LC$-3$: Random Number Generator $(50$ points$)$

Random numbers are an important concept in computer science because they are often used

to simulate real$-$world events. For example, in a game of chance, random numbers are used to

determine the outcome of the game. In a computer simulation, random numbers are used to model

the uncertainty of the system being simulated. Additionally, random numbers are used in many

security applications, such as generating secure cryptographic keys and simulating user behaviour

for testing purposes. Overall, the ability to generate random numbers allows computers to model

and analyse complex, uncertain systems, making them a fundamental tool in computer science.

However, computers can$$t just randomly generate numbers. They can make use of events of nature

that appear to be random $($or at least, infeasibly hard to trace a pattern$),$ but what also happens

regularly is that they use so$-$called pseudo$-$random number generators. An example of such a

pseudo$-$random number generator where each number can be defined from the previous number can

be seen in Equation $1,$ given the three non$-$negative integers a$,$ b$,$ and m$.$

Xn $=($aXn$1+$ b$)$ mod m $(1)$

$3$

Computer Architecture Homework $5$

Lastly, we need to define the initial number, X$0.$ For this, computers usually take some noise, like

the current time, but for your case, we will provide you with some artificial noise in the form of a

few random characters $($or maybe a few dozen$).$ Another name for this initial number X$0$ is the seed.