Scalar Multiplication

Thank you Walter Roberson.
So if I use Symbolic Toolbox or "vpi", will this solve my problem and just give me 10^23 as my result. I specifically need the answer to be 10^23 (only 1s and 0s). Also my numbers can go a little higher as well, upto (10^16)*(10^16).

Thank you for your answer.

Regards,
Somesh

Yes, the Symbolic Toolbox should give you 1 followed by 23 zeros. I would think it likely that vpi would as well.

Additional clarification:

IEE 754 double precision can store 10^16, 10^17, ..., 10^22 exactly, but these numbers do not have enough precision to do an operation such as 10^22-1 and get an exact result in the 1's digit. That is, you can't do integral arithmetic with numbers in these ranges exactly. The 10^15 is the largest IEEE 754 double precision number that can be stored exactly *and* have enough precision to do an operation like 10^15-1 exactly. That is, 10^15 is the largest power of 10 such that eps(10^15) <= 1.

Also, a uint64 can go up to 10^19:
>> log10(double(uint64(realmax)))
ans =
19.2659

However, MATLAB does not do the uint64/double conversion correctly for numbers in this range. E.g.,
>> uint64(10^19)
ans =
9999999999999999999

Neither does MSVC 2008 in a mex routine:
>> uint64double(10^19)
ans =
9223372036854775808

So whatever algorithms are used behind the scenes for these conversions do not appear to work correctly beyond some max double value (presumably the largest value for which integral arithmetic can still be done exactly using the underlying algorithm). I haven't investigated what that limit is for the various conversion methods.