Final answer:
The three basic hardware operations in a digital computer system are input processing, data storage, and output generation, made more efficient with the invention of the transistor.
Step-by-step explanation:
The three basic operations that the hardware in a digital computer system must perform are input processing, data storage, and output generation. First, the computer needs to receive input, which is data provided by the user or another device. Next, the computer processes this data by performing computations or manipulating the data according to the instructions given to it. This may involve storing the data temporarily or permanently, which is the second operation. Finally, the computer produces output, which is the result of the data processing, often sent to another device or presented to the user.
The invention of the transistor made it possible for digital computers to efficiently process large amounts of information. The integration of transistors into microprocessors marked a significant advancement, greatly enhancing the computational speed and efficiency of computers. This innovation allowed for the miniaturization of components, leading to the development of modern computing technology.