A 4-way set-associative cache memory unit with a capacity

A 4-way set-associative cache memory unit with a capacity of 16 KB is built using a block size of 8 words. The word length is 32 bits. The size of the physical address space is 4 GB. The number of bits for the TAG field is _____.

Physical address size = 32 bit
Cache size = 16k bytes = 2¹⁴ bytes
block size = 8 words = 8 × 4 byte = 32 byte

No. of blocks =	2¹⁴	= 2⁹
	2⁵

block offset = 9 bits

No. of sets =	2⁹	=	2⁹	= 2⁷
	4		2²

set offset = 7 bits
Byte offset = 8 × 4 bytes = 32 bytes = 2⁵
⇒ 5 bits
TAG = 32 – (7 + 5) = 20 bits