Direct Memory Mapping

Summary

This educational video script explains the concept of direct memory mapping in computer systems. It begins with an introduction to the organization of secondary and main memory, both divided into pages and frames of equal size. The script delves into the process of bringing elements from main memory into cache memory, highlighting the similarities in organization between blocks and lines. It discusses the significance of physical address bits, block and line offset, and tag bits in the mapping process. The explanation of round-robin mapping and the direct mapping technique's strictness concludes the session, promising numerical problems in upcoming lessons to solidify understanding.

Takeaways

• 😀 The video introduces different cache memory mapping techniques, starting with direct memory mapping.
• 🔍 The secondary memory and main memory are conceptually diagrammed, showing how programs are converted into processes and subdivided into pages and frames of equal size.
• 💾 The operating system is responsible for managing the subdivision of processes into pages and their loading into main memory, as detailed in a separate course on operating systems.
• 📚 Cache and main memory organization is similar, with main memory parts termed as 'blocks' and cache parts as 'lines', both having the same size.
• 📝 The smallest addressable memory unit is a 'word', and in a byte-addressable memory, each word is one byte in size.
• 📉 The script explains how to calculate the number of blocks in main memory and how they are numbered, using an example with 64-word size and block size of four words.
• 📍 It details the concept of physical address bits (PA bits), which are used to address locations in the main memory, split into block numbers and word offsets within blocks.
• 🔄 The mapping of main memory blocks to cache lines is done in a round-robin manner, which is a many-to-one relationship.
• 🔑 The PA bits are split into block or line offset, block numbers, and tag bits, with the tag bits identifying which block is present in the cache.
• 🔍 Direct mapping is a strict memory mapping technique where main memory blocks are directly mapped to cache lines, as opposed to other mapping techniques that may allow more flexibility.
• 📈 The video concludes with an explanation of why the tag bits are called so, as they act as identifiers or 'tags' for the blocks present in the cache.

Q & A

What is the main focus of the session described in the transcript?

The main focus of the session is to explain different cache memory mapping techniques, starting with direct memory mapping.

How is the secondary memory related to the main memory in terms of program execution?

In terms of program execution, programs permanently reside in secondary storage and during execution, they turn into processes. The operating system is responsible for subdividing these processes into equal-sized pages and bringing them into the main memory.

What is the term used for the smallest addressable memory unit?

The smallest addressable memory unit is called a 'word'.

What does the size of each block and frame represent in the context of the script?

The size of each block and frame represents the equal-sized subdivisions of the main memory and secondary memory, respectively, which are used for efficient memory management and access.

How are the main memory and cache memory organized in terms of blocks and lines?

In the script, parts of the main memory are termed as 'blocks', and parts of the cache are named as 'lines'. Both the block size and line size are the same, facilitating a direct correspondence between them.

What is the significance of the term 'byte addressable memory' in the script?

The term 'byte addressable memory' signifies that the size of each word is one byte, which is a standard unit for measuring memory capacity and addressing within the memory.

How many bits are required to address 64 words in the main memory?

To address 64 words in the main memory, 6 bits are required, as log2(64) equals 6.

What are the different parts of a physical address according to the script?

A physical address is split into the most significant bits for identifying blocks, and the least significant bits for addressing each word within a block.

What is the purpose of the round-robin mapping technique mentioned in the script?

The round-robin mapping technique is used to assign main memory blocks to cache lines in a cyclic order, ensuring that all blocks have an opportunity to be mapped to each cache line over time.

What is the role of 'tag bits' in direct memory mapping?

Tag bits are used to identify which block is present in the cache. They work as identifiers or 'tags' for the blocks within a cache line.

What is the significance of the least significant two bits in block numbering?

The least significant two bits in block numbering dictate which cache line a particular block will be mapped onto in the direct memory mapping technique.

Outlines

00:00

📚 Introduction to Cache Memory Mapping Techniques

This paragraph introduces the concept of cache memory mapping techniques, starting with direct mapping. It explains the process of how programs stored in secondary storage are executed as processes and subdivided into pages, with the main memory also divided into frames of the same size. The operating system is responsible for managing this subdivision. The paragraph also delves into the organization of cache and main memory, where parts are termed as blocks and lines respectively, with the line size equal to the block size. The smallest addressable memory unit, a word, and the concept of byte addressable memory are introduced. An example is given with a 64-word main memory and block size of four words, explaining how blocks and words are addressed using physical address bits. The significance of the PA split in identifying blocks and words within them is also highlighted.

05:04

🔄 Direct Memory Mapping and Round Robin Technique

This paragraph discusses the direct memory mapping technique, where main memory blocks are mapped onto cache lines in a round-robin fashion due to the limitation of cache size. It explains how blocks are mapped onto cache lines sequentially and then cycle back to the beginning once the end is reached. The paragraph clarifies the significance of the least significant bits in determining which cache line a block maps onto, creating a many-to-one relationship. It also introduces the concept of block or line offset, line number, and tag bits in the context of physical address bits. The tag bits are particularly important as they serve as identifiers for which block is present in the cache, functioning as 'tags'. The explanation includes an analysis of different block numbers and their corresponding tag bits to illustrate the direct mapping process. The paragraph concludes with a summary of the direct mapping technique and a preview of solving numerical problems in upcoming sessions.

