Convert floating point to binary

Hiii...

I want to ask how to convert floating point to binary in MATLAB

Thank you

Answer 1

[Andrei Bobrov]

e.g.:

a = 1234.57849; % your float point number
n = 16;         % number bits for integer part of your number      
m = 20;         % number bits for fraction part of your number
% binary number
d2b = [ fix(rem(fix(a)*pow2(-(n-1):0),2)), fix(rem( rem(a,1)*pow2(1:m),2))];  % 
% the inverse transformation
b2d = d2b*pow2([n-1:-1:0 -(1:m)].');

EDIT [16:32(UTC+4) 08.01.2012]

a = 1234.57849; % your float point number
n = 16;         % number bits for integer part of your number      
m = 25;         % number bits for fraction part of your number
% binary number
d2b = fix(rem(a*pow2(-(n-1):m),2)); 
% the inverse transformation
b2d = d2b*pow2(n-1:-1:-m).';

[Walter Roberson]

Been a while since I saw a 36 bit word ;-)

(Yes, I have used 36 bit computers.)

[Julien Cohen]

Much thanks (4 years later), this worked perfectly in my implementation of a genetic algorithm function.

[OMID Fattemi]

for implementing GA, I used randint function to generate initial population as

d2b=randint(1,m+n);

then by the following code, decimal floating number is obtained:

b2d = d2b*pow2(n-1:-1:-m)';

[Dave Amels]

DEC system 10

[An Vo]

This code works perfectly for positive number. I run with negative number, the binary sequence contains bit 0, 1 and -1. bit -1 is not right. How can I fix this problem?

[Walter Roberson]

As discussed below, for negative values, you need to be specific about which representation you want to use for the binary fraction.

[saba h]

Thanks.

Answer 2

[Oliver P]

Thank you for the cute and elegant solution! Unfortunately it's only working for positive floats. Negative floats will produce the same result as positive floats, but with negative bits. Which, of course, is not valid. And it's not the proper representation of negative values anyway.

[Walter Roberson]

The proper representation of negative values? As decreed by which King?

[Oliver P]

I'm not aware of a king here, but an association called IEEE. :-) The IEEE 754 format defines, for example, the leading bit convention. Matlab converts -22.9 properly to binary32 when you use:

dec2bin(typecast(single(-22.9), 'uint32'))

It's also possible to convert to binary64 in a similar way. But not to custom formats. Please do check this webpage for more info on this topic: IEEE 754 Converter

[Walter Roberson]

IEEE 754 defines one way to represent single precision numbers as binary, but it is far from being the only valid way.

When people ask about converting negative floating point to binary, the context is most typically the need to transmit quantized signals, which is almost always a fixed-point context, not a floating-point context. IEEE 754 does not deal with fixed point.

[Oliver P]

Yes, I agree. As far as I'm aware Matlab uses IEEE-754 for all floating-point (single, double and custom) and for unsigned fixed-point calculations. Only for signed fixed-point it's using two's-complement representation.

[Walter Roberson]

The "Fixed Point Toolbox" can handle floating point numbers, but are only IEEE 754 if you request very specific formats.

I do not recall that the internal format for floating point number in the Symbolic Toolbox is documented.

The Fixed Point Toolbox offers Separated Sign. I would need to recheck to see if it offers One's Complement.

Answer 3

[Walter Roberson]

You need to define the fraction representation in binary.

See also http://www.mathworks.com/matlabcentral/newsreader/view_thread/280927

[Walter Roberson]

(Thread moved to https://groups.google.com/g/comp.soft-sys.matlab/c/JNqcvo0WWSU/m/zvC968pq3fkJ )

Answer 4

[Muammar]

Thank you for all answers...

Answer 5

[naghma tabassum]

visit this link https://in.mathworks.com/matlabcentral/fileexchange/39113-floating-point-number-conversion

Answer 6

[Aneesh paulsagin]

convert complex number to binary number

A = [-0.0040383664156692-0.00294191598222591i, ...
     1.00279327279556+0.00768012699728154i, ...
     -0.00226521017869135+0.00526418383309796i, ...
     0.999498954084202-0.007158248828685i, ...
     -0.00549315262581557+0.00808461388120792i, ...
     0.998352426774419+0.00927983415466687i, ...
     0.00736345881927219+0.00540426830690426i, ...
     0.989408434745709-0.0144762821959683i, ...
     0.00827899268722473+0.0122398877118786i, ...
     0.999298739008971-0.0129949269950415i, ...
     -5.47057549608037e-07-0.0130605748664198i, ...
     1.01414402334238+0.0131228156923076i, ...
     0.000678728159952879-0.00434397278237206i, ...
     0.985341332736134+0.0239798712601118i, ...
     0.0109818351271128-0.00658607972360998i, ...
     1.01709879921672-0.00394256645505557i, ...
     0.000335417716939878-0.00461609765687651i, ...
     0.996785178287252-3.51718069407279e-05i, ...
     -0.0137042758344959+0.00734580139566216i, ...
     1.01389851161064+0.00526816880638668i, ...
     -0.0143246406043654-0.0173541476823603i, ...
     0.984838248467196-0.00274924075252472i, ...
     -0.00383017735389232-0.00877400220581385i, ...
     0.996013541706753+0.0113592028562242i, ...
     -0.00607963966107746-0.00701052911751136i, ...
     1.00401827238935-0.0163653626342944i]

[Walter Roberson]

A_binary = reshape(dec2bin(typecast(reshape([real(A(:).'); imag(A(:).')], 1, []),'uint64'),64).',1, []);

[Ian Ono]

Walter Robinson, If I use your line to create A_binary and then fwrite it to file. How would I fread it back?

[Walter Roberson]

format long g
A = [
         1.01709879921672-0.00394256645505557i, ...
         0.996013541706753+0.0113592028562242i, ...
        -0.00607963966107746-0.00701052911751136i, ...
]

A = 
           1.01709879921672 -   0.00394256645505557i          0.996013541706753 +    0.0113592028562242i       -0.00607963966107746 -   0.00701052911751136i

A_binary_out = reshape(dec2bin(typecast(reshape([real(A(:).'); imag(A(:).')], 1, []),'uint8'),8).',1, []);

tn = tempname();   %temporary file name

fid = fopen(tn, 'w');
fwrite(fid, A_binary_out, 'char');
fclose(fid);

fid = fopen(tn, 'r');
A_binary_in = char(fread(fid, [1 inf], 'uint8'));
fclose(fid);

pairs = typecast(uint8(bin2dec(reshape(A_binary_in, 8, []).')),'double');
A_reconstructed = pairs(1:2:end) + 1i .* pairs(2:2:end)

A_reconstructed = 
           1.01709879921672 -   0.00394256645505557i
          0.996013541706753 +    0.0113592028562242i
       -0.00607963966107746 -   0.00701052911751136i

If your original A did not happen to be a column vector, then you will need a step to reshape it to the original size.

[Ian Ono]

Great!

Much thanks