Page 53 - Computer_Science_F5

Computer Science (a) Direct mapping
Each block of main memory maps to a single, specific cache line. The formula used is:
Cache line number = (Address of the main memory block)modulo (Total number of lines in cache)
For example: For a cache with 8 lines and a main memory block address of 29, the
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calculation is 29 % 8 = 5. Thus, block 29 maps to cache line 5.

Consider a cache memory in Figure 1.42 with direct mapping. The cache memory
is divided into ‘n’ lines. Then, block ‘m’ from the main memory can map to line
number (m mod n) in the cache.

Tag Line 0 Block 0
Tag Line 1 Block 1

Tag Block m
Tag Line (m mod n) Block m+1

Cache Block m+2
Main memory
Figure 1.42: Direct mapping

In direct mapping, the cache address is divided into three parts: tag, line number,
and block offset. As shown in Figure 1.43, the tag uniquely identifies the cache line
where the data block resides, indicating if the desired data is in the cache or needs
fetching from main memory. The line number locates the cache line, and the block
offset pinpoints the exact data location within the block. This process is similar to
main memory addressing.
Memory address from processor
Tag Line number/
index

Cache memory

1

Line number/ Tag Block/line
offset
3 index
Read
2
Compare
Same Different
5 Cache miss Access main memory if
tag do not match
4 Cache hit
Access location

1 Figure 1.43: Direct mapping process
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Computer Science Form 5.indd 44 23/07/2024 12:32