The fastest and smoothest computer from the options provided would be the 64-bit processor with 16 gigabytes of RAM.
Here's why:
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Processor Architecture: A 64-bit processor can handle more data at once and can address more memory than a 32-bit processor, which is limited to about 4 GB of RAM. This allows for better performance, especially in demanding applications and multitasking scenarios.
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RAM Capacity: Having 16 gigabytes of RAM allows more applications to run simultaneously without slowing down the system. It is especially beneficial for tasks that require a lot of memory, such as gaming, video editing, or running virtual machines.
Therefore, the combination of a 64-bit architecture and a higher amount of RAM will provide the best performance and smoothness.