GATE CS 2017 Set 2 Q53 — Memory Hierarchy: Cache, Main Memory and Secondary Storage

In a direct-mapped cache, the physical address is divided into three fields:

[ Tag ] [ Line Index ] [ Block Offset ]

Let's calculate the size of each field based on the given parameters:

1. Total Physical Address Bits:
   The main memory is byte-addressable and has a size of $2^{32}$ bytes.
   $$\text{Physical Address Size} = \log_2(2^{32}) = 32\text{ bits}$$
2. Block Offset Bits:
   The block size is $32$ bytes.
   $$\text{Block Offset} = \log_2(32) = 5\text{ bits}$$
3. Line Index Bits:
   The cache has $512$ cache lines.
   $$\text{Line Index} = \log_2(512) = 9\text{ bits}$$

Now, we can find the size of the tag field:

Thus, the size of the tag field is 18 bits.