Autosave: 2024-07-12 07:00:03

zk/Memory_addresses.md

@@ -0,0 +1,83 @@
+---
+title: Memory_addresses
+tags: [memory]
+created: Friday, July 12, 2024
+---
+
+# Memory addresses
+
+> Computers assign numeric addresses to bytes of memory and the CPU can read or
+> write to those addresses
+
+We can think of the internals of RAM as grids of memory cells.
+
+Each single-bit cell in the grid can be identified using two dimensional
+coordinates, like in a graph. The coordinates are the location of that cell in
+the grid.
+
+Handling one bit at a time isn't very efficient so RAM accesses **multiple
+grids** of 1-bit memory cells in parallel. This allows for reads or writes of
+multiple bits at once, such as a whole byte.
+
+The location of a set of bits in memory is known as a **memory address**.
+
+### Demonstration
+
+Let's imagine we have a computer system that can address up to 64KB of memory
+and our system is byte addressable. This means there are
+$64 \cdot 1024 = 65,536$ bytes of memory because 1KB = 1024 bytes.
+
+We therefore have 65,536 addresses and each address can store one byte. So our
+addresses go from 0 to 65, 535.
+
+We now need to consider how many bits we need to uniquely represent an address
+on this system.
+
+What does this mean? Although there are approximately 64 thousand bytes of
+memory, to refer to each byte we can't just use 1, 2, 3... because computers use
+binary numbers. We need a binary number to refer to a given byte in the the 64KB
+of memory. The question we are asking is: how long does this binary number need
+to be to be able to represent each of the 64 thousand bytes?
+
+1 bit can represent two addresses: 0 and 1. 2 bits can represent four addresses:
+00, 01, 10, 11. The formula is as follows: number of addresses = $2^n$ where $n$
+is the number of bits.
+
+We need to reverse this formula to find out how many bits we need to represent a
+given number of addresses. We can do this with a [logarithm](Logarithms.md).
+
+We can reverse the formula as follows: number of bits = $\log_2$(number of
+addresses).
+
+In our case we have 65,536 addresses so we need $\log_2(65,536)$ bits to
+represent each address. This is approximately 16 bits. Thus a 16 bit memory
+address is needed to address 65, 546 bytes.
+
+Using memory addresses we end up with tables like the following:
+
+| Memory address   | Data             |
+| ---------------- | ---------------- |
+| 0000000000000000 | 1010101010101010 |
+| 0000000000000001 | 0010001001001011 |
+| 0000000000000010 | 0010001001001010 |
+
+This is hard to parse so we can instead use
+[hexadecimal numbers](Hexadecimal_number_system.md) to represent the addresses:
+
+| Memory address (as hex) | Data (as binary) |
+| ----------------------- | ---------------- |
+| 0x0000                  | 1010101010101010 |
+| 0x0001                  | 0010001001001011 |
+| 0x0002                  | 0010001001001010 |
+
+By itself, the the data is meaningless but we know from
+[binary encoding](Binary_encoding.md) that the binary data will correspond to
+some meaningful data, such as a character or a colour, depending on the encoding
+scheme used. The above table could correspond to the characters for 'A', 'B' and
+'C' in the ASCII encoding scheme:
+
+| Memory address (as hex) | Data (as binary) | Data (as ASCII) |
+| ----------------------- | ---------------- | --------------- |
+| 0x0000                  | 1010101010101010 | A               |
+| 0x0001                  | 0010001001001011 | B               |
+| 0x0002                  | 0010001001001010 | C               |

zk/Stack_memory.md

@@ -65,5 +65,3 @@ thread which is what makes it well suited for managing scoped function memory.
 
 4. Recursion: individuating each call of a function that calls itself and its
    given step to avoid infinite loops
-
-## Related notes

zk/VirtualMemory.md

@@ -2,18 +2,19 @@
 tags:
   - memory
   - Linux
+  - kernel
 ---
 
 # Virtual memory
 
 Virtual memory is an abstracted and idealised representation of the physical
-memory capacity of the machine that is presented to user space for its memory
+memory capacity of a machine that is presented to user space for its memory
 operations.
 
-When an OS implements virtual memory, processes in user space cannot directly
-read or write to the actual memory. Instead they execute memory operations
-against virtual memory and the kernel translates these into actual operations
-against the memory hardware.
+When an OS implements virtual memory, [processes](./Processes.md) in
+[user space](./User_Space.md) cannot directly read or write to the actual
+memory. Instead they execute memory operations against virtual memory and the
+kernel translates these into the actual operations against the memory hardware.
 
 The main benefits:
 
@@ -23,14 +24,14 @@ The main benefits:
   that memory cannot be accidentally corrupted by other processes in user space.
 
 Because the physical memory is abstracted, it can be the case that the physical
-memory addresses are non-contiguous or even distributed accross different
-hardware components (such as the cache and swap). Despite this, the memory
-addresses will appear contiguous in virtual memory. Each user space process is
-presented with the same range of available memory addresses and the same total
-capacity.
+[memory addresses](./Memory_addresses.md) are non-contiguous or even distributed
+accross different hardware components (such as the cache and swap). Despite
+this, the memory addresses will appear contiguous in virtual memory. Each user
+space process is presented with the same range of available memory addresses and
+the same total capacity.
 
-It is possible for the kernel to present user space with an available virtual
-memory capcacity that actually exceeds the current physical capacity of the
+It is also possible for the kernel to present user space with an available
+virtual memory capcacity that exceeds the current physical capacity of the
 machine:
 
 > _It's possible for the kernel and all running processes to request more bytes
@@ -40,6 +41,14 @@ machine:
 
 _How Computers Really Work_ (2021) p.206
 
+Furthermore the kernel itself utilises virtual memory. The difference with
+kernel virtual memory is that it has a different range of virtual addresses to
+work with than user space virtual memory.
+
+Also, unlike user address space, the kernel has access to everything running in
+kernel address space. Processes in user address space are partitioned from each
+other with separate address spaces that cannot interact.
+
 // Next: the kernel also uses virtual memory however isn't also responsible for
 the appportioning of virtual memory. Confused.