Master Boot Record maximum drive size [closed] - mbr

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I am reading up a bit on Master Boot Record layout and I was particularly interested in how the partition layout causes a size limitation on the size of the storage that can be used on a device with MBR.
Each partition within an MBR is defined using a 16 byte entry. The usage of those 16 bytes is as follows:
1st byte, if it has a value of 80, indicates active partition
2nd byte, the head number where the partition begins. This means MBR can address 256 different heads
3rd byte, the first 6 bits are used to capture the sector number of the 1st sector of the partition. This means MBR can address 64 different sectors
4th byte + last 2 bits of 3rd byte (total of 10 bits) store the track number where the partition begins. This means a total of 1024 tracks can be addressed using MBR partition entry.
5th byte (OS indicator)
6th byte the head number where the partition ends
7th byte, the first 6 bits are used to capture the sector number of the last sector of the partition
8th byte + last 2 bits of 7th byte store the track number where the partition ends
Bytes 9, 10, 11, and 12 capture how many sectors where there before the beginning of the partition
Bytes 13, 14, 15, and 16 capture how many sectors are there in the partition
Suppose we have only 1 partition in MBR and I make that the active partition. The zeroth sector is occupied by the MBR itself while the first partition starts from sector 1. Then the total number of sectors in this partition are:
2^10 = 1024 (number of tracks)
2^6 = 64 (number of sectors)
2^8 = 256 (number of heads)
1024 * 64 * 256 = 16,777,216 sectors
With every sector containing 512 bytes we get a maximum partition size of 8,589,934,592 (8.5 GB). If this is correct (which I doubt), shouldn't the maximum size of a disk addressable by MBR be 8.5 GB? I see everywhere they talk of 2.1 TBs and I am unable to understand how.

CHS addressing is long since obsolete. Recent MBR systems store partition information as LBA ("logical block address") and the drive internally maps it to cylinders/heads/sectors (after performing any necessary remapping for bad/spare sectors).
According to Wikipedia, LBA offset and size are stored as 32-bit little-endian values at offsets 0x08 and 0x0c (respectively) of a MBR partition table entry. This corresponds to your bytes 9-16.
32-bit addresses mean that limitation is in fact 2^32 * 512 = 2TB. This limitation is one of the main reasons why modern systems use GPT partitioning. Many drives also use 4096-byte sectors instead of 512.

Related

How far is it safe to regularly write to the ESP32 flash, considering the flash MTBF?

What would be the best practice for writing to the flash on a regular basis.
Considering the hardware I am working on is supposed to have 10 to 20 years longevity, what would be your recommandation? For example, is it ok I write some state variables every 15 minutes thru Preferences?
That depends on
number of erase cycles your Flash supports,
size of the NVS partition where you store data and
size and structure of the data that you store.
Erase cycles mean how many times a single sector of Flash can be erased before it's no longer guaranteed to work. The number is found in the datasheet of the Flash chip that you use. It's usually 10K or 100K.
Preferences library uses the ESP-IDF NVS library. This requires an NVS partition to store data, the size of which determines how many Flash sectors get reserved for this purpose. Every time you store a value, NVS writes the data together with its own overhead (total of 32 bytes for primitive data types like ints and floats, more for strings and blobs) into the current Flash sector. When the current sector is full, it erases the next sector and proceeds to write there; thereby using up sectors in a round robin fashion as write requests come in.
If we assume that your Flash has 100K erase cycles, size your NVS partition is 128 KiB and you store a set of 8 primitive values (any int or float) every 15 minutes:
Each store operation uses 8 * 32 = 256 bytes (32 B per data value).
You can repeat that operation 131072 / 256 = 512 times before you've written to every sector of your 128KiB NVS partition (i.e. erased every sector once)
You can repeat that cycle 100K times so you can do 512 * 100000 = 51200000 or roughly 5.1M store operations before you've erased every sector its permitted maximum number of times.
Considering the interval of 15 minutes creates 365 * 24 * 4 = 35040 operations per year, you'd have 51200000 / 35040 = 1461 years until Flash is dead.
Obviously, if your Flash chip is rated at 10K erase cycles, it drops to only 146 years.
There's probably some NVS overhead in there somewhere that I didn't account for, and the Flash erase cycle ratings are not 100% reliable so I'd cut it in half for good measure - I would expect 700 or 70 years in real life.
If you store non-primitive values (strings, blobs) then the estimate changes based on the length of that data. I don't know to calculate the exact Flash space used by those but I'd guess 32B plus length of your data multiplied by 10% of NVS overhead. Plug in the numbers, see for yourself.

