A computer has a 256 KB, K-way set associative write-back data cache with block size of 32 B. The address sent to the cache controller by the processor is of 32 bits. In addition to the address tag,...

A computer has a 256 KB, K-way set associative write-back data cache with block size of 32 B. The address sent to the cache controller by the processor is of 32 bits. In addition to the address tag, each cache tag directory contains 2 valid bits and 1 modified bit. If 16 bits are used to address tag. What is the minimum value of K?