Problem $1$:

Caches are important to providing a high$-$performance memory hierarchy to processors.

Below is a list of $32-$bit memory address references, given as word addresses.

$3,180,43,2,191,88,190,14,181,44,186,253$

Problem $2$:

Consider the following parameters of a virtual memory system:

Virtual Address $($bits$)$: $43$

Page Size: $4$ KB

PTE Size $($byte$)$: $4$

How much physical memory is needed for storing the page table?

Problem $3$:

Mean Time Between Failures $($MTBF$),$ Mean Time To Replacement$/$Repair $($MTTR$),$ and Mean Time To Failure $($MTTF$)$ are useful metrics for evaluating the reliability and availability of a storage resource. Explore these concepts by answering the questions about devices with the following metrics:

MTTF: $3$ Years

MTTR: $1$ Day

a$)$ Calculate the MTBF for each of the devices in the table.

b$)$ Calculate the availability for each of the devices in the table.

c$)$ What happens to availability as the MTTR approaches $0?$ Is this a realistic situation?

d$)$ What happens to availability as the MTTR gets very high, i$.$e$.,$ a device is difficult to repair? Does this imply the device has low availability?