Although learning with Arduino hardware and software is infinitely enjoyable and leads to many other endeavours, it is also useful to work with analog and digital electronics as well. With this in mind, a very useful open-source piece of software exists to allow you to design simulate digital logic circuits - called "Logic Circuit" - for example:
It allows you to use the usual logic gates, clock sources, outputs such as LEDs in single, 7-segment display and matrix form, and so on - to simulate logic circuits with ease and no cost. The software is simple to install albeit only available for Windows environments at this stage, and there is also a support forum and help available. For more information and to download, visit the website here.