Addressing a word inside memory frames

Suppose we have a 64 bit processor with 8GB ram with frame size 1KB.
Now main memory size is 2^33 B
So number of frames is 2^33 / 2^10 which is 2^23 frames.
So we need 23 bits to uniquely identify every frame.
So the address split would be 23 | 10 where 10 bits are required to identify each byte in a frame (total 1024 bytes)
As it is word addressable with each word = 8B, will the address split now be 23 | 7 as we have 2^7 words in each frame?
Also can the data bus size be different than word size ?
If suppose data bus size is 128 bits then does it mean that we can address two words and transfer 2 words at a time in a single bus cycle but can only perform 64 bit operations?
Most of the answers are dependent on how the system is designed. Also there is bit more picture to your question.
There is something called available addressable space on a system. In a 32 bit application this would be 2^32 and in a 64 bit application this would be 2^64. This is called virtual memory. And there is physical memory which commonly refereed as RAM. If the application is built as 64 bits, then it is able work as if there is 2^64 memory is available. The underlying hardware may not have 2^64 RAM available, which taken care by the memory management unit. Basically it breaks both virtual memory and physical memory into pages( you have refereed to this as frames) and keeps the most frequently used pages in RAM. Rest are stored in the hard disk.
Now you state, the RAM is 8GB which supports 2^33 addressable locations. When you say the processor is 64 bits, I presume you are talking about a 64 bit system which supports 2^64 addressable locations. Now remember the applications is free to access any of these 2^64 locations. Number of pages available are 2^64/2^10 = 2^54. Now we need to know which virtual page is mapped to which physical page. There is a table called page table which has this information. So we take the first 54 bits of the address and index in to this table which will return the physical page number which will be 2^33/2^10 = 23 bits. We combine this 23 bits to the least 10 bits of the virtual address which gives us the physical address. In a general CPU, once the address is calculated, we don't just go an fetch it. First we check if its available in the cache, all the way down the hierarchy. If its not available a fetch request will be issued. When a cache issues a fetch request to main memory, it fetches an entire cache line (which is usually a few words)
I'm not sure what you mean by the following question.
As it is word addressable with each word = 8B, will the address split now be 23 | 7 as we have 2^7 words in each frame?
Memories are typically designed to be byte addressable. Therefore you'll need all the 33 bits to locate a byte within the page.
Also can the data bus size be different than word size ?
Yes you can design a data bus to have any width, but having it less than a byte would be painful.
If suppose data bus size is 128 bits then does it mean that we can
address two words and transfer 2 words at a time in a single bus cycle
but can only perform 64 bit operations?
Again the question is bit unclear, if the data but is 128 bits wide, and your cache line is wider than 128 bits, it'll take multiple cycles to return data as a response to a cache miss. You wont be doing operations on partial data in the cache (at least to the best of my knowledge), so you'll wait until the entire cache line is returned. And once its there, there is no restriction of what operations you can do on that line.

Hardware Support for Paging

"The address consists of 16 bits, and the page size is 8KB. The page table thus consists of eight entries that are kept in fast registers."
How do we get the total entries in the page table as 8?
According to the calculation it should be 1.
Total Entries in the Page Table= ((2^16)/(2^3*2^10*2^3))=1.
(The first 2^3 is for 8 in 8KB, the second one is for bytes to bits conversion and 2^10 is for "Kilo" in 8KB.)
Thanks
Memory is byte-addressable hence, you do not need to divide by 2^3 for bytes to bit conversion.
Explaining it further, 16-bits for address means that the processor will generate memory addresses of length 16 bits which will be used to address the byte or half-word or word present starting (or ending - depends on the endianess of the machine) at that 16-bit value.
Now, the page size is the total size of a page in bits which in this case is 2^16 bits. But as memory is byte addressable, hence number of processor addresses in one page will be 2^16/2^3 i.e 2^13 addresses.
Hence number of page table entries are 2^16/2^13 = 8.

What is page table entry size?

