Cache Miss and Mapping Function
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Direct-Mapped Cache Structure
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Welcome, everyone! Let's start today's discussion by understanding the structure of a direct-mapped cache. Can anyone tell me what a cache line is?
Is it the smallest unit of data that can be stored in the cache?
Correct! A cache line holds a block of data. Each memory address is divided into three parts: the tag, index, and word offset. The index determines which cache line we will access.
How do we know if the data we need is in the cache?
Good question! We check the tag in the cache line corresponding to the index. If it matches the tag from our memory address, that’s a cache hit!
What happens if there is no match?
That is called a cache miss. In this case, we go to main memory to fetch the required data and may replace the existing data in the cache line.
So, the tag plays a crucial role in identifying data?
Exactly! Always remember: Tag = Match means cache hit, otherwise it's a miss. Let's summarize: A direct-mapped cache has cache lines identified by indices, and tags are essential for ensuring data integrity.
Understanding Hits and Misses
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Now that we've covered the basics, let’s look at some examples. If we access the address 22, what's the first step?
We convert it to binary to see what it looks like.
Correct! The binary for 22 is 10110. Which parts can we identify?
I think the last 3 bits represent the cache line, while the first bits are the tag!
Exactly! What do we do next if the cache is initially empty and we access address 22?
We have a miss and need to load address 22 into the cache.
That's right! It goes to the corresponding line based on the index, and we store the tag as well. Let’s review: A cache hit means we retrieve data directly, while a miss means fetching from memory.
Calculating Cache Bits
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Next, let’s calculate the total number of bits in a cache. Suppose we have a 16 KB cache with 4-word blocks. How do we start?
First, we need to figure out how many words fit in the cache!
Right! Since 16 KB is 16,384 bytes, and each word is 4 bytes, we have 4K words in the cache. How many lines do we have?
That's 4K divided by 4 words per line, which gives us 1K lines!
Perfect! Now, if each line needs 18 bits for the tag and 1 bit for valid, how many bits are needed for data?
It's 4 words multiplied by 32 bits, which is 128 bits for data.
Excellent! So, the total bits in the cache would be calculated. Remember this method; it’s valuable for assessing cache sizes! To summarize, always check the cache line size and the number of lines to calculate total cache bits.
Introduction & Overview
Read summaries of the section's main ideas at different levels of detail.
Quick Overview
Standard
The section explains how a direct-mapped cache works, highlighting the critical terms such as cache lines, tags, and the lookup process for hits and misses. It also provides detailed examples to clarify the mapping of addresses and caching mechanics.
Detailed
Detailed Summary
This section delves into the organization of a direct-mapped cache. A key principle in cache design is that memory addresses comprise two parts: tags and data. In a direct-mapped cache, each memory address is segmented into bits that define the tag, index, and word offset within a block. The memory address consists of s + w bits where s refers to the addressable space, w refers to the word size, r identifies the number of cache lines, and s - r represents the tag length used for verifying data integrity.
To determine whether data resides in the cache (a cache hit) or needs to be fetched from main memory (a cache miss), the cache uses the index to locate the cache line and compares the stored tag against the fetched tag from memory. The section illustrates this through a series of examples, showing how addresses such as 22, 26, and 16 can result in hits and misses based on the organization of the cache. Furthermore, practical examples clarify how to calculate the necessary bits required to address the cache effectively, including evaluating the total bits in the cache and mapping memory addresses to cache lines. The latter part of the section examines a real-world scenario involving a specific processor architecture, illustrating the separations of instruction and data caching.
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Organization of a Direct Mapped Cache
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So, this figure shows the organization of a direct mapped cache. We see that the memory address consists of 𝑠 +𝑤 bits. The tag is 𝑠−𝑟 bits long. The cache line index, the cache index the cache is indexed by an 𝑟 bit length quantity and each word within a particular block or line is identified by this word offset.
Detailed Explanation
A direct mapped cache is structured in a way where the memory address is divided into three parts: the tag, the cache line index, and the word offset. The tag is meant to identify which block of memory a cache line corresponds to, whereas the cache line index tells us which line in the cache to use. The word offset specifies which specific word within the block we are accessing.
Examples & Analogies
Think of the cache as a set of mailboxes. The tag is like the mailbox number, telling you which mailbox belongs to which resident (block of memory). The cache line index is like the row where the mailbox is located, and the word offset tells you which particular letter you want to read from that mailbox.
