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* This post is a continuation for: An introduction to binary – Part 1

Continuing our introduction to binary, let’s think about how could we express numbers using an alphabet with only 2 elements:

The first two numbers are quite obvious:

But how can we go any further? Well, in decimal, when our alphabet is not enough to write a number, we increment the leftmost number and “reset” any number on its right side; so:

In binary we just do the same:

If it’s not clear enough, think about the numbers as a car’s odometer (click to learn more about it):

When a digit reaches 9 then it becomes 0 and the next digit is incremented. If you bring this to the binary world, when a digit reaches 1, it becomes 0 and the next digit is incremented.

So, we might say that:

Looking at those numbers, we can find a pattern: some of them have only one “1″ and some zeros: 1, 10, 100, 1000, 10000. If we look at their values, we’ll be able to notice that they are, respecively, 1, 2, 4, 8 and 16. All those numbers are powers of 2:

What if we replace the number 2 from the base of the multipliers for its binary notation?

To represent other numbers, we can work in an analogue fashion:

In other words: binary is just the same as decimal!

If we generalize the concept, we might say that:

Do I need to explain how to proceed for base 8 (octal) and base 16 (hexadecimal)?

Stay tuned and wait for An introduction to binary – Part 3 (I didn’t know how to sum).

* This post is a continuation for: An introduction to binary – Part 1