Negative floats to Binary

I have a matrix of 1 column with floats between -1 and 1. Something like [0.245 -0.942 0.424 -0.543]. I want to convert each number to binary in two's complement form. I've seen dec2bin only works for positive intergers. Any suggestions?

Answer 1

[John D'Errico]

Just extract the bits. I'll get you started, like this.

X = -0.942;
hex = sprintf('%bx',X)
hex =
    'bfee24dd2f1a9fbe'

The sign bit is bit #1. Bits #2-12 are the exponent, offset by 1023. So convert the exponent bits to an 11 bit integer between 0 and 2047. bin2dec can do that. Then subtract 1023 to write it as a power of 2.

But what you are asking for is the mantissa, in twos complement form. Just extract bits #13-64. This hack (extracted from some code I once wrote) should work:

tablout = dec2bin(0:15);
tablin = transpose('0123456789abcdef');
      
% ismember does the work here
[~,hexind] = ismember(hex,tablin);
      
Xbin = tablout(hexind,:);
Xbin = reshape(Xbin',64,[])';

Xbin
Xbin =
    '1011111111101110001001001101110100101111000110101001111110111110'

You need to be a little careful in representing de-normal numbers (sometimes called subnormals.) For example:

realmin/2^20
ans =
     2.12199579096527e-314

is a denormal number, represented as a double. But that is not your real question, which the code I gave should help you to solve. You can recognize a denormal because the exponent you would get will be -1023.

(I need to get around to posting num2bin one day.)

[João Fernandes]

So i get the result as a char. I've never worked with binary values in Matlab. Should i work with Xbin as a char or is it possible use it as a binary value?

[John D'Errico]

Oh, you can use it in any you want.

Xbin
Xbin =
    '1011111111101110001001001101110100101111000110101001111110111110'

For example, you can convert it to a vector of 0-1 integers.

Xbin - '0'
ans =
  Columns 1 through 31
     1     0     1     1     1     1     1     1     1     1     1     0     1     1     1     0     0     0     1     0     0     1     0     0     1     1     0     1     1     1     0
  Columns 32 through 62
     1     0     0     1     0     1     1     1     1     0     0     0     1     1     0     1     0     1     0     0     1     1     1     1     1     1     0     1     1     1     1
  Columns 63 through 64
     1     0

Character is my preference, since it takes less space to display. The chars are stored as two bytes per binary digit there. So a character vector of length 64 used 128 bytes.

whos Xbin
  Name      Size            Bytes  Class    Attributes
  Xbin      1x64              128  char               

Or I suppose you could store it as a logical vector, so one byte per.

Xlog = Xbin == '1'
Xlog =
  1×64 logical array
  Columns 1 through 46
   1   0   1   1   1   1   1   1   1   1   1   0   1   1   1   0   0   0   1   0   0   1   0   0   1   1   0   1   1   1   0   1   0   0   1   0   1   1   1   1   0   0   0   1   1   0
  Columns 47 through 64
   1   0   1   0   0   1   1   1   1   1   1   0   1   1   1   1   1   0

whos Xlog
  Name      Size            Bytes  Class      Attributes
  Xlog      1x64               64  logical              

Just a matter of personal preference as I see it.

You can't really work in true binary as easily. For example, can you directly access the mantissa bits of a double?

bitget(1.234,1)
Error using bitget
Double inputs must have integer values in the range of ASSUMEDTYPE. 

[James Tursa]

I don't understand what "two's complement" has to do with any of this, given that the underlying values are floating point and not integers.

[Mervat Zarour]

was ist das Inverse von Xbin - '0' ??