Cache Hit and Miss
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So, to identify whether a particular line is in cache or not, we first come to the line identified by these 𝑟 bits and then compare the tag field. If this comparison is 1, we have a match and a hit in cache. When we have a hit in cache, we read the word in the cache and retrieve it. If there is a miss, we go to the main memory.
Detailed Explanation
When the processor needs to access data, it first checks the cache. It identifies the relevant cache line using the index derived from the memory address. If the tag stored in that cache line matches the tag from the memory address, it's a cache hit, meaning the required data is readily available in the cache. If not, it's a cache miss, and the processor has to fetch the data from the slower main memory.
Examples & Analogies
Imagine you're looking for a book. If you find it on your shelf (the cache), it's a hit; you can quickly read it. If it's not there and you have to go to a library (the main memory) to find the book, that's a miss, which takes more time.
Accessing Memory Addresses Example
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Now, we take an example of a very simple example of a direct mapped cache. For this cache we only have 8 blocks or 8 lines in the cache. We have a sequence of memory accesses 22, 26, 16, 3, 16, 18.
Detailed Explanation
In this example, we initiate with an empty cache comprising 8 blocks. As we reference the memory addresses, we perform the necessary conversions from the addresses to binary formats. Each resulting binary address determines both the line index and the tag. If the required data isn't already in the cache (miss), we will retrieve it from the main memory and place it in the corresponding cache line.
Examples & Analogies
Consider this as a game where you have a limited number of slots to fill with your favorite toys. When you want to play with a toy (memory address), you first check your shelf (the cache). If the toy isn't there, you go to the toy store (main memory) to buy it and add it to your shelf.
Calculating Total Bits in Cache Example
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Given, a 16 KB direct mapped cache, having 4-word blocks with word size being 32 bits. We need to find the total actual number of bits in the cache.
Detailed Explanation
To determine the total bits, we start by calculating how many lines and words the cache contains. We know the size of each block (4 words) and the total cache size (16 KB). This helps us find the total number of blocks. Once we know the bits required for each line (data bits, tag bits, and valid bits), we multiply to find the total bits for the entire cache.
Examples & Analogies
Think of it like packing a suitcase. You need to know how many items (bits) you can fit, how much individual items weigh (data bits), and any tags you must keep attached (tag bits). You calculate how many items fit in total and how that will affect your travel who needs to carry the luggage.
Mapping Byte Addresses
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Consider a cache with 64 blocks and a block size of 16 bytes. To what line number does byte address 1200 map? The main memory block number in which byte 1200 belongs is given by 1200/16.
Detailed Explanation
In this mapping scenario, we first need to determine which block of memory contains the byte at address 1200. By dividing the address by the block size, we can find the corresponding block number. Then, we take this block number and find the line number in the cache by using the modulo operation based on the total number of cache lines.
Examples & Analogies
Imagine you’re attending a big conference with many different sessions happening. Each session has a block of seats (cache lines), and you need to find where your specific session (byte address) is located. By figuring out the section and seat within that section, you can easily find where to sit in the vast auditorium (cache).
Key Concepts
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Direct-Mapped Cache: A simple cache organization where each memory block maps to exactly one cache line.
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Cache Hit: When requested data is found in the cache.
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Cache Miss: When requested data is not found in the cache, requiring fetching from main memory.
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Mapping Function: Determines how data blocks from main memory correspond to cache lines.
Examples & Applications
Example 1: Accessing address 22 results in a cache miss if the cache is empty. The data is then fetched from memory and stored in the corresponding cache line.
Example 2: Accessing address 16 after accessing it previously hits the cache, as the data is already present, allowing for immediate retrieval.
Memory Aids
Interactive tools to help you remember key concepts
Rhymes
In cache we seek, hits we seek, but when it misses, fetch we tweak.
Stories
Imagine walking into a library (the cache) and finding the book you want (the data) right on the shelf (cache hit). But sometimes, you must order it from another branch (the main memory) if it’s missing (cache miss).
Memory Tools
Remember HIP (Hit or Miss) for cache: H for Hit found in a cache, I for Index for checking, P for Pull from memory if missing.
Acronyms
TIC for Cache
for Tag
for Index
for Cache line as key terms to remember.
Flash Cards
Glossary
- Cache Miss
Occurs when the requested data is not found in the cache and must be obtained from main memory.
- Tag
A unique identifier stored in the cache to check whether the required data from memory is present.
- Cache Line
A block of data in the cache where associated data from main memory is stored.
- Cache Hit
A situation where the requested data is found in the cache, allowing for faster access.
- Mapping Function
The algorithm that determines how data is transferred between main memory and cache.
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