Given The Cache Specifications: (S, E, B, M) ✓ Solved

Given The Following Cache Specifications: (S, E, B, m)

1. (25 points) 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.

a. Construct a block diagram of the cache.

b. Identify the tag bits, set bits and block offset bits for the address field.

c. The cache replacement policy is: Last-in First-out. Step 1: Initial State Define the initial structure and state of the cache as done in class. The # of rows in the table below must be changed to fit your cache model.

Set Line Valid Tag Block 0 Block 1 Step 2: Read Address 0 Show how the cache contents change as the processer requests data from the following memory locations: 0, 32, 17, 33, 22, 9. Comment whether you have a cache hit/miss after each read. Data at Address x is referred to as m[x] If a cache line has to be overwritten, cross out the old line and write the new one or draw a new table.

2. (25 points) Repeat Q1 for the following cache specifications: (S, E, B, m) = (4, 1, 4, 6) Basically, answer any and all case questions you like.

Format preference is Arial 10 font, 1.5 spacing. There's no need to repeat the case questions; just answer them. Try to fill up one complete page with your analysis (target a word count of 500 or more). Sometimes the case will be too short and you will not be able to do this easily. Still, try to write all you can.

Finally, for full credit on your report, be sure to upload your report BEFORE the beginning of the class where we discuss the case.

Paper For Above Instructions

## Introduction

Understanding cache memory is crucial in the design of efficient computer systems. A cache is a small, fast storage location that holds copies of frequently accessed data from main memory, thereby reducing the average time to access data from the main memory. In this analysis, we will explore the cache configurations provided in the assignment. This includes building a block diagram, identifying the bits for memory addressing, simulating the changes to the cache as data is requested, and understanding the implications of different cache parameters.

## Cache Specifications (S, E, B, m) = (4, 2, 2, 6)

Given the cache parameters:

• Number of Sets (S): 4
• Lines per Set (E): 2
• Blocks per Line (B): 2
• Memory Address Length (m): 6 bits

The number of sets indicates how many independent sections exist within the cache, while the lines per set suggest the number of 'slots' available for storing blocks of data. Each block in this case carries two memory addresses, allowing for efficient storage and retrieval.

### Block Diagram Construction

To construct the block diagram of the cache, we recognize that:

• Memory Address = Tag + Set + Block Offset
• Tag Bits = m - (log2(S) + log2(B))
• Set Bits = log2(S)
• Block Offset Bits = log2(B)

Calculating the bits based on our parameters:

• Set Bits = log2(4) = 2 bits
• Block Offset Bits = log2(2) = 1 bit
• Tag Bits = 6 - (2 + 1) = 3 bits

Thus, the memory address would be organized as follows:

| Tag (3 bits) | Set (2 bits) | Block Offset (1 bit) |

### Initial Cache State

The initial cache state can be represented in a simple table format:

### Cache Operations

The processor will request data from the memory locations: 0, 32, 17, 33, 22, and 9. We will assess whether each request results in a cache hit or miss. For each address, calculate the tag, set, and block offset:

• Address 0: Tag = 000, Set = 00, Block Offset = 0; Miss (load into cache)
• Address 32: Tag = 100, Set = 00, Block Offset = 0; Miss (load into cache)
• Address 17: Tag = 010, Set = 01, Block Offset = 1; Miss (load into cache)
• Address 33: Tag = 100, Set = 01, Block Offset = 1; Miss (load into cache)
• Address 22: Tag = 010, Set = 10, Block Offset = 0; Miss (load into cache)
• Address 9: Tag = 001, Set = 00, Block Offset = 1; Miss (load into cache)

With each read, since we are using a Last-in First-out policy, any overwrites will replace the most recently loaded entry in the cache.

## Cache Specifications (S, E, B, m) = (4, 1, 4, 6)

Following the similar structure above for the next specification, we set parameters:

• Number of Sets = 4
• Lines per Set = 1
• Blocks per Line = 4
• Memory Address Length = 6 bits

Here, we have a different setup, whereby each set can only hold one entry, but that entry can contain more data (4 blocks). The organization of memory remains the same: Tag + Set + Block Offset.

### Conclusion

The efficiency of a cache can significantly affect overall system performance. By analyzing different cache configurations, we gain insights into memory access patterns and replacement policies. Understanding these elements helps in designing robust systems capable of efficiently managing data storage and retrieval, ultimately enhancing performance.

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