Ymodem Buffer Start Address - memory

I am looking this source codes to use Ymodem protocole,
https://github.com/STMicroelectronics/STM32CubeF4/blob/master/Projects/STM324xG_EVAL/Applications/IAP/IAP_Main/inc/ymodem.h
But I've a question about that,
Line 65 says to us as in below:
/* /-------- Packet in IAP memory ------------------------------------------\
* | 0 | 1 | 2 | 3 | 4 | ... | n+4 | n+5 | n+6 |
* |------------------------------------------------------------------------|
* | unused | start | number | !num | data[0] | ... | data[n] | crc0 | crc1 |
* \------------------------------------------------------------------------/
* the first byte is left unused for memory alignment reasons
According to this informaton PACKET_DATA_INDEX define 4. But I dont understand this because in the Ymodem includes data in 3th byte, why we choose the 4th byte or SOH is the 0th index of the frame, why we get this as a 1

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How to forecast (or any other function) in Google Sheets with only one cell of data?

My sheet:
+---------+-----------+---------+---------+-----------+
| product | value 1 | value 2 | value 3 | value 4 |
+---------+-----------+---------+---------+-----------+
| name 1 | 700,000 | 500 | 10,000 | 2,000,000 |
+---------+-----------+---------+---------+-----------+
| name 2 | 200,000 | 800 | 20,000 | ? |
+---------+-----------+---------+---------+-----------+
| name 3 | 100,000 | 150 | 6,000 | ? |
+---------+-----------+---------+---------+-----------+
| name 4 | 1,000,000 | 1,000 | 25,000 | ? |
+---------+-----------+---------+---------+-----------+
| name 5 | 2,000,000 | 1,500 | 30,000 | ? |
+---------+-----------+---------+---------+-----------+
| name 6 | 2,500,000 | 3,000 | 65,000 | ? |
+---------+-----------+---------+---------+-----------+
| name 7 | 300,000 | 300 | 12,000 | ? |
+---------+-----------+---------+---------+-----------+
| name 8 | 350,000 | 200 | 9,000 | ? |
+---------+-----------+---------+---------+-----------+
| name 9 | 900,000 | 1,200 | 28,000 | ? |
+---------+-----------+---------+---------+-----------+
| name 10 | 150,000 | 100 | 5,000 | ? |
+---------+-----------+---------+---------+-----------+
What I am attempting is to predict the empty columns based on the data that I do have. Maybe just one of the columns that contain data in every row or maybe I should be only focusing on one column that contains data in every row?
I have used FORECAST previously but had more data in the column that I was predicting values for which the lack of data I think is my root problem(?). Not sure if FORECAST is best for this so any recommendations for other functions are most welcome.
The last thing I can add though is that the known value in column E (value 4) is a confident number and ideally it's used in any formula that I end up with (although I am open to any other recommendations).
The formula I was using:
=FORECAST(D3,E2,$D$2:$D$11)
I don't think this is possible without more information. If you think about it, Value 4 can be a constant (always 2,000,000), be dependent on only one other value (say 200 times value 3), or be a complex formula (say add values 1, 2, and 3 with a constant). Each of these 3 models agree with the values for name 1, however they generate vastly different value 4 predictions.
In the case of name 2, the models would output the following for value 4:
Constant: 2,000,000
Value 3: 8,000,000
Sum: 2,489,700
Each of those values could be valid without providing further constraints (either through data points or specifying the kind of model, but probably both).

How to copy a whole row as a template and replace one columns value in Google Sheets

I have a sheet which im using to build product data. I need to handle some custom SKU's and id like to have them stored in a string like "XYZ,ABC,FGH" in an alternate sheet.
The generic products are generated in the other sheet for various sizes automatically. I would like on the end of this list to be able to take one of these automatic rows as a template and replace the SKU with one of the custom SKU's if they exist in the other config sheet.
So for example:
SKU'S | Name | Width | Height | Weight | Quantity
--------------------------------------------------
PARENT| X | 10 | 20 | 100 | 0
M1 | X | 10 | 20 | 100 | 1
M2 | X | 10 | 20 | 100 | 2
M3 | X | 10 | 20 | 100 | 3
M4 | X | 10 | 20 | 100 | 4
M5 | X | 10 | 20 | 100 | 5
Then append:
ABC | X
XYZ | X
FGH | X
Keeping the existing columns the other products use.
The X's are just a representation for the other columns I want to copy (ive added some further columns as example data). The only thing I want to change is the SKU. Its a duplicate apart from the SKU (which I want to replace) and the Quantity. The consistent one to copy and use as the template would be the row with PARENT as the SKU.
The result is to just be a new row underneath M5 row. These are additional rows to just be tagged onto the end except for a change in the SKU.
The import is a lot of duplication to the database which is the product attributes like width, height, depth, weight, etc. This is set in a sheet I made with the name VARS. So I would create a simple field in VARS for 'Custom Additional SKUs' in say VARS!$B$10 with the value 'ABC,XYZ,FGH'. These would then use the same columns as the SKU's in say a sheet called INVENTORY.
The end result would be something like:
SKU'S | Name | Width | Height | Weight | Quantity
--------------------------------------------------
PARENT| X | 10 | 20 | 100 | 0
M1 | X | 10 | 20 | 100 | 1
M2 | X | 10 | 20 | 100 | 2
M3 | X | 10 | 20 | 100 | 3
M4 | X | 10 | 20 | 100 | 4
M5 | X | 10 | 20 | 100 | 5
ABC | X | 10 | 20 | 100 | 0
XYZ | X | 10 | 20 | 100 | 0
FGH | X | 10 | 20 | 100 | 0
Final solution based on feedback to help others.
Based on the great input from pnuts I went with the following in column A underneath:
=sort(transpose(split(VARS!A1,",")),1,TRUE)
In column B:
=IF(ISBLANK(A7),"",QUERY(SKU!A2:F2,"select B,C,D,E,F",0))
Works like a charm!
Maybe try:
=sort(transpose(split(NamedRange1,",")),1,TRUE)
and next to the above something like:
=QUERY(SKU!A:F,"select B,C,D,E,F where A='PARENT'",0)
copied down to suit.

