Maximum decimal and binary values

Hi

I use Matlab R2011b. I need to work with huge number, say greater than 10^19. I understood that Matlab cannot process the values greater than 2^53. For example, the decimal to binary conversion of A=(2^54) - 1 is not calculated properly. In order to understand what I am saying, you can run the following code and then check the value of B. B should be a matrix whose size is 1*54 and all the values should be one.

A = (2^54) - 1; B = de2bi(A, 'left-msb');

I want to know that whether there is any other command for decimal to binary conversion or not?

Regrds

Answer 1

[David Sanchez]

de2bi is the only Matlab built-in function to perform the operation. If you need something different you have to code it yourself. Sorry.

Answer 2

[Iain]

The maximum integer value matlab can innately handle is 2^64 - 1 (uint64) (approx 8*10^18)

The maximum number matlab can handle is approx 10^307, but its precision is limited to about 15 digits.

You can convert a value to a different datatype using "typecast".

What are you actually trying to achieve?

Answer 3

[José-Luis]

This function should work

    function  [binStr sign biasExp frac] = my_fun(h)
    ieee74 = '';
    h = num2hex(h); 
    for ii = h
    switch ii
        case {'0'}
            b = '0000';
        case {'1'}
            b = '0001';
        case {'2'}
            b = '0010';
        case {'3'}
            b = '0011';
        case {'4'}
            b = '0100';
        case {'5'}
            b = '0101';
        case {'6'}
            b = '0110';
        case {'7'}
            b = '0111';
        case {'8'}
            b = '1000';
        case {'9'}
            b = '1001';
        case {'A', 'a'}
            b = '1010';
        case {'B', 'b'}
            b = '1011';
        case {'C', 'c'}
            b = '1100';
        case {'D', 'd'}
            b = '1101';
        case {'E', 'e'}
            b = '1110';
        case {'F', 'f'}
            b = '1111';
    end
    ieee74 = [ieee74 b];
    end
    sign = ieee74(1); 
    biasExp = ieee74(2:12); 
    frac = ieee74(13:end);

    expVal = bin2dec(biasExp) - 1023

    binStr =  repmat('0',1,1078);
    binStr (538) = '1';
    binStr (539:539+51) = frac;

    if (expVal ~= 0)
        binStr = circshift(binStr,[0 -expVal]);
    end
    binStr = insert_dot(binStr);

    function [newStr] = insert_dot(oldStr)
        newStr = [oldStr(1:538) '.' oldStr(539:end)];
        %trimming left
        idx_left = find(newStr == '1', 1, 'first');
        if idx_left > 539
            idx_left = 538;
        end
        idx_right = find(newStr == '1', 1, 'last');
        if idx_right < 539
            idx_right = 538;
        end
        newStr = newStr(idx_left:idx_right);
        if sign == '1'
            newStr = ['-' newStr];
        end

    end

    end

For example:

your_string = my_fun(10^100);

[Mahdiyar]

Thank you for your reply.

But it is not working for A=(2^64) - 1; in this case the output should be a vector with 64 elements whose values are equal to 1. For example, if you put 3 instead of 64 you have to get 1 1 1

[José-Luis]

I should have said that the function works for doubles. In that case the maximum precision is limited by the width of the fractional field, that is 52 bits, according to the IEEE convention. In the documentation for dec2bin, it says that the largest integer that can be exactly represented is 2^52. 2^64 is beyond that range.

If you do my_fun(7), you indeed get 111. If you want an exact representation of very large numbers, or with a large number of significant numbers (>15) then the limits imposed by the double precision become an hindrance, as you cannot store them exactly.

In that case you should use variable precision arithmetic. It is freely available in the file exchange:

http://www.mathworks.com/matlabcentral/fileexchange/22725-variable-precision-integer-arithmetic

Once it is installed and in the path:

   >> d = vpi(2)^63-1
  d =
      9223372036854775807
  >> vpi2bin(d)

ans =

111111111111111111111111111111111111111111111111111111111111111