How to decrement a bitstring?

I want to have a decrement operator for a bitstring. I currently have an incremement operator defined as follows:

void increment(boost::dynamic_bitset<> &bitset)
{   
    for (int loop = 0; loop < bitset.size(); ++loop)
    {
        if ((bitset[loop] ^= 0x1) == 0x1)
        {
            break;
        }
    }
}

How would I decrement in a bitstring?

It seems like this would work.

void decrement(boost::dynamic_bitset<> &bitset) 
{    
    for (int loop = 0; loop < bitset.size(); ++loop) 
    { 
        if ((bitset[loop] ^= 0x1) == 0x0) 
        { 
            break; 
        } 
    } 
}