Converting vector to binary and summing it

Greetings,

I have a large vector 2048 x 1 of numbers I need to convert into binary and add them all togather (disregarding overflow) to create a checksum. Can I convert all the numbers to binary with a

dec2bin( decimal number) followed by a sum(vector)

Commands? This data is written to flash memory and we need to impliment a checksum

Thanks

[Walter Roberson]

Is binary 11 + 11 to result in 10 ? That is, carry is used within the word, but overflow beyond the word is discarded?

[Image Analyst]

Which checksum algorithm are you using? http://en.wikipedia.org/wiki/Checksum

Answer 1

[Jan]

What kind of checksum are you talking of?

If the numbers have a range of 0-255 a simple CRC32 could be helpful:

% Create CRC lookup table:
CRC_Table  = zeros(1, 256);
POLYNOMIAL = 79764919;      % 0x04c11db7L
shift24    = 16777216;
for i = 0:255
   % crc = bitshift(i, 24);
   crc = i * shift24;  % Faster
   for j = 0:7
      if crc >= 2147483648  % if bitget(crc, 32)
         %crc = bitand(bitxor(crc * 2, POLYNOMIAL), 4294967295);
         crc = rem(bitxor(crc * 2, POLYNOMIAL), 4294967296);
      else
         crc = crc * 2;
      end
   end  % for j
   % CRC_Table(i + 1) = bitand(crc, 4294967295);
   CRC_Table(i + 1) = rem(crc, 4294967296);
end  % for i

S  = 0;
c1 = 16777216;     % 2^24
c3 = 256;
c5 = 4294967296;   % 2^32: REM instead of BITAND
for n = 1:length(Data)
   m = rem(bitxor(fix(S / c1), Data(n)), c3);
   S = bitxor(rem(S * c3, c5), CRC_Table(m + 1));
end

S = sprintf('%.8X', S);

For another range, you can cast the values:

Data = typecast(Data, 'uint8');

Further hash methods can be found in: FEX: DataHash. E.g.:

Engine  = java.security.MessageDigest.getInstance('SHA-256');
Engine.update(tyepcast(Data, 'uint8'));
Hash    = typecast(Engine.digest, 'uint8');
HashHex = sprintf('%.2x', Hash);

[Saira Williams]

Can you please show an example using CRC16 -CCITT?

Thank you!

[Saira Williams]

With a range of numbers 0-252. It would be really helpful your support.

Answer 2

[Thomas]

dec2bin gives the output as a string.. You will need to do more processing to actually get it numerically useful..

[William]

That was kind of my questions. As far As I know MATLAB treats Hex and Bin number like strings. This means I cannot to math to them

[Walter Roberson]

subtract '0' (the character string that is a zero). That will get you numeric 0 and 1. But doing arithmetic on that can be tedious if you need to compute all the carries yourself. Hence my question, above which you have not answered :(

Answer 3

[James Tursa]

What is the range of your numbers? You might be able to simply convert them to double, then add them, then mod the result with an appropriate value for your target wordsize.

Answer 4

[Walter Roberson]

Use John D'Errico's MATLAB File Exchange contribution vpi package. Add the numbers without converting them to decimal. Take the result mod 2^(your word size) to get the result.

Answer 5

[Walter Roberson]

Use the fixedpoint arithmetic package with the arithmetic properties set to "wrap" instead of "saturate".

Answer 6

[William]

The basic idea behind this is that I am writing data to flash memory. I would like to take sixteen bytes and sum the entire 1024 number vector and take the twos compliment. I would then add the checksum I just created to the very last place when I wrote the data into flash.

Upon retirival of the data I would read the first number, store it, read the second number and add it to the first and store the result. The last number I add should be the two's compliment of the sum and adding the sum and it's two's compliment would mean I get zero as a result passing the checksum.

[Walter Roberson]

I do not understand how the 1024 number vector relates to the 16 bytes? If the 16 bytes are to be sort of added on to a constant 1024 number vector, then pre-calculate the sum on the 1024 number vector so there is less work to do.

These vectors of 1024 numbers: what data type and range are those? There is a difference in approach if they are uint8 compared to if they are 8 byte IEEE double precision floating point numbers.

[William]

To offer a more clear explanation each one of the 1024 numbers is stored in 16 bits. not bytes., my mistake.

[Jan]

What is the purpose of the checksum? It will detect some 1-bit errors, but not all and even less 2 bit errors.

[Walter Roberson]

Still it is a very common checksum, still in wide use as a "sanity check"

Answer 7

[Walter Roberson]

convert the vector to 32 bit unsigned. sum() it. Extract the last 16 bits with bitget() or bitand() or mod()

[NGR MNFD]

hi dear

can you help me ? I want to know

How can I check the checksum of the force signal binary file? This force signal is measured by a 12-bit adc. I was able to display it through the following method.

fileID1=fopen('control1.let','r');
A= fread(fileID1, [3, 45000], 'uint8')';  % matrix with 3 rows, each 8 bits long, = 2*12bit
fclose(fileID1);
M2H= bitshift(A(:,2), -4);
M1H= bitand(A(:,2), 15);
PRL=bitshift(bitand(A(:,2),8),9);     % sign-bit
PRR=bitshift(bitand(A(:,2),128),5);   % sign-bit
M( : , 1)= bitshift(M1H,8)+ A(:,1)-PRL;
M( : , 2)= bitshift(M2H,8)+ A(:,3)-PRR;
N1 = reshape(M',[90000,1]); plot(N1);

Can I also check to see if it is correct or not? I do not know what code to use in MATLAB to calculate checksum? Please show me. Thank you.

[Walter Roberson]

A= fread(fileID1, [3, 45000], 'uint8')';  % matrix with 3 rows, each 8 bits long, = 2*12bit

To be clear, the above code would store into A(1,1) then A(2,1), then A(3,1) then A(1,2) then A(2,2) then A(3,2) and so on. 3 rows, stored along the rows.

But when talking about binary data created by something else, it is common for data to be stored across the columns, rather than down the rows -- for the first entry to be A(1,1), then A(1,2), A(1,3) ... then after all the columns, A(2,1), A(2,2) and so on.

You need to be clear as to which arrangement you have.

Also your comment talks about 3 rows each each bits long, implying that it forms two 12 bit numbers. Is the implication But again it is important to know which order the data is stored in.

Answer 8

[Fa Fa]

Hi All, i like to create lookup tables of 511 local binary pattern, also from 10000000 bis 111111110, can somebody help, Thanks

[Walter Roberson]

I recommend opening a new Question for this topic.