There are 8 cache lines and block address is of 8-bits. What is the maximum value of the tag?

Question

BlackTom AI · Accepted Answer

First, identify the components of the memory address in a cache organization. The total address width is 8 bits. The cache has 8 lines, which requires log2(8) = 3 bits for the index to select a cache line. The remaining bits are used for the tag, while the block offset bits depend on the block size.

To maximize the tag value, consider the smallest possible block size, which means the block offset requires 0 bits (block size of 1 word). In this case, there are no offset bits, so all of the remaining bits beyond the index are used for the tag.

Compute the tag bits: total address bits (8) minus index bits (3) minus offset bits (0) = 8 - 3 - 0 = 5 tag bits.

A 5-bit tag can represent values from 0 to 2^5 - 1, i.e., 0 to 31. Therefore, the maximum possible value for the tag is 31.

If the block size were larger (adding offset bits), the number of tag bits would decrease accordingly, reducing the maximum tag value from 31.

There are 8 cache lines and block address is of 8-bits. What is the maximum value of the tag?

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