Consider a computer system with $2$K byte addressable main memory which is grouped into blocks of $64$ bits each. Assume that a cache of $64$ bytes is used in this system.

$($a$)$

$($i$)$

Calculate the address width to address all the locations within the main memory.

$(2$ marks$)$

$($ii$)$

For direct mapped cache, determine the values of the tag, line and words fields.

$(6$ marks$)$

$($b$)$

When a given program is executed, the processor reads data from the following sequence of hexadecimal addresses:

$18$A

$375$

$64$B

$12$E

$12$E

$5$CF

$569$

$491$

$18$A

$569$

$366$

$0$FA

$4$C$4$

$4$C$4$