This is related with microcontrollers but thought to post it here because it is a problem with algorithms and data types and not with any hardware stuff. I'll explain the problem so that someone that doesn't have any hardware knowledge can still participate :)
In Microcontroller there is an Analog to Digital converter with 10
bit resolution. (It will output a
value between 0 and 1023)
I need to send this value to PC using the serial port.
But you can only write 8 bits at once. (You need to write bytes). It is
a limitation in micro controller.
So in the above case at least I need to send 2 bytes.
My PC application just reads a sequence of numbers for plotting. So
it should capture two consecutive
bytes and build the number back. But
here we will need a delimiter
character as well. but still the delimiter character has an ascii value between 0 - 255 then it will mixup the process.
So what is a simplest way to do this? Should I send the values as a sequence of chars?
Ex : 1023 = "1""0""2""3" Vs "Char(255)Char(4)"
In summary I need to send a sequence of 10 bit numbers over Serial in fastest way. :)
You need to send 10 bits, and because you send a byte at a time, you have to send 16 bits. The big question is how much is speed a priority, and how synchronised are the sender and receiver? I can think of 3 answers, depending on these conditions.
Regular sampling, unknown join point
If the device is running all the time, you aren't sure when you are going to connect (you could join at any time in the sequence) but sampling rate is slower than communication speed so you don't care about size I think I'd probably do it as following. Suppose you are trying to send the ten bits abcdefghij (each letter one bit).
I'd send pq0abcde then pq1fghij, where p and q are error checking bits. This way:
no delimiter is needed (you can tell which byte you are reading by the 0 or 1)
you can definitely spot any 1 bit error, so you know about bad data
I'm struggling to find a good two bit error correcting code, so I guess I'd just make p a parity bit for bits 2,3 and 4 (0, a b above) and q a parity bit for 5 6 and 7 (c,d,e above). This might be clearer with an example.
Suppose I want to send 714 = 1011001010.
Split in 2 10110 , 01010
Add bits to indicate first and second byte 010110, 101010
calculate parity for each half: p0=par(010)=1, q0=par(110)=0, p1=par(101)=0, q1=par(010)=1
bytes are then 10010110, 01101010
You then can detect a lot of different error conditions, quickly check which byte you are being sent if you lose synchronisation, and none of the operations take very long in a microcontroller (I'd do the parity with an 8 entry lookup table).
Dense data, known join point
If you know that the reader starts at the same time as the writer, just send the 4 ten bit values as 5 bytes. If you always read 5 bytes at a time then no problems. If you want even more space saving, and have good sample data already, I'd compress using a huffman coding.
Dense data, unknown join point
In 7 bytes you can send 5 ten bit values with 6 spare bits. Send 5 values like this:
byte 0: 0 (7 bits)
byte 1: 1 (7 bits)
byte 2: 1 (7 bits)
byte 3: 1 (7 bits)
byte 4: 0 (7 bits)
byte 5: 0 (7 bits)
byte 6: (8 bits)
Then whenever you see 3 1's in a row for the most significant bit, you know you have bytes 1, 2 and 3. This idea wastes 1 bit in 56, so could be made even more efficient, but you'd have to send more data at a time. Eg (5 consecutive ones, 120 bits sent in 16 bytes):
byte 0: 0 (7 bits) 7
byte 1: 1 (7 bits) 14
byte 2: 1 (7 bits) 21
byte 3: 1 (7 bits) 28
byte 4: 1 (7 bits) 35
byte 5: 1 (7 bits) 42
byte 6: 0 (7 bits) 49
byte 7: (8 bits) 57
byte 8: (8 bits) 65
byte 9: (8 bits) 73
byte 10: (8 bits) 81
byte 11: 0 (7 bits) 88
byte 12: (8 bits) 96
byte 13: (8 bits) 104
byte 14: (8 bits) 112
byte 15: (8 bits) 120
This is quite a fun problem!
The best method is to convert the data to an ASCII string and send it that way - it makes debugging a lot easier and it avoids various communication issues (special meaning of certain control characters etc).
If you really need to use all the available bandwidth though then you can pack 4 10 bit values into 5 consecutive 8 bit bytes. You will need to be careful about synchronization.
Since you specified "the fastest way" I think expanding the numbers to ASCII is ruled out.
In my opinion a good compromise of code simplicity and performance can be obtained by the following encoding:
Two 10bit values will be encoded in 3 bytes like this.
first 10bit value bits := abcdefghij
second 10bit value bits := klmnopqrst
Bytes to encode:
1abcdefg
0hijklmn
0_opqrst
There is one bit more (_) available that could be used for a parity over all 20bits for error checking or just set to a fixed value.
