Gate2020 cs Q25

25A direct mapped cache memory of 1 MB has a block size of 256 bytes. The cache has an access time of 3 ns and a hit rate of 94%. During a cache miss, it takes 20 ns to bring the first word of a block from the main memory, while each subsequent word takes 5 ns. The word size is 64 bits. The average memory access time in ns (round off to 1 decimal place) is _______.

Note – Numerical Type question

Option : B
Explanation :
Cache Memory = 1 MB
Word size = 64 bit = 8 B
Block size = 256 B
Hit rate, x = 0.94 miss rate= 1-x = 0.06
Cache access time, Tc = 3ns
Number of words / Block = 256/8 = 32
Using Hierarchical Approach,
Tavg= ( x.Tc ) + (1-x)[ Tc + 1st word access time + remaining word access time]
Tavg = (0.94 × 3) + (1 – 0.94) [3 + 20 + (31 × 5)]
Tavg = 13.5 ns

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