I found this example.
Consider a system with a 32-bit logical address space. If the page
size in such a system is 4 KB (2^12), then a page table may consist of
up to 1 million entries (2^32/2^12). Assuming that
each entry consists of 4 bytes, each process may need up to 4 MB of physical address space for the page table alone.
What is the meaning of each entry consists of 4 bytes and why each process may need up to 4 MB of physical address space for the page table?
A page table is a table of conversions from virtual to physical addresses that the OS uses to artificially increase the total amount of main memory available in a system.
Physical memory is the actual bits located at addresses in memory (DRAM), while virtual memory is where the OS "lies" to processes by telling them where it's at, in order to do things like allow for 2^64 bits of address space, despite the fact that 2^32 bits is the most RAM normally used. (2^32 bits is 4 gigabytes, so 2^64 is 16 gb.)
Most default page table sizes are 4096 kb for each process, but the number of page table entries can increase if the process needs more process space. Page table sizes can also initially be allocated smaller or larger amounts or memory, it's just that 4 kb is usually the best size for most processes.
Note that a page table is a table of page entries. Both can have different sizes, but page table sizes are most commonly 4096 kb or 4 mb and page table size is increased by adding more entries.
As for why a PTE(page table entry) is 4 bytes:
Several answers say it's because the address space is 32 bits and the PTE needs 32 bits to hold the address.
But a PTE doesn't contain the complete address of a byte, only the physical page number. The rest of the bits contain flags or are left unused. It need not be 4 bytes exactly.
1) Because 4 bytes (32 bits) is exactly the right amount of space to hold any address in a 32-bit address space.
2) Because 1 million entries of 4 bytes each makes 4MB.
Your first doubt is in the line, "Each entry in the Page Table Entry, also called PTE, consists of 4 bytes". To understand this, first let's discuss what does page table contain?", Answer will be PTEs. So,this 4 bytes is the size of each PTE which consist of virtual address, offset,( And maybe 1-2 other fields if are required/desired)
So, now you know what page table contains, you can easily calculate the memory space it will take, that is: Total no. of PTEs times the size of a PTE.
Which will be: 1m * 4 bytes= 4MB
Hope this clears your doubt. :)
The page table entry is the number number of bits required to get any frame number . for example if you have a physical memory with 2^32 frames , then you would need 32 bits to represent it. These 32 bits are stored in the page table in 4 bytes(32/8) .
Now, since the number of pages are 1 million i.e. so the total size of the page table =
page table entry*number of pages
=4b*1million
=4mb.
hence, 4mb would be required to store store the table in the main memory(physical memory).
So, the entry refers to page table entry (PTE). The data stored in each entry is the physical memory address (PFN). The underlying assumption here is the physical memory also uses a 32-bit address space. Therefore, PTE will be at least 4 bytes (4 * 8 = 32 bits).
In a 32-bit system with memory page size of 4KB (2^2 * 2^10 B), the maximum number of pages a process could have will be 2^(32-12) = 1M. Each process thinks it has access to all physical memory. In order to translate all 1M virtual memory addresses to physical memory addresses, a process may need to store 1 M PTEs, that is 4MB.
Honestly a bit new to this myself, but to keep things short it looks like 4MB comes from the fact that there are 1 million entries (each PTE stores a physical page number, assuming it exists); therefore, 1 million PTE's, which is 2^20 = 1MB. 1MB * 4 Bytes = 4MB, so each process will require that for their page tables.
size of a page table entry depends upon the number of frames in the physical memory, since this text is from "OPERATING SYSTEM CONCEPTS by GALVIN" it is assumed here that number of pages and frames are same, so assuming the same, we find the number of pages/frames which comes out to be 2^20, since page table only stores the frame number of the respective page, so each page table entry has to be of atleast 20 bits to map 2^20 frame numbers with pages, here 4 byte is taken i.e 32 bits, because they are using the upper limit, since page table not only stores the frame numbers, but it also stores additional bits for protection and security, for eg. valid and invalid bit is also stored in the page table, so to map pages with frames we need only 20 bits, the rest are extra bits to store protection and security information.

Operating System: Paging Question

I have a question that I am trying to answer that gives the following situation:
16K Pages
32-bit Virtual Addresses
512MB hard disk, sector-addressable with 16K sectors
8 processes currently running
I am asked:
i) How many process page tables are required?
I think this is a trick question? Surely the answer is just 1.
ii) If a process address register PAR can be up to 32 bits, what is the maxmimum amount of physical memory that can be supported on this machine?
iii) How wide in bits should each entry in a process table be if 64MB physical memory is installed?
Please could anyone give me help/hint with the last two parts as I'm really stuck on them? Thanks!
In case you look on here before the exam later today, it is because it doesn't mean Process address register, it means Page address register!
Try looking at http://cseweb.ucsd.edu/classes/fa03/cse120/Lec08.pdf for some more information including help about segmentation and paging combined
Also, the book in the IC library called Operating Systems concepts with code 005.43SIL says that each process has it's own process page table and can even be segmented itself!
i) I said 8
ii) Well, 32 bits of virtual memory addressing with 14 bits of offset in the page table (2^14 = 16K page length) means there are 18 bits left for the page number. In 32 bits of PAR, this means 14 bits for the page location. If you multiple the amount of page locations by the page size, you get 2^14 * 2^14 = 2^18 which is 256MB of RAM
iii) I got 30 bits. 64MB is 2^26 divided by the page size is 2^26/2^14 = 2^12 which means 12 bits for the page location. From (ii) I calculated that 18 bits are left in the virtual memory address for the page number meaning that it should be 30 bits wide. I also put a comment that since it should be byte-aliged maybe the extra 2 bits can be used so that we know whether it has been written to and whether it is currently being stored on the disk.
Hope this helps!