Keywords

💡Cache Memory

Cache memory is a type of high-speed data storage used in computing to reduce the average time to access data from the main memory. In the video, cache memory is discussed in the context of its mapping techniques and its organization, which is similar to main memory but operates at a faster speed to improve system performance.

💡Direct Memory Mapping

Direct memory mapping is a technique where each block of main memory is mapped directly to a specific cache line. The video explains this concept by describing how main memory blocks are associated with cache lines in a one-to-one correspondence, which is a strict and direct mapping process.

💡Secondary Memory

Secondary memory, also known as auxiliary or external memory, is a non-volatile data storage device that supplements the computer's main memory. In the script, it is mentioned that programs reside in secondary storage before they are loaded into the main memory as processes.

💡Process

A process is a program that is currently being executed by the CPU. The video uses the analogy of a person, Mr. Clark Joseph, to illustrate that just like a person can't hear, a process is a dynamic entity that is created when a program is executed.

💡Page

In the context of computer memory management, a page is a fixed-size block of data from a secondary storage that the operating system can read into the main memory. The script explains that processes are subdivided into pages of equal size for efficient memory management.

💡Frame

A frame is a fixed-size block of data in the main memory that is used to store a page from secondary storage. The video script describes how the main memory is split into frames of equal size to the pages, facilitating the process of bringing elements into the cache memory.

💡Operating System

The operating system is the most important type of system software, which manages computer hardware resources and provides various services. The script mentions that the operating system is responsible for the process of subdividing processes into pages and bringing them into the main memory.

💡Block

In the context of cache and main memory, a block refers to a part of the memory that is involved in the mapping process. The script explains that parts of the main memory are termed as blocks, which are the same size as the cache lines, and are used in the direct mapping technique.

💡Line

A line in cache memory corresponds to a block in main memory. The video script describes how the cache is organized into lines, each of which is the same size as a block, and how these lines are used in the direct mapping process.

💡Round Robin Mapping

Round robin mapping is a method of assigning resources in a cyclic order, one after the other. The script uses this concept to explain how main memory blocks are mapped onto cache lines in a sequential order, and when all lines are filled, the mapping starts again from the first line.

💡Tag Bits

Tag bits are part of the physical address used to differentiate between different blocks that can be mapped to the same cache line. The video script explains that tag bits, along with line number bits, help identify which block is present in the cache, acting as a tag for identification.

💡Offset

In computer memory addressing, an offset is the displacement from one reference point to another. The script describes how the least significant bits of a block number, known as the block or line offset, determine the position of a word within a block or line.

Highlights

Introduction to different cache memory mapping techniques starting with direct memory mapping.

Conceptual block diagrams of secondary memory and main memory are presented for understanding.

Explanation of how programs in secondary storage turn into processes and are subdivided into pages.

Main memory is split into frames of equal size to match the page size.

Operating system's role in subdividing processes into pages and bringing them into main memory.

Cache and main memory organization similarities, with main memory parts termed as blocks and cache parts as lines.

Cache line size is the same as the block size, ensuring consistency between cache and main memory.

Introduction of the smallest addressable memory unit, a word, and its byte addressability.

Assumption of a main memory with 64 word size and block size of four words, leading to 16 blocks.

Explanation of how memory blocks are organized and addressed using physical address bits (PA bits).

PA bits split into block number identification and word addressing within each block.

Illustration of how a physical address points to a specific word in memory using bit place values.

Assumption of a 16-word cache with a block size of four words, resulting in four cache lines.

Description of the round-robin mapping technique used in direct memory mapping.

Explanation of how the least significant bits of the block number dictate cache line mapping.

PA bits split into block or line offset, block number, and tag bits for direct mapping.

Tag bits' role in identifying which block is present in the cache, serving as a tag for each block.

Conclusion summarizing the direct mapping technique and its strict mapping procedure.

Announcement of future sessions focusing on solving numerical problems related to direct memory mapping.

Transcripts

[Music]

hello

everyone welcome back in our previous

session we learned about the cashier

memory

from this session onwards we will focus

on different cache memory mapping

techniques starting with the direct

memory mapping

so gear up and let's get to learning so

as you can see in here this is the

conceptual block diagram of the

secondary memory

and this is a conceptual block diagram

of main memory

now we already know programs in the

computer permanently reside in the

secondary storage

during execution the same programs turn

into processes

just like our friend mr clark joseph

can't hear

now every process is subdivided into

equal sized pages

likewise the main memory is also split

into equi-sized frames

and the size of each frame is as same as

the size of each page

the process of subdividing the processes

into the pages and then bringing them

into the main memory

is the job of the operating system and

for the details of that

you can refer to our beautifully

presented operating systems course

but for today we are here to learn about

how the elements are brought from the

main memory into the cache memory

the organization of the cache and the

main memory is almost similar to this

organization

in this the parts of the main memory are

termed as blocks

and the parts of the cache are named as

lines

also the line size is as same as the

block size

now remember these all are concepts we

won't just go on drawing the lines and

the blocks

on the caches and the rams these

illustrations are just for the sake of

understanding

now a smallest addressable memory unit

is called a word

and a byte addressable memory means the

size of each word is one byte

let's assume we have a main memory with

64 word size and the size of each block

is given as

four words hence the number of blocks in

the main memory

is 64 by 4 that is 16 so that blocks are

numbered as

0 1 2 3 up to 15.

