How can I convert a binary fraction to decimal?

To convert from binary to decimal I use this function: bin2dec('1001')

But how I could like to know how can I convert binary fractions to decimal, just like this: bin2dec('0.110001')

Answer 1

[Jan]

'11001' means: 1*2^0 + 0*2^1 + 0*2^2 + 1*2^3 + 1*2^4 or:

[1,1,0,0,1] * 2 .^ (4:-1:0).'

(this is what happens inside bin2dec - examine its source code.)

'0.10011' means: 1*2^-1 + 0*2^-2 + 0*2^-3 + 1*2^-4 + 1*2^-5, or:

[1,0,0,1,1] * 2 .^ (-1:-1:-5).'

So all you have to do is to split the part before and after the decimal dot and to convert the character to numbers. Both is easy in Matlab:

S = strsplit('11001.10011', '.');
intV      = S{1} - '0';
fracV     = S{2} - '0';
intValue  = intV  * (2 .^ (numel(intV)-1:-1:0).')
fracValue = fracV * (2 .^ -(1:numel(fracV)).')
% or:
            sum(fracV ./ (2 .^ (1:numel(fracV))))
% [EDITED] Typo fixed: ^  this was \ before

[John D'Errico]

+1 of course. I once wrote a tool that goes the other way. Converting to decimal number to a binary "bicimal" form.

[David K]

This is great, thank you! I think you have a typo in your last code block though. I believe the ldivide on the last line should actually be a rdivide.

[Jan]

Thanks David K. Typo fixed now.