Construct Cache Details And Simulate Replacements Based On S

Construct cache details and simulate replacements based on specifications

Construct cache details and simulate replacements based on specifications

Given the following cache specifications: (S, E, B, m) = (4, 2, 2, 6) where S is the number of sets, E is the number of lines per set, B is the number of blocks per line, and m is the memory address length.

Perform the following tasks:

  1. Construct a block diagram of the cache.
  2. Identify the tag bits, set bits, and block offset bits for the address field.
  3. Initialize the cache with a last-in first-out replacement policy and show how the cache contents evolve as data is requested from addresses 0, 32, 17, 33, 22, and 9, indicating hits or misses after each access. Update the cache state accordingly, crossing out or rewriting lines when overwritten.

Paper For Above instruction

The task involves analyzing a cache with specific parameters and simulating its behavior under a sequence of memory accesses. The cache configuration specified is (S, E, B, m) = (4, 2, 2, 6). Here, S is the number of sets, E indicates that each set contains 2 lines (ways), B is 2 blocks per line, and m is the 6-bit address length. The goal is to understand the cache architecture, determine the division of address bits, and simulate cache performance with a FIFO replacement policy.

Constructing the Cache Block Diagram

The cache consists of four sets (since S=4), with each set containing two lines (E=2). Each line contains 2 blocks (B=2). The total number of blocks in the cache is S×E×B = 4×2×2 = 16 blocks. Structured as a multi-level hierarchy, each set is designed to allow block replacement under the FIFO policy.

Address Breakdown: Tag, Set, and Block Offset Bits

Given a total address length of 6 bits (m=6), we need to partition these bits into three fields: the tag, set index, and block offset. The block offset is determined by the number of blocks per line (B=2); thus, 1 bit (since 2 blocks per line require 1 bit). The number of sets is 4, so 2 bits are used for the set index. The remaining bits are used for the tag.

  • Block Offset Bits: 1 bit (since B=2)
  • Set Index Bits: 2 bits (since S=4)
  • Tag Bits: 6 - (2 + 1) = 3 bits

Therefore:

  • Tag bits: 3 bits
  • Set bits: 2 bits
  • Block offset bits: 1 bit

Initial Cache State and Data Structures

The cache is empty initially, with all valid bits set to 0. The cache structure can be visualized as:

Set Line 0 Valid Line 0 Tag Line 0 Blocks Line 1 Valid Line 1 Tag Line 1 Blocks
0            
1            
2            
3            

Each set contains two lines, each with a valid bit, a tag, and two blocks (B=2). Since initially empty, all valid bits are 0.

Memory Addresses and Cache Behavior

Address Requests: 0, 32, 17, 33, 22, 9

We analyze each address step-by-step. First, convert addresses to binary, extract bits for tag, set index, and block offset, then determine if the data hits or misses in the cache, updating contents following FIFO rules.

Address 0 (000000):

  • Binary: 000000
  • Tag (bits 5-3): 000
  • Set index (bits 2-1): 00
  • Block offset (bit 0): 0

Since cache is initially empty, this results in a miss. Line 0 of set 0 is loaded with tag 000, and it is marked valid.

Address 32 (100000):

  • Binary: 100000
  • Tag: 100
  • Set index: 00
  • Block offset: 0

Set 0 has one line with tag 000. No match; cache miss. Load set 0, line 1 with tag 100, applying FIFO which for now simply inserts since only one line has data.

Address 17 (010001):

  • Binary: 010001
  • Tag: 010
  • Set index: 00
  • Block offset: 1

Set 0 now has two lines with tags 000 and 100. Neither matches 010, resulting in a miss. Depending on FIFO, the oldest line (tag 000) is replaced with 010.

Address 33 (100001):

  • Binary: 100001
  • Tag: 100
  • Set index: 00
  • Block offset: 1

Set 0 has lines with tags 010 and 100. Tag 100 matches, so it's a hit; no replacement occurs.

Address 22 (010110):

  • Binary: 010110
  • Tag: 010
  • Set index: 01
  • Block offset: 1

Set 1 is initially empty, so cache miss occurs. Load with tag 010 into set 1, line 0.

Address 9 (001001):

  • Binary: 001001
  • Tag: 001
  • Set index: 00
  • Block offset: 1

Set 0 currently contains tags 010 and 100. Tag 001 does not match, leading to a miss. Applying FIFO, the oldest line (tag 010) is replaced by tag 001.

Summary of Cache Behavior

Throughout the sequence, misses and hits occur depending on whether the requested data's tag matches one in the identifier lines of the relevant set. FIFO replacement ensures oldest data is evicted when necessary, thus affecting subsequent hits or misses.

Repeating for the second cache configuration

For the second cache configuration with parameters (S, E, B, m) = (4, 1, 4, 6), the address bits distribution shifts as B=4 blocks per line, requiring 2 bits for the block offset. The set index remains 2 bits, and the tag length reduces accordingly.

The process of initialization, address breakdown, and simulation follows similarly, with updated bit divisions influencing cache replacement dynamics.

Conclusion

This exercise underscores the importance of cache architecture parameters in dictating performance. Understanding how S, E, B, and m influence address segmentation and replacement policies allows for optimized cache designs tailored to specific workloads. FIFO policies, as illustrated, provide simple and predictable behaviors, although more sophisticated algorithms (e.g., LRU) may enhance hit rates in certain scenarios.

References

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