now coming to the 64 main memory words

that is starting from 0 up until 63

they are organized in the main memory

somewhat like this

because each and every memory block is

supposed to have only four words

now we know using one bit place we can

address two locations

that is zero to the memory location zero

and one to the memory cell one

similarly with two bit places four

locations can be addressed

zero zero for m zero zero 1 for m 1

1 0 for m 2 and 1 1 for m 3

so for 8 memory cells we will be needing

log 8 base 2 that is log 2 cube base 2

that is 3 bit

places similarly in order to address

0 to 63 that is 64 words

we will be needing log 64 base 2

which actually results in 6 bits

now these 6 bits are called pa bits or

physical address bits

and the reason behind that is the main

memory is sometimes referred to as

physical address space

and in this particular physical address

space there are 0 to 15 that is 16

blocks

and in order to locate each one of them

we will be needing

log 16 base 2 that is logs 2 to the

power 4

base 2 which is 4 bits so the pa bits

are split like

the most significant 4 bits are used for

identifying the blocks

and the least significant two bits are

used for addressing

each word in each block so the zero zero

will be addressing to the zeroth word

zero one for the first word one zero for

the second word and similarly one one

for the third word

now let me show you how meaningful the

pa split is

suppose the processor generates the

physical address zero followed by five

ones

now following our ps plate the most

significant four bits that is zero

triple one which is nothing but seven

will be referring to the

block number seven and the least

significant two bits one one

will refer to the last word of that

particular block

let's analyze the generated physical

address

if we consider all the bit places

magnitudes and

add up all the values which has ones

underneath of them

we get the value as 31 and that is the

exact value of the word

which was being pointed out by the

physical address

isn't it beautiful now let's assume we

have a cache of 16 words

and the block size was already given to

us as four words

now we already know both the block and

the line are equal in sizes

in that case line size is also going to

be 4 words

therefore number of lines in the cache

is 16 by 4

that is 4 which is 0 1

2 and 3. and in order to identify four

different lines

we will be needing log 4 base 2 that is

log 2 square base 2 which is 2 bits

well it's pretty obvious that all the

main memory blocks can't really be

assigned to all the cache aligns at once

therefore we have to perform something

called mapping now the mapping takes

place in round robin manner

so these are the blocks of the main

memory and these are the cache lines

the zeroth block will be mapped onto the

zeroth line the first block will be

mapped onto the first line

the second block is going to be mapped

onto the second line and the third block

will be mapped onto the third line at

this point we might think that for the

fourth block and the rest there are no

available cache lines

but there the round robin manner comes

at rescue

so the fourth block will be mapped onto

the zeroth line and the fifth one is

going to be mapped onto the first line

and this keeps on following

now this is the complete mapping if we

observe closely

the least significant two bits of the

block number is actually dictating which

cache a line to map onto

like the block number zero four eight

twelve they are going to get mapped on

to the line number zero

the block numbers one five nine and

thirteen

mapped on to the line number one for

blocks

two six ten and fourteen they are going

to get mapped onto the line number

two and finally block number 3 7

11 and 15 these are going to get mapped

onto the

line number three so this is a many to

one relation

so finally the pa bits are split like

this

the least significant two bits are

called block or line offset

they determine each word inside either

block or line

now the rest are called block numbers

now from the block numbers the last two

bits

are known as line number because they

actually dictate

which cache a line that particular block

will be mapping onto

so the remaining bits are known as tag

bits

now let's try and understand why these

are called tag bits

now let's select block number 3 and

analyze its contents

12 13 14 15 and these are their 6-bit

binary equivalents

also we witnessed that like block number

three block number seven

eleven and fifteen are also mapped onto

the same cache line that is

client number three so let's observe

their contents as well

block number seven's got 28 29 30 and 31

11 has 44 45 46 and 47

and for 15 there is 60 61 62 and 63.

now observe this for block number three

the tag bits are

0 0 for block number 7 the tag bits are

0

1 for 11 the tag bits are 1 0

and 15 it's 1 1. so do you understand

the pattern

so actually these bits will identify

which one of the blocks

is present in the caching basically they

work as the tags

and thus the naming so to conclude

this memory mapping technique is called

direct mapping as the main memory blocks

are mapped directly onto the cache

alliance

and the mapping procedure is strict

so that was all for this session i hope

now you have a lucid understanding about

the entire concept of direct memory

mapping technique

from the next session onwards we will

solve interesting numerical problems

related to this concept hope to see you

in the next one

thank you all for watching

[Music]

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