Cache Parameters

There are many parameters that can vary in the design of a cache memory system, but many of them can be derived from other ones. For example, looking at the first two tables below, if you know the number of bytes per word and the number of words per block, you can calculate the number of bits per word, the number of bytes per block, and the number of bits per block.

On symbols: I’ve always thought that obscure symbols were an evil ruse on the part of mathematicians to make simple concepts difficult to understand. So I’ve tried to use mnemonic symbols as best I can here. Everything is uppercase except b (for bits) and B (for bytes), a common convention. I used a lowercase L in PBl because there were no more variants on the latin letter 'B' for distinguishing among bits, bytes, and blocks, and I didn’t want to go the evil mathematician route by introducing a letter from some other alphabet.

Also, I used the term “primary memory” as the basis for the symbols that refer to what is commonly called “main memory” to avoid confusion with the prefix letter M used for Mega.

Primary Memory Capacity

Capacity can be measured in bits, bytes, words, or blocks.
Bits	Pb	total capacity, in bits
Bytes	PB	total capacity, in bytes
Words	PW	total capacity, in words
Blocks	PBl	total capacity, in bocks

Capacity Ratios
Pb ÷ PB	bits per byte: always 8
PB ÷ PW	bytes per word
PW ÷ PBl	words per block

Cache Capacity

Bits	Cb	cache capacity, in bits
Bytes	CB	cache capacity, in bytes
Words	CW	cache capacity, in words
Lines	CL	number of cache lines
Sets	CS	number of cache sets

Ratios
Cb ÷ CB	Same as Pb ÷ PB (8)
CB ÷ CW	Same as PB ÷ PW
CW ÷ CL	Same as PW ÷ PBl
CL ÷ CS	Set Size (n)

Set Size = Lines per Set (n)
n == 1	Direct Mapped
n == CL	Fully Associative
1 < n < CL	n-way Set Associative

Bit fields in a Primary Memory address, from left-to-right

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

Total number of bits is A, the number of Primary Memory Address bits.

A == tag + index + block or line offset + byte offset

Number of byte offset bits is zero for word-addressable memory.
Number of byte offset bits is log2(bytes per word) for byte addressable memory.
Number of block or line offset bits is log2(words per line)
Number of index bits is log2(CS), where CS is the number of sets.
- For Fully Associative, CS is 1. Since log2(1) is 0, there are no index bits.
- For Direct Mapped, CS is equal to CL, the number of lines, so the number of index bits is log2(CS) === log2(CL).
- For n-way Associative CS = CL ÷ n: log2(CL ÷ n) index bits.
Number of tag bits is A - (index + line offset + byte offset)

Cache parameters are always powers of two, so log2(whatever) is always an integer. No need to use ceil(log2(whatever)).