Question

Consider a set-associative cache of size 2 KB (1 KB = 2¹⁰ bytes) with cache block size of 64 bytes. Assume that the cache is byte-addressable and a 32-bit address is used for accessing the cache. If the width of the tag field is 22 bits, the associativity of the cache is _______

Answer 1

Data:

Main memory size (MM) = 232 B (32 bit address)

Cache Memory Size (CS) = 2 KB = 211 B

Block Size (BO) = 64 B = 26 

Tag = 22 bits

Set Associative Mapped Cache:

let 2^x - way set associative mapping

\(number~of~lines=\frac{{{2}^{11}}}{{{2}^{6}}}={{2}^{5}}\)

\(number~of~sets=\frac{{{2}^{5}}}{2^x}={{2}^{5-x}}\)

Formula: To find number of bits in tag in set associative mapping

MM = tag + set + BO

32 = 22 + 5 - x + 6

∴ x = 1

Therefore it is 21 - way set associative mapping

The associativity of the cache is 2.