This document discusses different types of memory mapping techniques used in computer systems. Memory mapping is a mechanism that maps portions of files or entire files stored on disk to addresses in an application's memory space. There are three main types of memory mapping: direct mapping, associative mapping, and set associative mapping. Direct mapping assigns each memory block to a single cache line. Associative mapping allows memory blocks to be placed in any cache line but requires complex circuitry. Set associative mapping divides the cache into sets, each with multiple lines, providing a compromise between direct and full associative mappings.

1. Memory
● A essential component of the computer system
● Stores binary instructions and datum for the microcomputer
● The place where the computer holds current programs and data that are in
use

2. Cache Memory
● A essential component of the computer system
● Stores binary instructions and datum for the microcomputer
● The place where the computer holds current programs and data that are in
use

3. Memory Mapping
● A mechanism that maps a portion of a file, or an entire file, on disk to a range
of addresses within an application’s address space
● The translation between the logical address space and physical memory
Objects:
○ To translate physical address from logical address
○ To aid in memory protection
○ To enable better memory management
● Mapping is important to computer performance both
○ Locally( how long it takes to execute an instruction) and
○ Globally( how long it takes to run a set of program)
Types:
○ Direct mapping
○ Associated Mapping
○ Set Associated Mapping

4. Direct Mapping
● The procedure used to assign each memory block in the main memory to a
particular line in the cache (if a line is already filled with a memory block and a
new block needs to be loaded, then the old block is discarded from the cache)
● the simplex technique, maps each block of main memory into only one
possible cache line
i = j modulo m
Where I = cache line number; j = main memory block number; m = number of
lines in the cache

5. Direct Mapping (contd..)

6. Direct Mapping (contd..)

7. Direct Mapping (contd..)
● Direct mapping divides an address into three parts: t tag bits, l line bits, and
w word bits.
○ The w(word) bits are the least significant bits that identify the specific
word within a block of memory.
○ The l(line) bits are the next least significant bits that identify the line of
the cache in which the block is stored.
○ The remaining bits are stored along with the block as the tag which
locates the block’s position in the main memory.

8. Direct Mapping (contd..)
● Prons:
○ Simple
○ Inexpensive
○ Fixed location for given block
But, If a program accesses 2 blocks that map to the same line repeatedly, cache
misses are very high

9. Associated Mapping
● Overcomes the disadvantage of direct mapping by permitting each main
memory block to be loaded into any line of cache.
● Cache control logic interprets a memory address simply as a tag and a word
field
● Tag uniquely identifies block of memory
● Cache control logic must simultaneously examine every line’s tag for a match
which requires fully associative memory
● very complex circuitry, complexity increases exponentially with size
● Cache searching gets expensive (slow)

10. Associated Mapping (contd..)

11. Set Associated Mapping

12. Set Associated Mapping (contd..)
● It is a compromise between direct and associative mappings that exhibits the
strength and reduces the disadvantages
● Cache is divided into v sets, each of which has k lines;
● number of cache lines M = v X k
● I = j modulo v
● Where, i = cache set number; j = main memory block number; m = number of
lines in the cache

13. Set Associated Mapping (contd..)
● The most common set associative mapping is 2 lines per set, and is called two-
way set associative. It significantly improves hit ratio over direct mapping, and
the associative hardware is not too expensive