n5ims, you just totally missed the whole point of his question. he wasnt even asking about the difference between 32 bit and 64 bit, he was asking can 64 bit software run in a 32 bit environment.
Let's see his question. "I was given the above mentioned laptop to use. The system is 32 bit. Is 64 bit a better thing to have? If so is there a way to update this laptap? I have a external drive connected which has 364 GB space availuable. Thank you in advance for your help with this"
Their question indicates that the "The system is 32 bit.", which states that they're running the 32 bit version of Windows Vista Home Premium but doesn't indicate if they have 64 bit capable hardware or not.
They then asked "Is 64 bit a better thing to have?". This is a simple question, but has a rather difficult answer, assuming you go into more detail than simply stating "That depends". My answer was that they're probably fine running the 32 bit version with an explaination on why as well as why one might need the 64 bit version. Since the answer was already out there that 64 bit software required 64 bit capable hardware, I didn't bring this point up again.
The OP indicated that they understood my answer in their follow-up post "Since I only barely know how to use this computer I think you are telling me I will be alright with the 32 bit system.Thank you very much for your time and consideration on this." Since it was my post that they quoted in their reply and not yours, I don't see how it was me that misunderstood their question.
