$4\mathrm{.}4$ For computers the machine epsilon $$ can also be thought as the smallest number that when added to one gives a number greater than l$.$ An algorithm based on this idea can be developed as Step $1$: Set $=1.$ Step $2$: If $1+$ is less than or equal to $1,$ then go to Step $5.$ Step $3$: $=/2.$ Step $4$: Return to Step $2.$ Step $5$: $=2$ x $.$ Write your own M$-$file based on this algorithm to determine the machine epsilon $.$Validate the result by comparing it with the value computed with the built$-$in function eps.