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# GATE | GATE-CS-2017 (Set 1) | Question 56

A cache memory unit with capacity of N words and block size of B words is to be designed. If it is designed as 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.

Note: This questions appeared as Numerical Answer Type.

(A)

12

(B)

14

(C)

16

(D)

18

Explanation:

Formula:

cache size=N words

No. of bits to address cache size =log2 N

Block size=B words

No. of bits to address block size =log2 N

No of blocks in cache=N/B

No. of bits  to represent blocks =log2 (N/B)

No. of sets in cache=(N/B)/16

No. of bits to represent sets=log2 (N/B)/16

For direct map cache,

For  associative map cache,

Calculation:

10 +log2 (N/B)=k+log2 (N/B)/16

10 +log2 (N/B)=k+log2 (N/B)/16-log2 16

10 =x-4

x=14, So no. of tag bits for 16-way set associative cache are14 bits.

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