1. An adaptive computing system having a modular control, switching, and power supply architecture, comprising: a base module having a common power supply and a switch connected to a common input/output device set, wherein the common input/output device set includes a keyboard device, one or more video devices, and a mouse device; multiple computer modules that mechanically interconnect with the base module via one or more mechanical alignment and securing mechanisms to form a vertical stack with the base module, wherein the base module and the multiple computer modules have identical widths and identical depths; a backplane architecture that electrically interconnects the multiple computer modules and the base module in the vertical stack, wherein the backplane architecture includes: a power supply backplane configured to share the common power supply among the base module and the multiple computer modules; and a switching backplane configured to transport input/output signals associated with the common input/output device set between the multiple computer modules and the switch in the base module.