Question

Targeted Course Learning Outcomes: CLO 2.1

Question 1: Using the “Direct Mapped Cache”, assume that

• 4-blocks, 1 word/block, direct mapped
• Initial state is empty as shown below.

Index	V	Tag	Data
00	N
01	N
10	N
11	N

And the following addresses have been requested in the following sequences:

Request 1: Word Addresses 4, 5 and 7

Request 2: Word Addresses 0, 1 and 3

Request 3: Word Addresses 1, 2 and 3

Request 4: Word Addresses 3, 4 and 6

1. Show the cache state Before and After each time that addresses have been requested.
2. Calculate the Hit Ratio and Miss Ratio.

Hint: Follow the example in the next page and fill up all missing data accordingly and calculate the Hit and Miss ratios.

Request 1:

Word addr	Binary addr	Hit/miss	Cache block
4	100	Miss	00
5	101	??	??
7	??	??	??

Before	After
Index V Tag Data 00 N 01 N 10 N 11 N	Index V Tag Data 00 N 01 N 10 N 11 N

Request 2:

Word addr	Binary addr	Hit/miss	Cache block
0	??	??	??
1	??	??	??
3	??	??	??

Before	After
Index V Tag Data 00 ?? ?? ?? 01 ?? ?? ?? 10 ?? ?? ?? 11 ?? ?? ??	Index V Tag Data 00 ?? ?? ?? 01 ?? ?? ?? 10 ?? ?? ?? 11 ?? ?? ??

Hit Ratio :

Miss Ratio :

Answer 1

Total # of block inside cache = 4. Therefore index offset =2 (Least Significant 2 bits since block offset is 0)

Tag (1 bit)

Index Offset (2 bit)

Word Offset (0 bits)

Requesr 1:

Word Address	Binary Address	Hit/miss	Cache block
4	100	Miss	00
5	101	Miss	01
7	111	Miss	11

After Index	Valid	Tag	Data		After Index	Valid	Tag	Data
00	N				00	V	1	4
01	N				01	V	1	5
10	N				10	N
11	N				11	V	1	7

Request 2:

Word Address	Binary Address	Hit/miss	Cache block
0	000	Miss	00
1	001	Miss	01
3	011	Miss	11

After Index	Valid	Tag	Data		After Index	Valid	Tag	Data
00	V	1	4		00	V	0	0
01	V	1	5		01	V	0	1
10	N				10	N
11	V	1	7		11	V	0	3

Request 3:

Word Address	Binary Address	Hit/miss	Cache block
1	001	Hit	00
2	010	Miss	10
3	011	Hit	11

After Index	Valid	Tag	Data		After Index	Valid	Tag	Data
00	V	0	0		00	V	0	0
01	V	0	1		01	V	0	1
10	N				10	V	0	2
11	V	0	3		11	V	0	3

Request 4:

Word Address	Binary Address	Hit/miss	Cache block
3	011	Hit	11
4	100	Miss	00
6	110	Miss	10

After Index	Valid	Tag	Data		After Index	Valid	Tag	Data
00	V	0	0		00	V	1	4
01	V	0	1		01	V	0	1
10	V	0	2		10	V	1	6
11	V	0	3		11	V	0	3

Total # of reference = 12

Total # of miss reference = 9

Total # of hit reference = 3

Therefore miss ratio= # of hit reference/ Total # of reference = 9/12=0.75

Hit ratio = # of hit reference/ Total # of reference = 3/12 =0.25

If you have any doubts, comment down. Also please upvote, thanks.