A cache memory unit with capacity of N words and block size

A cache memory unit with capacity of N words and block size of B words is to be designed. If it is designed as a direct mapped cache, the length of the TAG field is 10 bits. If the cache unit is now designed as a 16-way set-associative cache, the length of the TAG field is______ bits.

In Direct Mapped :

No. of line in direct mapped cache =		N		bits
		B

For No. of line = log		N
		B

In Set Associative :

TAG₁ + log		N		+ log(B) = TAG₂ + log		N		+ log(B)
		B				16 B

By cancelling the same terms
As given that
TAG₁ = 10 bits for Direct Mapping.
TAG₂ let say X bits.

Then , 10 + log		N		= X + log		N
		B				16 B

By taking exponentation both side w.r.t 2.

(2^{^10})*		N		= (2^{^X})*		N
		B				16 B

(2^{^10}) = (2^{^X})		1
		16

(2^{^10}) = (2^{^X})		1
		2^{^4}

(2^{^14}) = (2^{^X})

X = 14

So, the required length of TAG field in Set Associative mapped is = 14.