max RAM in 32 bit machine - 64-bit

I am aware of possible duplicate questions already in stackoverflow. But those questions do not address my question directly. My understanding is that 32 bit machine uses 32 bit to store memory addresses, therefore, the maximum memory it can have is 2^32 bit. However, 2^32 bit = 2^29 byte = 2^29/10^9 = 0.5 Gigabyte.
I know that the answer should be 4 gigabyte. But I simply cannot figure out where is my mistake. HELP!

I believe that the 2^32 refers to the number of addressable bytes not the total number of bits in memory. you can address 4 billion bytes ( 32 billion bits) or 4 gigs of memory. For instance
Address 0 | Address 1 |... | Address 2^32
........................................
8 bits | 8 bits | ...| 8 bits
EDIT:
The 32 bit machine usually refers to the number of bits you can stuff into the CPU's registers (not RAM). Thus 1 register allows for 32 bits which can address 2^32 bytes of RAM.
EDIT:
Here is a good explanation on superuser:
https://superuser.com/questions/56540/32-bit-vs-64-bit-systems

Related

Are only 2 bytes and a half available for ASLR stack randomization on 64 bits Linux?

I tried running Apache a few times to see the effect of ASLR
I know that because of alignment, the last byte and a half is 0, and because of "canonization" the first two bytes are irrelevant, so that leaves 4 bytes and a half to randomize which is quite a lot
But I noticed that the first two bytes are always 7fff so does that mean only 2 bytes and a half are random ?

How to determine the addressable memory capacity in bytes knowing the bits for the operand address?

If I have say a 64-bit instruction, which has 2 bytes (16 bits) for opcode and the rest for operand address, I can determine that I have 48bits for the address (64-16). The maximum value that can be displayed with 48 bits plus 1 to account for address 0 is my go to number. This would be 2^48. However, I have the problem with the understanding of this in terms of the iB units.
2^48 is 2^40 (TiB) x 2^8 = 256TiB. But since TiB = 2^40 BYTES, when did the 2^48 become a BYTE? I generally believed that to get the number of bytes I'd have to divide by 8, but this doesn't seem to be the case.
Could someone explain why this works?
A byte is by definition the smallest chunk of memory which has an address. Whatever number of address bits, the resulting address is the address of a byte, by definition. In all (or at least, most) computer architectures existing today, a byte is the same as an octet, that is, eight bits; but historically there were popular computer architectures with 6 bit bytes, or 12 bit bytes, or even other more exotic number of bits per byte.

How to determine the highest addressable memory?

"A memory has 1024 storage units with a width of 64. Suppose the memory is byte addressable. What is the address of the highest addressable memory position?"
Please correct me if I'm wrong.
byte addressable means individual bytes in a word have their own addresses.
there are 8 bytes in a 64 bit word.
therefore 8 x 1024 = 8192 addresses overall.
highest address therefore 8191.
I believe this to be true but am not a 100% sure. Please indicate where my logic falters if indeed it does.
I would say 1023.
There are 1024 storage locations, each numbered 0 to 1023, and each storage location holding 64 bits.
So you have a computer where a byte contains 64 bits. A byte is not 8 bits, but the minimum size of a memory location. All modern computers use 8 bits on a byte, but some older computers used 7, 9 og 14 bits on each byte.
But it's a really badly written question, because it does not define what a storage location is. So your interpretation might be right assuming a standard 8 bit in a byte cpu.

What is the difference between address size(width) and addressability?

What I understand so far is address width is the number of bits in an address.
For example, 4 bits width address can have 2^4 = 16 cases. And what I'm really uncertain is addressability. Based on what I learned is "the size of the most basic unit that can be named by address". So, if we have 4 bits address width and 2 bits addressability, what happens?
I've been really curious about it for a couple of weeks, but still bummer.
Could you guys explain those things by drawing or something?
I think you do get it. There is the number of address bits, the width if you will, and there is the size of the unit those things address. so 8 bits means you have 256 things, 16 bits of address 65536 things. The size of thing is completely independent of the number of address bits. From a programmers perspective almost always we deal in units of bytes, so 8 bits of address would be 256 bytes, 32 bits of address would be 4 gigabytes. As you dig into the logic it is often wasteful to use a byte based address, if you have a peripheral that has 32 bit wide registers and you can only access those as whole 32 bit registers then do you need to connect address line 0 or 1? often not. so at that peripheral the address bus however wide it is (often the whole address bus to the peripheral is a subset of the address bus higher up closer to the processor/software, and those address bits are in units of 32 bit words.
To make things even more confusing, memory parts are often defined in terms of bits, even if they have an 8 or 16 bit data bus. So you might have a 4M part but that is megabits not megabytes...