Some example code (puts 0 at the position _):
#include <assert.h>
#include <inttypes.h>
void
write_byte(uint8_t byte); /* writes byte to serial */
void
encode(uint16_t a, uint16_t b)
{
write_byte(((a >> 3) & 0x7f) | 0x80);
write_byte(((a & 3) << 4) | ((b >> 6) & 0x7f));
write_byte(b & 0x3f);
}
uint8_t
read_byte(void); /* read a byte from serial */
void
decode(uint16_t *a, uint16_t *b)
{
uint16_t x;
while (((x = read_byte()) & 0x80) == 0) {} /* sync */
*a = x << 3;
x = read_byte();
assert ((x & 0x80) == 0); /* put better error handling here */
*a |= (x >> 4) & 3;
*b = x << 6;
x = read_byte();
assert ((x & 0xc0) == 0); /* put better error handling here */
*b |= x;
}
I normally use a start byte and checksum and in this case fixed length, so send 4 bytes, the receiver can look for the start byte and if the next three add up to a know quantity then it is a good packet take out the middle two bytes, if not keep looking. The receiver can always re-sync and it doesnt waste the bandwidth of ascii. Ascii is your other option, a start byte that is not a number and perhaps four numbers for decimal. Decimal is definitely not fun in a microcontroller, so start with something non-hex like X for example and then three bytes with the hex ascii values for your number. Search for the x examine the next three bytes, hope for the best.
Related
When we only have 6 bits of data on a byte, what do we fill the byte with up to 8? In the picture below the important data , it's only 10 03 , but what is the science behind, how that neimportant bits are choosen ? What mean [55] or [AA]? I mention 10 03 is a request for diagnosis and 50 03 are a response.
The communication its on CAN and that it's a trace with CAN DATA .
I dont understand what are you talking about, but that looks like a Hex representation.
1 byte -> 2 hex characters -> 8 bits. AA -> 10, 10 in decimal -> 1010 1010 (binary)
explicit bits are always the right side or LSB (less significant bits)
example, in javascript regular integer is 32 bit long.
`
const number = 0b1010 //binary
const hexNumber = 0xA // hex
` -> 10 in decimal. As you can see we have only tell the less significant 4 bits. every other bit is an implicit 0
After reading this, https://httpwg.org/specs/rfc7541.html#integer.representation
I am confused about quite a few things, although I seem to have the overall gist of the idea.
For one, What are the 'prefixes' exactly/what is their purpose?
For two:
C.1.1. Example 1: Encoding 10 Using a 5-Bit Prefix
The value 10 is to be encoded with a 5-bit prefix.
10 is less than 31 (2^5 - 1) and is represented using the 5-bit prefix.
0 1 2 3 4 5 6 7
+---+---+---+---+---+---+---+---+
| X | X | X | 0 | 1 | 0 | 1 | 0 | 10 stored on 5 bits
+---+---+---+---+---+---+---+---+
What are the leading Xs? What is the starting 0 for?
>>> bin(10)
'0b1010'
>>>
Typing this in the python IDE, you see almost the same output... Why does it differ?
This is when the number fits within the number of prefix bits though, making it seemingly simple.
C.1.2. Example 2: Encoding 1337 Using a 5-Bit Prefix
The value I=1337 is to be encoded with a 5-bit prefix.
1337 is greater than 31 (25 - 1).
The 5-bit prefix is filled with its max value (31).
I = 1337 - (25 - 1) = 1306.
I (1306) is greater than or equal to 128, so the while loop body executes:
I % 128 == 26
26 + 128 == 154
154 is encoded in 8 bits as: 10011010
I is set to 10 (1306 / 128 == 10)
I is no longer greater than or equal to 128, so the while loop terminates.
I, now 10, is encoded in 8 bits as: 00001010.
The process ends.
0 1 2 3 4 5 6 7
+---+---+---+---+---+---+---+---+
| X | X | X | 1 | 1 | 1 | 1 | 1 | Prefix = 31, I = 1306
| 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 1306>=128, encode(154), I=1306/128
| 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 10<128, encode(10), done
+---+---+---+---+---+---+---+---+
The octet-like diagram shows three different numbers being produced... Since the numbers are produced throughout the loop, how do you replicate this octet-like diagram within an integer? What is the actual final result? The diagram or "I" being 10, or 00001010.
def f(a, b):
if a < 2**b - 1:
print(a)
else:
c = 2**b - 1
remain = a - c
print(c)
if remain >= 128:
while 1:
e = remain % 128
g = e + 128
remain = remain / 128
if remain >= 128:
continue
else:
print(remain)
c+=int(remain)
print(c)
break
As im trying to figure this out, I wrote a quick python implementation of it, It seems that i am left with a few useless variables, one being g which in the documentation is the 26 + 128 == 154.
