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Cache addressing: index length, block offset, byte offset, and tag?

Let's say I know the following values:

W = Word length (= 32 bits) S = Cache size in words B = Block size in words M = Main memory size in words

How to calculate how many bits are needed for:

 - Index - Block offset - Byte offset - Tag

a) in Direct Mapped Cache b) in a fully associative cache?

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The address can be divided into the following parts:

 [ tag | index | block or line offset | byte offset ]

The number of byte offset bits

0 for address memory, log 2 (bytes per word) for byte address memory

The number of bits to offset a block or row

log 2 (words per line)

The number of index bits

log 2 (CS), where CS is the number of cache sets.

  • For a complete association, CS is 1. Since log 2 (1) is 0, there are no index bits.
  • For Direct Mapped CS is CL, the number of cache lines, so the number of index bits is log 2 (CS) === log 2 (CL).
  • For n-way associative CS = CL ÷ n: log 2 (CL ÷ n) index bits.

How many cached lines can you calculate by dividing the cache size by block size = S / B (assuming that both of them do not include the size for the tag and the actual bits).

Tag bits

Address length minus the number of bits used for offset (s) and index. The length of the addresses can be calculated using the size of the main memory, for example. any byte must be addressed if it is an address byte memory.

Source: http://babbage.cs.qc.edu/courses/cs343/cache_parameters.xhtml

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