Set Associative Mapping | Set Associative Cache

Cache Mapping-

 

Before you go through this article, make sure that you have gone through the previous article on Cache Mapping.

 

Cache mapping is a technique by which the contents of main memory are brought into the cache memory.

 

Different cache mapping techniques are-

 

 

1. Direct Mapping
2. Fully Associative Mapping
3. K-way Set Associative Mapping

 

In this article, we will discuss about set associative mapping in detail.

 

Set Associative Mapping-

 

In k-way set associative mapping,

• Cache lines are grouped into sets where each set contains k number of lines.
• A particular block of main memory can map to only one particular set of the cache.
• However, within that set, the memory block can map to any freely available cache line.
• The set of the cache to which a particular block of the main memory can map is given by-

 

Cache set number = ( Main Memory Block Address ) Modulo (Number of sets in Cache)

 

Division of Physical Address-

 

In set associative mapping, the physical address is divided as-

 

 

Set Associative Cache-

 

Set associative cache employs set associative cache mapping technique.

 

The following steps explain the working of set associative cache-

 

After CPU generates a memory request,

• The set number field of the address is used to access the particular set of the cache.
• The tag field of the CPU address is then compared with the tags of all k lines within that set.
• If the CPU tag matches to the tag of any cache line, a cache hit occurs.
• If the CPU tag does not match to the tag of any cache line, a cache miss occurs.
• In case of a cache miss, the required word has to be brought from the main memory.
• If the cache is full, a replacement is made in accordance with the employed replacement policy.

 

Implementation-

 

The following diagram shows the implementation of 2-way set associative cache-

 

(For simplicity, this diagram shows does not show all the lines of multiplexers)

 

The steps involved are as follows-

 

Step-01:

 

• Each multiplexer reads the set number from the generated physical address using its select lines in parallel.
• To read the set number of S bits, number of select lines each multiplexer must have = S.

 

Step-02:

 

• After reading the set number, each multiplexer goes to the corresponding set in the cache memory.
• Then, each multiplexer goes to the lines of that set using its input lines in parallel.
• Number of input lines each multiplexer must have = Number of lines in one set

 

Step-03:

 

• Each multiplexer outputs the tag bit it has selected from the lines of selected set to the comparators using its output line.
• Number of output line in each multiplexer = 1.

 

UNDERSTAND   It is important to understand- A multiplexer can output only a single bit on output line. So, to output one complete tag to the comparator, Number of multiplexers required = Number of bits in the tag If there are k lines in one set, then number of tags to output = k, thus- Number of multiplexers required = Number of lines in one set (k) x Number of bits in the tag Each multiplexer is configured to read the tag bit of specific line at specific location. So, each multiplexer selects the tag bit for which it has been configured and outputs on the output line. The complete tags as whole are sent to the comparators for comparison in parallel.

 

Step-04:

 

• Comparators compare the tags coming from the multiplexers with the tag of the generated address.
• This comparison takes place in parallel.
• If there are k lines in one set (thus k tags), then-

Number of comparators required = k

and

Size of each comparator = Number of bits in the tag

• The output result of each comparator is fed as an input to an OR Gate.
• OR Gate is usually implemented using 2 x 1 multiplexer.
• If the output of OR Gate is 1, a cache hit occurs otherwise a cache miss occurs.

 

Hit latency-

 

• The time taken to find out whether the required word is present in the Cache Memory or not is called as hit latency.

 

For set associative mapping,

Hit latency = Multiplexer latency + Comparator latency + OR Gate latency

 

Also Read- Direct Mapped Cache | Implementation & Formulas

 

Important Results-

 

Following are the few important results for set associative cache-

• Block j of main memory maps to set number (j mod number of sets in cache) of the cache.
• Number of multiplexers required = Number of lines in one set (k) x Number of bits in tag
• Size of each multiplexer = Number of lines in one set (k) x 1
• Number of comparators required = Number of lines in one set (k)
• Size of each comparator = Number of bits in the tag
• Hit latency = Multiplexer latency + Comparator latency + OR Gate latency

 

To gain better understanding about set associative mapping,

Watch this Video Lecture

 

Next Article- Practice Problems On Set Associative Mapping

 

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