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I want to start working on a small project like making my own digital clock then gradually scale to larger projects.
For a beginner Arduino is the best and easiest choice for starting. You can visit www.instructables.com for some projects. Once you are able to make small projects then the most important part of embedded programming is the programming itself so you need to practice and understand whichever programming language you use. For this purpose use projects described on the arduino forum as well as in the examples of the arduino IDE. These will get you started with embedded programming.