I recently got a new PC which has a 64-bit Windows 7 installed. The current PC that I am using has a 32-bit Windows 7 installed.

I would like to know if there is a software that can copy all my installed programs and files in the hard disk with the 32-bit Windows 7 PC and transfer it to the newer PC's hard disk which has a 64 bit version of Windows 7. This is essentially like "cloning" a hard disk but I would like to use a 64-bit OS in the target drive, instead of also using the 32-bit OS of the source drive.

I would like to do this I can avoid reinstalling and reconfiguring my installed programs and files again on the new PC. If possible, I would like the new PC to work as it was in my previous PC, with the installed programs, configuration and files intact except that the OS is now 64-bit and the hard disk has a larger capacity. I have heard of programs that can clone a hard disk, but my concern is that the 32-bit Windows 7 OS will also be cloned to the new 64-bit PC.

If it is not possible to transfer my installed programs and settings like the way I described, are there software that can make it easier to migrate my installed programs, their configurations and my files from a 32-bit Windows 7 PC to a 64-bit Windows 7 PC?

Details:
I have a SATA to USB connector/adapter to copy files in the current hard disk to the newer one.
The two PCs are connected through LAN, so I can also transfer files through LAN.
Both PCs only have one hard disk.