Consider a physical main memory$/$cache system with the following properties:

Main memory is byte addressable. Memory accesses are to $1-$byte words $($not $4-$byte words$).$ Main memory addresses are $13$ bits wide. Cache is $4-$way set associative $($E$=4),$ with a $4-$byte block size $($B$=4)$ and eight sets $($S$=8).$

The contents of the cache are as shown below, with all numbers given in hexadecimal.

$4-$way Set Associative Cache Index Tag V Bytes $0-3$ Tag V Bytes $0-3$ Tag V Bytes $0-3$ Tag V Bytes $0-30$ FO $1$ ED $320$A A$28$A $1$ BF $801$D FC $141$ EF $09862$A BC $025446$F $1$A $1$ BC $0033$E CD $38$ AO $0167$B ED $5$A BC $18$E $4$C DF $18$ E$41$ FB B$712022$ BC $1549$E $1$E FA B$61$ DC $81$ B$214000$ B$61$F $7$B $4474010$ F$5$ B$82$E $3$ BE $02$F $7$E $3$D A$8$ CO $12795$ A$474$ C$4007116$B D$8$ BC $0$ C$7$ B$7$ AF C$247$E $132211$C $2$C $8$A $122$ C$2$ DC $34$ BC $1$ BA DD $37$ D$8$ DC $0$ E$7$ A$239$ BA $5980$ A$9762$B EE $540$ BC $91$ D$59298180$ BA $9$B F$6$ BC $14816810$A $63805$D $4$D F$7$ DA BC $169$ C$28$C $748$A $1$ A$8$ CE $7$F DA $381$ FA $93$ EB $4878$A $1042$A $326$A $9$ E $0$ B$186560$E CC $1963047$ F$2$ BC $1$ F$81$D $4230$

a$.$ What is the size $($C$)$ of this cache in bytes?

Explain your answer below:

b$.$ The diagram below shows a $13-$bit main memory address. Identify the bits of the main memory address that constitute the following fields for addressing the cache:

CO cache block offset

Cl cache set index

CT cache tag c$.$ Suppose that the CPU reads a byte from main memory address $\backslash (0\backslash$times $071\backslash$mathrm$\{$~A$\}\backslash ).$

i$.$ Write the binary equivalent of the main memory address in the diagram below:

ii$.$ Fill in the table below for main memory address $\backslash (0\backslash$times $071\backslash$mathrm$\{$~A$\}\backslash ).$ All values should be given in hexadecimal.

d$.$ Suppose that the CPU reads a byte from main memory address $\backslash (0\backslash$times $16\backslash$mathrm$\{$E$\}8\backslash ).$

i$.$ Write the binary equivalent of the main memory address in the diagram below.

ii$.$ Fill in the table below for main memory address $\backslash (0\backslash$times $16\backslash )$ E$8.$ All values should be given in hexadecimal. c$.$ Suppose that the CPU reads a byte from main memory address $0$x$071$A$.$

i$.$ Write the binary equivalent of the main memory address in the diagram below:

ii$.$ Fill in the table below for main memory address $\backslash (0\backslash$times $071\backslash$mathrm$\{$~A$\}\backslash ).$ All values should be given in hexadecimal.

d$.$ Suppose that the CPU reads a byte from main memory address $0$x$16$E$8.$

i$.$ Write the binary equivalent of the main memory address in the diagram below.

ii$.$ Fill in the table below for main memory address $\backslash (0\backslash$times $16\backslash )$ E$8.$ All values should be given in hexadecimal.

e$.$ List all main memory addresses $($in hex$)$ that will result in a cache hit in set index $2.$