can answer in plain language. The way that computer programs typically get random numbers is through a combination of two important devices 1. Get the system time as the random number seed. This begins a sequence of numbers 2. Use a pseudo-random number generator once a sequence has been started by (1), so that the relationship between one number and the next in the sequence is not detectable. This is done by applying a complex mathematical transformation You need both these things, for good reasons. Just one or the other by itself wont cut it When you get the system time in milliseconds, Im assuming - youre getting a number that is gradually increasing, but as a typical human (Im assuming youre not Superman and youre not carrying a special device to measure time in milliseconds), youll be unable to predict what the last few digits are.Then, the psuedo-random generator transforms that seed into the next number in the pseudo random sequence This pseudo-random generator creates a kind of Butterfly Effect. Simply put, tiny differences between the starting seed values (the system time, remember) result in huge, unpredictable differences in the second item in the sequence produced by the algorithm. That second item can then be used as the first random number. And thats how a computer programs produce random numbers! They are random in the sense that they defy human prediction and human ability to detect patterns The numbers are not random in principle. However, they defy any predictability that could be observed by all but a very few humans The initial number produced depends on the precise number returned by the system time function But as the system time changes by even the smallest amount, this results in arbitrarily large changes in the 2nd number in the random series The random series itself is deterministic, but reverse engineering the series is deliberately made exceptionally difficult by the nature of the algorithm, which is a complex mathematical transformation that eludes obvious patterns So, for example, nothing so obvious as odd/even/odd/even will emerge from a good random-number generator Note that the randomness, which holds for all practical purposes, depends on both the seed from system time, as well as having an adequate algorithm to get the next number in the sequence. If the same seed were used during

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