Have you ever added in another base? It’s easy! It’s just like base 10. Binary is the base we’re most interested about in computing because we can easily represent the two numbers 0 and 1 as states of a transistor. But ANY physical thing in the real world that has two states can store a binary digit. In this video, a 6 bit number is stored in little wooden switches. Each switch has two states, representing 1 and 0.
For more on how to add in binary, including a discussion of how a computer accomplishes the task, visit the wikipedia article.