Lastly, where does 128 come from? I can't find any relation between the numbers besides the fact 2 raised to the 7th power is 128, but why is that significant? Is this because the first bit is reserved as a continuation flag? and an octet contains 8 bits so 8 - 1 = 7?
For one, What are the 'prefixes' exactly/what is their purpose?
Integers are used in a few places in HPACK messages and often they have leading bits that cannot be used to for the actual integer. Therefore, there will often be a few leading digits that will be unavailable to use for the integer itself. They are represented by the X. For the purposes of this calculation it doesn't make what those Xs are: could be 000, or 111, or 010 or...etc. Also, there will not always be 3 Xs - that is just an example. There could only be one leading X, or two, or four...etc.
For example, to look up a previous HPACK decoded header, we use 6.1. Indexed Header Field Representation which starts with a leading 1, followed by the table index value. Therefore that 1 is the X in the previous example. We have 7-bits (instead of only 5-bits in the original example in your question). If the table index value is 127 or less we can represent it using those 7-bits. If it's >= 127 then we need to do some extra work (we'll come back to this).
If it's a new value we want to add to the table (to reuse in future requests), but we already have that header name in the table (so it's just a new value for that name we want as a new entry) then we use 6.2.1. Literal Header Field with Incremental Indexing. This has 2 bits at the beginning (01 - which are the Xs), and we only have 6-bits this time to represent the index of the name we want to reuse. So in this case there are two Xs.
So don't worry about there being 3 Xs - that's just an example. In the above examples there was one X (as first bit had to be 1), and two Xs (as first two bits had to be 01) respectively. The Integer Representation section is telling you how to handle any prefixed integer, whether prefixed by 1, 2, 3... etc unusable "X" bits.
What are the leading Xs? What is the starting 0 for?
The leading Xs are discussed above. The starting 0 is just because, in this example we have 5-bits to represent the integers and only need 4-bits. So we pad it with 0. If the value to encode was 20 it would be 10100. If the value was 40, we couldn't fit it in 5-bits so need to do something else.
Typing this in the python IDE, you see almost the same output... Why does it differ?
Python uses 0b to show it's a binary number. It doesn't bother showing any leading zeros. So 0b1010 is the same as 0b01010 and also the same as 0b00001010.
This is when the number fits within the number of prefix bits though, making it seemingly simple.
Exactly. If you need more than the number of bits you have, you don't have space for it. You can't just use more bits as HPACK will not know whether you are intending to use more bits (so should look at next byte) or if it's just a straight number (so only look at this one byte). It needs a signal to know that. That signal is using all 1s.
So to encode 40 in 5 bits, we need to use 11111 to say "it's not big enough", overflow to next byte. 11111 in binary is 31, so we know it's bigger than that, so we'll not waste that, and instead use it, and subtract it from the 40 to give 9 left to encode in the next byte. A new additional byte gives us 8 new bits to play with (well actually only 7 as we'll soon discover, as the first bit is used to signal a further overflow). This is enough so we can use 00001001 to encode our 9. So our complex number is represented in two bytes: XXX11111 and 00001001.
If we want to encode a value bigger than can fix in the first prefixed bit, AND the left over is bigger than 127 that would fit into the available 7 bits of the second byte, then we can't use this overflow mechanism using two bytes. Instead we use another "overflow, overflow" mechanism using three bytes:
For this "overflow, overflow" mechanism, we set the first byte bits to 1s as usual for an overflow (XXX11111) and then set the first bit of the second byte to 1. This leaves 7 bits available to encode the value, plus the next 8 bits in the third byte we're going to have to use (actually only 7 bits of the third byte, because again it uses the first bit to indicate another overflow).
There's various ways they could go have gone about this using the second and third bytes. What they decided to do was encode this as two numbers: the 128 mod, and the 128 multiplier.
1337 = 31 + (128 * 10) + 26
So that means the frist byte is set to 31 as per pervious example, the second byte is set to 26 (which is 11010) plus the leading 1 to show we're using the overflow overflow method (so 100011010), and the third byte is set to 10 (or 00001010).
So 1337 is encoded in three bytes: XXX11111 100011010 00001010 (including setting X to whatever those values were).
Using 128 mod and multiplier is quite efficient and means this large number (and in fact any number up to 16,383) can be represented in three bytes which is, not uncoincidentally, also the max integer that can be represented in 7 + 7 = 14 bits). But it does take a bit of getting your head around!
