They were built up from less complex machines over the years.
We harnessed electricity and started building simple circuits. Eventually we had telegraphs, electrical adding machines & typewriters, radios, radar, and electronically controlled factory machines. The number of types of components you could put into a circuit grew. The invention of the transistor, which is a special kind of switch, was revolutionary. We figured out how to the parts smaller and smaller, and to do more and more complex things with them.
Calculators, for example, took input, applied your choice of algorithms to those numbers, and gave you an output. Computers were much the same, but also allowed you to make your own algorithms. Methods of input, output, and information (number) storage evolved.
Computer parts continued to get more powerful and ever smaller. All along the way, a lot of effort went into making computers able to pass information back and forth to each other.
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