Question

3) Direct-Mapped Cache Determine the Cache line holding an address EEL 3801 UCF Given: An 8-bit computer system with 4 MB of main memory. It has a 16K-words direct-mapped cache with a block size of 16 Bytes. Sought: Calculate the cache line number when Byte address 5678ten from main memory is mapped to cache. Consider that numbering of main memory blocks and cache lines starts from zero. Express your answer in hexadecimal. It is required to show ALL incremental steps of the solution.

Answer 1

Since this is a 8-bit computer, so the word-size is also 8 bits = 1 byte.

Now, each cache-block/cache-line contains 16 = (2⁴) bytes, so the lowest 4 bits of the physical address are used to denote the byte-offset in cache-block/cache-line.

Also, total cache size is 16K (= 2¹⁴) words = 2¹⁴ bytes.

Thus, total number of cache blocks/lines

= (total cache size) / (size of one cache block)

= 2¹⁴ / 2⁴

= 2¹⁰

Thus, the next 10 bits of the physical address denote the cache-block/cache-line.

Writing 5678_ten in binary, we get

0001 0110 0010 1110

Thus, the cache line number is given by (bolded bits)

= binary 01 0110 0010

= decimal 354

= 0x162