A computer is a type of electronic device that is capable of performing mathematical operations. For the most part, they just do extremely simple stuff like basic arithmetic and move data between the CPU and RAM. Now, a theoretical computer can solve any solvable problem with the appropriate algorithm. (there are a few provably unsolvable problems). Every computer program in existence uses those extremely simple operations I mentioned earlier, so you can imagine how these extremely simple operations can be combined to form amazing computer software.
About your example – there is probably a computer in there, yes. Essentially, what you’re telling your irrigation system to do is: “Every x seconds, run the irrigation system for x seconds.” I use “seconds” here because that’s the unit of time computers use. That could, in and of itself, be a program. But we could also say: “Grab the user-specified frequency and duration from memory, and run the irrigation system according to the stored frequency and duration.”
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