If it's bigger than 16,383 then we need to do another round of overflow in a similar manner.
All this seems horrendously complex but is actually relatively simply, and efficiently, coded up. Computers can do this pretty easily and quickly.
It seems that i am left with a few useless variables, one being g
You are not print this value in the if statement. Only the left over value in the else. You need to print both.
which in the documentation is the 26 + 128 == 154.
Lastly, where does 128 come from? I can't find any relation between the numbers besides the fact 2 raised to the 7th power is 128, but why is that significant? Is this because the first bit is reserved as a continuation flag? and an octet contains 8 bits so 8 - 1 = 7?
Exactly, it's because the first bit (value 128) needs to be set as per explanation above, to show we are continuing/overflowing into needing a third byte.
This is a quiz question which I failed in the past and despite having access to the solution, I don't understand the different step to come to the correct answer.
Here is the problem :
Which of these adress is line cache aligned
a. 0x7ffc32a21164
b. 0x560c40e05350
c. 0x560c40e052c0
d. 0x560c3f2d71ff
And the solution to the problem:
Each hex char is represented by 4 bits
It takes 6 bits to represent 64 adress, since ln(64)/ln(2) = 6
0x0 0000
0x4 0100
0x8 1000
0xc 1100
________
2^3 2^2 2^1 2^0
8 4 2 1
Conclusion: if the adress ends if either 00, 40, 80 or c0, then it is aligned on 64 bytes.
The answer is c.
I really don't see how we go from 6 bits representation to this answer. Can anyone adds something to the solution given to make it clearer?
The question boils down to: Which number is a multiple of 64? All that remains is understanding the number system they're using.
In binary, 64 is written as 1000000. In hexadecimal, it's written as 0x40. So multiples of 64 will end in 0x00 (0 * 64), 0x40 (1 * 64), 0x80 (2 * 64), or 0xC0 (3 * 64). (The cycle then repeats.) Answer c is the one with the right ending.
An analogy in decimal would be: Which number is a multiple of 5? 0 * 5 is 0 and 1 * 5 is 5, after which the cycle repeats. So we just need to look at the last digit. If it's a 0 or a 5, we know the number is a multiple of 5.
i am really confused on the topic Direct Mapped Cache i've been looking around for an example with a good explanation and it's making me more confused then ever.
For example: I have
2048 byte memory
64 byte big cache
8 byte cache lines
with direct mapped cache how do i determine the 'LINE' 'TAG' and "Byte offset'?
i believe that the total number of addressing bits is 11 bits because 2048 = 2^11
2048/64 = 2^5 = 32 blocks (0 to 31) (5bits needed) (tag)
64/8 = 8 = 2^3 = 3 bits for the index
8 byte cache lines = 2^3 which means i need 3 bits for the byte offset
so the addres would be like this: 5 for the tag, 3 for the index and 3 for the byte offset
Do i have this figured out correctly?
Do i figured out correctly? YES
Explanation
1) Main memmory size is 2048 bytes = 211. So you need 11 bits to address a byte (If your word size is 1 byte) [word = smallest individual unit that will be accessed with the address]
2) You can calculating tag bits in direct mapping by doing (main memmory size / cash size). But i will explain a little more about tag bits.
Here the size of a cashe line( which is always same as size of a main memmory block) is 8 bytes. which is 23 bytes. So you need 3 bits to represent a byte within a cashe line. Now you have 8 bits (11 - 3) are remaining in the address.
Now the total number of lines present in the cache is (cashe size / line size) = 26 / 23 = 23
So, you have 3 bits to represent the line in which the your required byte is present.
The number of remaining bits now are 5 (8 - 3).
These 5 bits can be used to represent a tag. :)
3) 3 bit for index. If you were trying to label the number of bits needed to represent a line as index. Yes you are right.
4) 3 bits will be used to access a byte withing a cache line. (8 = 23)
So,
11 bits total address length = 5 tag bits + 3 bits to represent a line + 3 bits to represent a byte(word) withing a line
Hope there is no confusion now.
I didn't understand what do the Huffman tables of Jpeg contain, could someone explain this to me?
Thanks
Huffman encoding is a variable-length data compression method. It works by assigning the most frequent values in an input stream to the encodings with the smallest bit lengths.
For example, the input Seems every eel eeks elegantly. may encode the letter e as binary 1 and all other letters as various other longer codes, all starting with 0. That way, the resultant bit stream would be smaller than if every letter was a fixed size. By way of example, let's examine the quantities of each character and construct a tree that puts the common ones at the top.
