solve: 5.3 For a direct-mapped cache design with a 32-bit address, the following

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5.3 For a direct-mapped cache design with a 32-bit address, the following bits of the address are used to access the cache. Index 9-5 Offset Tag 31-10 5.3.1 [5] What is the cache block size (in words)? -Since block size can be determined by the offset bits. In this question we have 4 offset bits (0-4), therefore we have 25 or 32 words in a block (basic binary problem). 5.3.2 [5] How many entries does the cache have? 5.3.3 [51 What is the ratio between total bits required for such a cache implementation over the data storage bits? Starting from power on, the following byte-addressed cache references are recorded Address 0 4 16 132 232 160 1024 30 140 3100 180 2180 considering a simple scenario with no dirty bit of valid bit for each line of the cache, we need 54 bits for tag field, and 32 words of suppose size w each. Therefore Total bits/Total data bits (54+32w)/(32"w). 5.3.4 [10] How many blocks are replaced? 5.3.6[10] What is the hit ratio? 5.3.6 [20]

Explanation / Answer

5.3.1:
What is the block size?
.........................

Block size = 2(number of offset bits)
= 25
= 32
In words = 8 words (1 word = 4 bytes)

5.3.2:
How many entries does the cache have?
........................................
No.of entries = 2(index)
= 25
= 32 entries

5.3.3:
What is the ratio between total bits required for such a cache implementation over the data storage bits?
.........................................................................................................

As per given data, tere are
Each block has 32 bytes of data = 256 bits + 22 bits of tag information + 1 valid bit

Starting from power on, the following byte-addressed cache references are recorded.

Address
0 4 16 132 232 160 1024 30 140 3100 180 2180

5.3.5:

What is the Hit ratio:
.......................
there are four cache hits out of 12 references. Hit ratio = 4/12 = 33%

5.3.6:

<00100, 0010, mem[2176]>
<00101, 0000, mem[160]>
<00000, 0011, mem[3072]>
<00111, 0000, mem[224]>

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