I don't know if an entire floating-point number is necessary to keep track of precision. If we are willing to accept precision to the closest decimal digit, and

I don't know if an entire floating-point number is necessary to keep track of precision. If we are willing to accept precision to the closest decimal digit, and my calculations of the max mantissa of a double-precision floating-point is 9.0071993e+15, we could store the precision in 4 bits.