From the ↑Charles Babbage biography at ↑The MacTutor History of Mathematics archive (University of St Andrews, Scotland):

Babbage is without doubt the originator of the concepts behind the present day computer. The computation of logarithms had made him aware of the inaccuracy of human calculation around 1812. He wrote in [C Babbage, Passages from the life of a philosopher (London, 1864).]:-
    … I was sitting in the rooms of the Analytical Society, at Cambridge, my head leaning forward on the table in a kind of dreamy mood, with a table of logarithms lying open before me. Another member, coming into the room, and seeing me half asleep, called out, Well, Babbage, what are you dreaming about?” to which I replied “I am thinking that all these tables” (pointing to the logarithms) “might be calculated by machinery.”
    Certainly Babbage did not follow up this idea at that time but in 1819, when his interests were turning towards astronomical instruments, his ideas became more precise and he formulated a plan to construct tables using the method of differences by mechanical means. Such a machine would be able to carry out complex operations using only the mechanism for addition. Babbage began to construct a small difference engine in 1819 and had completed it by 1822. He announced his invention in a paper Note on the application of machinery to the computation of astronomical and mathematical tables read to the Royal Astronomical Society on 14 June 1822.