Last week, one of my friends updated his office computer to a newer one. He had an old desktop with Windows XP. He updated his hardware with an HP office station and his operating system to a Windows 7 64bit.
When he tried to reinstall all the old software he immediately run into trouble. One of the problem was with 16-bit software. The problem is that this software are not compatible with the new 64-bit operating system. The basic idea is that Windows offers only one level of back-compatibility. Therefore, if you really need to use 16-bit applications, you need to install an 32-bit operating system.
Of course, the elegant solution is to find an updated version of the software that is compatible with 322/64 bit OS.
P.S.: 32-bit OS RAM is limited to 4 GB.
P.S.2: You can create a 32 bit virtual machine that can run your 16-bit application.