The size of the physical address space of a processor is 2⁴⁰ bytes. The capacity of cache memory is 512 Kbytes. The word length is 32 bytes. The size of each cache block is 16 words. For a 16-way set-associative cache memory, the length (in number of bits) of the tag field is _______________ .
(A) 21
(B) 8
(C) 16
(D) 25


Answer: (D)

Explanation: Given physical address space = 40 bits,
Cache memory size = 512 Kbytes = 2¹⁹ bytes,

The word length is 32 bytes, and size of each cache block is 16 words. So, word offset is

= 32*16 bytes 
= 512 bytes 
= 29 bytes 

Line offset is,

= 219 bytes / 29 bytes
= 210 

So, set offset is,

= 210 / 16
= 210 / 24
= 26
= 6 bits 

Hence, the length (in number of bits) of the tag field is,

= 40 - 6 - 9
= 25 bits 

Option (D) is correct.

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