Letter Count
------ -----
e 10
<SPC> 4
l 3
sy 2
Smvrkgant. 1
<EOF> 1
The end of file marker EOF is there since you generally have to have a multiple of eight bits in your file. It's to stop any padding at the end from being treated as a real character.
__________#__________
________________/______________ \
________/________ ____\____ e
__/__ __\__ __/__ \
/ \ / \ / \ / \
/ \ / \ / SPC l s
/ \ / \ / \ / \ / \
y S m v / k g \ n t
/\ / \
r . a EOF
Now this isn't necessarily the most efficient tree but it's enough to establish how the encodings are done. Let's first look at the uncompressed data. Assuming an eight-bit encoding, those thirty-one characters (we don't need the EOF for the uncompressed data) are going to take up 248 bits.
But, if you use the tree above to locate the characters, outputting a zero bit if you take the left sub-tree and a one bit if you take the right, you get the following:
Section Encoding
---------- --------
Seems<SPC> 00001 1 1 00010 0111 0101 (20 bits)
every<SPC> 1 00011 1 001000 00000 0101 (22 bits)
eel<SPC> 1 1 0110 0101 (10 bits)
eeks<SPC> 1 1 00101 0111 0101 (15 bits)
elegantly 1 0110 1 00110 001110 01000 01001 0110 00000 (36 bits)
.<EOF> 001001 001111 (12 bits)
That gives a grand total of 115 bits, rounded up to 120 since it needs to be a multiple of a byte, but that's still about half the size of the uncompressed data.
Now that's usually not worth it for a small file like this, since you have to add the space taken up by the actual tree itself(a), otherwise you cannot decode it at the other end. But certainly, for larger files where the distribution of characters isn't even, it can lead to impressive savings in space.
So, after all that, the Huffman tables in a JPEG are simply the tables that allow you to uncompress the stream into usable information.
The encoding process for JPEG consists of a few different steps (color conversion, chroma resolution reduction, block-based discrete cosine transforms, and so on) but the final step is a lossless Huffman encoding on each block which is what those tables are used to reverse when reading the image.
(a) Probably the best case for minimal storage of this table would be something like:
Size of length section (8-bits) = 3 (longest bit length of 6 takes 3 bits)
Repeated for each byte:
Actual length (3 bits, holding value between 1..6 inclusive)
Encoding (n bits, where n is the actual length)
Byte (8 bits)
End of table marker (3 bits) = 0 to distinguish from actual length above
For the text above, that would be:
00000011 8 bits
n bits byte
--- ------ -----
001 1 'e' 12 bits
100 0101 <SPC> 15 bits
101 00001 'S' 16 bits
101 00010 'm' 16 bits
100 0111 's' 15 bits
101 00011 'v' 16 bits
110 001000 'r' 17 bits
101 00000 'y' 16 bits
101 00101 'k' 16 bits
100 0110 'l' 15 bits
101 00110 'g' 16 bits
110 001110 'a' 17 bits
101 01000 'n' 16 bits
101 01001 't' 16 bits
110 001001 '.' 17 bits
110 001111 <EOF> 17 bits
000 3 bits
That makes the table 264 bits which totally wipes out the savings from compression. However, as stated, the impact of the table becomes far less as the input file becomes larger and there's a way to avoid the table altogether.
That way involves the use of another variant of Huffman, called Adaptive Huffman. This is where the table isn't actually stored in the compressed data.
Instead, during compression, the table starts with just EOF and a special bit sequence meant to introduce a new real byte into the table.
When introducing a new byte into the table, you would output the introducer bit sequence followed by the full eight bits of that byte.
Then, after each byte is output and the counts updated, the table/tree is rebalanced based on the new counts to be the most space-efficient (though the rebalancing may be deferred to improve speed, you just have to ensure the same deferral happens during decompression, an example being every time you add byte for the first 1K of input, then every 10K of input after that, assuming you've added new bytes since the last rebalance).
This means that the table itself can be built in exactly the same way at the other end (decompression), starting with the same minimal table with just the EOF and introducer sequence.
During decompression, when you see the introducer sequence, you can add the byte following it (the next eight bits) to the table with a count of zero, output the byte, then adjust the count and re-balance (or defer as previously mentioned).
That way, you do not have to have the table shipped with the compressed file. This, of course, costs a little more time during compression and decompression in that you're periodically rebalancing the table but, as with most things in life, it's a trade-off.
The DHT marker doesn't specify directly which symbol is associated with a code. It contains a vector with counts of how many codes there are of a given length. After that it contains a vector with symbol values.
So when you want to decode you have to generate the huffman codes from the first vector and then associate every code with a symbol in the second vector.