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Yes. A 64-bit operating system requires a minimum 2 GB RAM as Microsoft suggests. But there's no point in running 64-bit with just 2 GBs of RAM. 2 GBs is the minimum required, meaning it's enough RAM to just load and boot the operating system. More or less, you have no more RAM left for services, processes or anything except for endless virtual writes on your hard disk (which likely leads to hard disk failure). Your PC will most likely to run very slow because of endless writes on RAM.
If we say 20 GBs of hard disk space is the minimum requirement for a 64-bit OS to be installed, it doesn't mean that a 20GB hard disk is enough. You need a larger hard disk capacity for OS updates, programs to be installed including antivirus, frameworks, runtime environments, and hardware drivers which are a necessity for a PC.
64-bits OSs are designed to run efficiently and effectively on systems running on 4GBs of RAM or higher because they carry larger instructions thus requiring more RAM.