Question

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 address2271len 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

This is what we are going to do.

• We will calculate the number of blocks inside the cache.
• Then we will use the modulo formula of the direct mapping to see where the block is going to be mapped.

Word size = 1B
Cache size = 16k words = 2¹⁴ words
Block size = 16B = 16 = 2⁴ words

Number of blocks = (Cache size) / (Block size) = (2¹⁴) / (2⁴) = 2¹⁰

In a direct mapping, the block in which the byte is going to be transferred can be determines using the formula XmodY where X is the byte address and Y is the size of the cache respectively.
The given byte address is (2271)₁₀
Therefore (2271)mod 2¹⁰ = 2271 mod 1024 = 223

It means, the byte at address 2271 is going to be placed at block number 223 of the cache which is hexadecimal is equivalent to 0xDF.