For a 9 bit block address; tag value range is [0,31]. How many cache lines are there in the cache?

Question

BlackTom AI · Accepted Answer

The problem provides a 9-bit block address and a tag value range of [0, 31].
First, note that the tag range 0–31 corresponds to 32 distinct values, which is 2^5. This means the tag field uses 5 bits.
In a typical cache address decomposition, the block address is split into tag, index, and block offset bits. Since the total block address length is 9 bits and the tag occupies 5 bits, the remaining bits are allocated to the index and the block offset. Assuming the block offset within a cache block is zero (i.e., we’re working with the block address length and not the full address with an offset), the index bits are 9 − 5 = 4 bits.
The number of cache lines is determined by the number of possible index values, which is 2^(number of index bits) = 2^4 = 16.
Therefore, there are 16 cache lines in the cache.

For a 9 bit block address; tag value range is [0,31]. How many cache lines are there in the cache?

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