Cache capacity =N words
Block size= B words,bits for block offset=log(B)
No of lines in Direct Mapped cache =N/B,bits for no. of lines=log(N/B)
No of Sets in 16-way set associative cache=N/16B,,bits for no. of sets=log(N/16B)
In direct mapped length of tag =10 bits
Length of PHYSICAL ADDRESSES :-
DIRECT-MAPPED
TAG-10 |
LINE.NO:-LOG(N/B) |
BLOCK OFFSET:-LOG(B) |
16-WAY SET ASSOCIATIVE
TAG-X |
SET.NO-LOG(N/16B) |
BLOCK OFFSET:-LOG(B) |
As Physical address is same for both cache mappings,
10+LOG(N/B)+LOG(B)=X+LOG(N/16B)+LOG(B)
10+LOG(N/B)=X+LOG(N/16B) //AFTER CANCELLING LOG(B)
2^(10+LOG(N/B))=2^(X+LOG(N/16B)) //EXPONENTIATION WITH 2 ,BOTH SIDES
(2^10) *(N/B)=(2^X) *(N/16B)
(2^10) =(2^X) *(1/2^4)
2^14=2^X
X=14 //APPLYING LOG TO BOTH SIDES