Does endianness refer to ordering within a defined array or memory or also the actual memory used?

I'm having trouble expressing my question in words, but I think I can express it visually quite simply. Storing the string abcd, is the difference between Big and Little Endian this:
memory address | 0 | 1 | 2 | 3 | 4 | 5 | 6 | ...
little endian | d | c | b | a |
big endian | a | b | c | d |
Or this:
memory address | 0 | 1 | 2 | 3 | 4 | 5 | 6 | ...
little endian | d | c | b | a |
big endian | a | b | c | d |
My attempt in words: does "endianness" refer to the ordering of bytes within a specific memory "array", where in both cases the array begins at the same point in memory, or does it refer to both the ordering and the actual array used?
Endianness refers to the ordering of bytes used to store a single multi-byte numerical value. The "big endian" system in your second image is storing 4-byte integers unaligned, which no system would normally do.

Rails Many to many relationships with connecting or cloning two table with references?

I'm a new with Rails and I'm having trouble with some types of associations that seem a bit more complex than the ones I've been exposed to so far.
Zombie_users Body_parts_status Body_parts
| id | name | | id | user_id | body_part_id | recovery | | id | name |
|-----------| --> |----------------------------------------| --> |---------------|
| 1 | Joe | | 1 | 1 | 2 | 10% | | 1 | left leg |
| 2 | Max | | 2 | 1 | 3 | 43% | | 2 | brain |
| 3 | hair |
| 4 | blue eye |
Zobmie_users Recovery_tools Body_parts_impacts
| id | name | | id |user_id| name | | id|recovery_tool_id| body_part_id | impact |
|-----------|-->|-------------------|-->|--------------------------------------------|
| 1 | Joe | | 1 | 1 |hammer| | 1 | 1 | 2 | 10% |
| 2 | Max | | 2 | 1 |magic | | 2 | 2 | 3 | 43% |
graphic illustration of the needed functionality
We have users and a list of body parts.
I need that the users will be able to create recovery tools with which they can through Body Parts impact recover their body parts status :)
and be able to check what part of the body still need to be fixed(compared to the list) and what body parts they have already corrected.
My problem is that I do not know how to implement such connections.
because I need to have some kind of clone of the body parts to body parts status for each user.
But how I reference it so it also works with Body Parts impacts
I do not have even a concept of where to start :)
body parts table is just a long listing of all the parts of the human body
and each user should have their own "copy" of all these parts.

How to do a goedel numbering for bit strings?

I'm looking for a concept for doing a Gödel numbering for bit strings, i.e. for arbitrary binary data.
Approach 1 (failing): Simply interpret the binary data as data of an unsigned integer.
This fails, because e.g. the two different strings "01" and "001" both represent the same integer 1.
Is there a standard way of doing this? Is 0 usually included or excluded from the Gödel numbering?
The original Gödel numbering used prime numbers and unique encoding of symbols. If you want to do it for strings consisting of "0" and "1", you need positive codes for "0" (say 1) and "1" (say 2). Then numbering of "01" is
21 * 32
while numbering of "001" is
21 * 31 * 52
For longer strings use next prime numbers. However, note that Gödel numbering goals did not include any practical considerations, he simply needed numbering as a tool in the proof of his theorem. In practice for fairly short strings you will exceed range of integers in your language, so you need to use either a language with arbitrary large integers built-in (like Scheme) or a library supporting bignums in language without them built-in.
A super simple solution is to prepend a 1 to the binary data and then interpret the result as an unsigned integer value. This way, no 0-digits get lost at the left side of the bit string.
Illustration how well this works:
One obvious way to order bit strings is to order them first by length and then lexicographically:
+------------+
| bit string |
+------------+
| ε |
| 0 |
| 1 |
| 00 |
| 01 |
| 10 |
| 11 |
| 000 |
| 001 |
| 010 |
| 011 |
| 100 |
| 101 |
| 110 |
| ... |
+------------+
(ε denotes the empty string with no digits.)
Now we add an index number n to this table, starting with 1, and then look at the binary representation of the index number n. We will make a nice discovery there:
+------------+--------------+-------------+
| bit string | n in decimal | n in binary |
+------------+--------------+-------------+
| ε | 1 | 1 |
| 0 | 2 | 10 |
| 1 | 3 | 11 |
| 00 | 4 | 100 |
| 01 | 5 | 101 |
| 10 | 6 | 110 |
| 11 | 7 | 111 |
| 000 | 8 | 1000 |
| 001 | 9 | 1001 |
| 010 | 10 | 1010 |
| 011 | 11 | 1011 |
| 100 | 12 | 1100 |
| 101 | 13 | 1101 |
| 110 | 14 | 1110 |
| ... | ... | ... |
+------------+--------------+-------------+
This works out surprisingly well, because the binary representation of n (the index of each bit string when ordering in a very obvious way) is nothing else than a 1 prepended to the original bit string and then the whole thing interpreted as an unsigned integral value.
If you prefer a 0-based Goedel numbering, then subtract 1 from the resulting integer value.
Conversion formulas in pseudo code:
// for starting with 1
n_base1 = integer(prepend1(s))
s = removeFirstDigit(bitString(n_base1))
// for starting with 0
n_base0 = integer(prepend1(s)) - 1
s = removeFirstDigit(bitString(n_base0 + 1))

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