20Suppose a computer using set associative cache has 218 byt

20.Suppose a computer using set associative cache has 2¹⁸ bytes of byte-addressable main memory and a
cache of 128 blocks, and each cache block contains 8 bytes.If this cache is 4-way set associative, what is the
size in bits of the tag field?.

Solution

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Answer:
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Given
   Set associative cache has 2^18 bytes of byte-addressable main memory
   Cache of 128 blocks
   Each cache block contains 8 bytes
  

   A four-way set implied 4 lines / set in the cache.
  
   ----------------------------------------------------------------
   Calculating total number of lines in the cache
   ----------------------------------------------------------------
       => Cache blocks * number of bytes in each block
       = 128 * 8
       = 1024 lines in the cache
      

   Therefore, The cache consists of 1024 lines/4 lines/set = 256 sets
   Threfore 8 bits are required to identify the set number.
  
  
   Given 2^18 bytes of byte-addressable main memory
   => 18-bit address is needed;

   Main memory consists of 2^18 byte/8 bytes = 2^15 blocks
  
   => The length of
          Tag + Set = 15
          Tag = 15-8
          Tag = 7  
         
   => Hence The length of tag field is 7 bits.
         

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