Question

The tag for address 0xd1804 is ------- (hexadecimal). as many letters as tag width. cache size: 512bytes ways: 2 sets: 32` address width: 20 bits 1 kilobyte = 1024 bytes 1 megabyte = 1024 * 1024 bytes

a) 0xd1
b) 0xd18
c) 0xd180
d) 0xd1804

Answer 1

The tag for address 0xd1804 is 0xd1 (hexadecimal).

Step-by-step explanation:

The address width is given as 20 bits. To find the tag for address 0xd1804, we need to determine the tag width. The formula for calculating tag width is tag width = address width - index width - offset width. In this case, the index width is given as log base 2 (number of sets), and the offset width is given as log base 2 (block size). The cache size is given as 512 bytes, which is equivalent to 1 kilobyte. Therefore, the block size is 1 kilobyte divided by the number of sets.

Using the formula mentioned earlier, we can calculate the tag width as follows: tag width = 20 - log2 (32) - log2 (block size in bytes).

Substituting the values, the tag width is 20 - log2 (32) - log2 (1024/32) = 20 - 5 - 3 = 12 bits. Since the tag width is 12 bits and the address 0xd1804 is given in hexadecimal, the tag for that address is the first 3 digits, which is 0xd1 (option A).