Manual Virtual Address Translation

I've looked at a few different articles related to this already but none of them explain the solution in a way that I can understand and replicate. I need to know how to translate a physical address to a virtual address in memory based on the following:
A simple virtual memory system has 32KB physical memory with 16-bit virtual address, of which 12 bits are used as offset. The following is the current content of the page table of one of the processes:
So basically I think the page size of this virtual memory system is 1024KB. I need a process to find the corresponding PA of VA B2A0. If you can give me the process I can go from there, you don't have to give me the final solution :)
Thanks in advance guys. Also, if you know of an article that does this already and I've just missed it, feel free to just link me to that.
Cheers.
32 KB is 2^15.
so there are 15 bits for every physical address, lower 12 of them are used as offset, higher 3 as a number of pageframe.
What virtual page does 0xb2a0 resides in? To determine this, we need to take bits of the address, higher than 2^12. The size of a page is 2^12, that is 4096 or 0x1000, so it is a virtual page number 0xb = 11 (floor of 0xb2a0 / 0x1000). Offset inside the page is 0xb2a0 modulo 0x1000, it's 0x2a0.
Then use the table to translate the virtual page number 11 to a physical pageframe. The virtual page is present (1), and it corresponds to the physical frame number with higher bits 111, that is 111 + twelve 0 in binary, => 0x7000 - it is the address of the start of the physical frame.
Our physical address resides at offset 0x2a0, so, the sought physical address is 0x7000 + 0x2a0 = 0x72a0.
Please, follow this flow and make it clear for you. If you have questions, read the Wikipedia first and if something is still not clear, ask :)
I was trying to do my examination review and study, and I couldn't find a solid answer to this same question. I consolidated what I have learnt, and I hope that whatever I summed up here will help those like me. :)
I find the explanation in the answer above a little hard to understand for my little brain.
I think this link below gives a better overview than Wikipedia's explanation:
http://williams.comp.ncat.edu/addrtrans.htm
This youtube video also offers an excellent guide in explaining the process of virtual address translation:
https://www.youtube.com/watch?v=6neHHkI0Z0o
Back to the question ->>>
The first question is - what is the 'page size' of this virtual memory system?
based on the definition here - https://en.wikipedia.org/wiki/Page_(computer_memory)
I was initially confused between 'pages' and 'page size' but I kinda figured it out now. Pages determines the number of pages available (like in a book), and page size is like (A4,A5,A6 pages in the book!).
As such, since the virtual memory and physical memory offset is the same and is mapped accordingly, we can determine the page size via the offset size. If the offset size is given as 12-bit, then 2^12 = 4,096 Byte a.k.a 4-KB.
Side question for curious minds, how many virtual memory pages are there?
- 16-bit of virtual address space minus 12-bit of offset = 4-bit
- which equals to 2^4 = 16-pages available (thus the table we see!)
Another side question for other curious minds, how many PHYSICAL memory pages are there?
- 32KB of physical Memory = 32 x 1024bytes = 32,768 bytes
- Log(32768) / Log(2) = 15-bits which also means 2^15 for total physical MEMORY
- minus the offset of 12-bit that we already know...
- 15-bit (total physical memory) minus 12-bit (offset) = 3-bit for physical address space
Going to the next question, what is the corresponding physical address of virtual address 0xb2a0 (that is currently set in hex notation)?
#Dmytro Sirenko answer above explains it quite well, I will help to rephrase it here.
We need to remember that our virtual address is - 16-bit, and that address space now contain is value = b2a0 (ignoring the 0x).
My short-cut (please correct me if am wrong), is that since the ratio of the address : offset (page size) is 4:12 = 1:3...
b | 2 a 0
^
page number | offset
When converting hex value b to decimal = 11.
I look into the table, and I found Page Frame = 111 in the table entry number 11.
111 is noted in binary and it correlates to the physical memory frame.
Remember, we were looking at 15-bit of Physical Memory Address space, as such, we can determine that:
1 1 1 | 0 0 0 0 0 0 0 0 0 0 0 0
Address | offset
As Offset are mapped directly from virtual memory to physical memory, we bring the value of (2a0) right into the physical memory. Unfortunately, we can't represent it right away in here because it's in hexadecimal format while my above address space is set in binary.
Considering that I am going to be tested in an examination and I won't be allowed to bring in a calculator... I will do a reverse and answer in Hexadecimal instead. :)
When we convert 111 into decimal (I go by 001 = 1, 010 = 2, 100 = 4, 101 = 5, 110 = 6, 111 = 7).
Now I need to convert from decimal to Hex! = 7 (dec) = 7
As such, the corresponding Physical Memory location of this virtual memory address is.... (loud drums and curtain open....)
7 2 a 0
which is notated in this manner 0x72a0.

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