He invented the computer at the age of 30.
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Charles Babbage made several plans to completing the computer in London. Babbage was born in London in 1791 and spent most of his life in or near that city, other than attending school (various secondary schools, then Cambridge University) and a short time after his marriage (when he lived in the West Midlands, not far from Wales), so it would have been there.
Technically, one could argue that the first computer was invented by Charles Babbage in 1837. It was named the "Analytical Engine" and included basic flow control, an ALU (Arithmetic Logic Unit), and integrated memory. Sadly, it was never built while Charles Babbage alive, but his son, Henry Babbage, managed to finish a part of this machine and got it to make basic calculations. However, if you are talking about the first "personal computer" (pc), that was invented in 1975 by Ed Roberts when he made the Altair 8800 which relied on many switches and lights for input and output. The switches being this input, and the lights being the output.
The earliest recorded discussion that's been found regarding Babbage's ideas for a calculating engine were in 1822. However, Babbage himself never actually completed a design; although, he continued working on several computer prototypes throughout the remainder of his life.
While Charles Babbage did invent a calculator as well as what is considered the first programmable computer, he did not invent the abacus. This basic counting tool was invented in China around 3000 B.C. Babbage most certainly would have known of the abacus, indeed he likely would have used one himself, but it is not a tool of his original design.
That depends on what you regard as a computer. There have been many types of computer, both electronic, as we know them now, and mechanical ones. Charles Babbage is often regarded as the father of computers because of some machines he designed in the 18th century. They had the basic components that all modern computer systems are based on. Other names include John Napier and Herman Hollerith. The oldest computer can be argued to be the abacus, used by the Chinese as long as 5000 years ago.