Question

I am doing Arithmetic Coding now, and I have got the final start position and distance, then I add them.
How can I convert the result to binary mode?

For example, how can I convert 0.125 decimal to 0.001 binary in C++?

void CArithmeticCoding::Encode()
{
    if ( 0 == m_input )
        return;
    printf("The input is [%s].\n", this->m_input);

    while (*m_input)
    {
        if ( *m_input == m_MPS )
        {
            DOMPS();
        }
        else
        {
            DOLPS();
        }
        ++m_input;
    }
    double ret = m_start + m_dis;

    return;
}

Answer 1

Converting anything to binary means finding out how many of each kind of power of 2 is involved. In the case of a decimal number, the powers involved are negative.

For .125, the sequence is like this:

.125 x 2 =  .250 (< 1)
.250 x 2 =  .500 (< 1)
.500 x 2 = 1.000 (>= 1)
.000     = 0     done

So, the binary representation is 0x2^-1 + 0x2^-2 + 1x2^-3 = .001 binary. As an exercise, contrast this technique with converting a normal integer into binary representation.

Just as regular decimals can have non-terminating patterns (like 1/3 or pi/4), the same can happen for the binary representations. In those cases, you have to stop the calculation when you reach your desired precision.