He invented a programable general purpose mechanical digital computer that he called the Analytical Engine in the late 1840s. However he could never get funding for it from parliament and was still arguing with his machinist over unpaid bills and specifications on his earlier never finished Difference Engine machine.
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The machine allowed data input and it included a storage location to hold data for processing. It also had a processor to calculate numbers and to direct tasks to be performed, as well as an output device to print out information.
Babbage had a vision of being able not only to compute trigonometric tables with a machine, logarithmic tables with a machine, astronomic tables with a machine, but to compute any of these and more with the same machine. So he built the programmable Analytical Engine.
It depends on your definition of a computer. The analytical engine was an early version of the computer, but built with mechanical components instead of electric/electronic ones.
Charles Babbage's analytical engine was a general-purpose computer. It is widely accepted as the first non-manual machine capable of mathematical calculations.
It would be possible to argue that the abacus is the first mechanical computer, but the analytical engine is the best candidate for that title.
An analytical engine is a mechanical general-purpose computer which was designed and envisaged by Charles Babbage, but never built.
Analytical Engine
Though Charles Babbage achieved many things. But Charles Babbage Does not achieve his all goals. Without completing his Difference Engine he went to Analytical Engine. He designed the first programmable machine , the analytical engine. Though he did not complete it fully due to lack of resources and money. But he was right in theory. After some the Analytical engine was finished by some computer scientists and Charles Babbage was credited the "Father of Computers"..
The computers invented by Charles Babbage were the Difference Engine and the Analytical Engine. Neither was finished in his lifetime but gave him fame as a computer pioneer.
Lady Ada Lovelace collaborated with Charles Babbage on the Analytical Engine. Her notes on this engine include what is recognized as the first algorithm for a machine.