Why does the binary number system exist?

Answer

See question 32549 for the origin of the binary system.

Gottfried Wilhelm laid the foundations of the binary system in the 17th century. It was then an honor to come up with something new. Gottfried and his successors (including Blaize Pascal) developed a kind of mechanical calculator from this (the Pascaline). Calculating and processing numbers was therefore an application of the binary system.

In the 18th century, machines were developed based on the binary system. For example, there were ‘automatic’ looms that worked with paper tapes. This was also applied to machine music systems (pianolas).

In the 19th century, further work was done on automatic mechanical calculators by Charles Babbage. He invented the ‘Difference Engine’ and the ‘Analytic Engine’. These calculators were the forerunners of computers. The first computer program for this was written by Ada Lovelace, but she never saw it work because the Analitic Engine was never built. With the introduction of the punch card, Herman Hollerith (1860-1929) realized an enormous acceleration in the automatic processing of data. And then there was George Boole who developed boolean logic, the building block for our computers today.

It was not until the 20th century that calculators and computer systems were really developed in a practical way. It was Konrad Zuse who made digital electromechanics applicable. He completed the first modern fully electromagnetic computer in 1941: the Z3

You can therefore say that in the 19th century there was not really a need for the binary system, apart from a number of calculation systems, but that pioneering work was done to develop concrete applications in the 20th century.