Random colorful binary numbers!

If you have used a computer for more than five minutes, then you have heard the words **bits** and **bytes**. Both RAM and hard disk capacities are measured in bytes, as are file sizes when you examine them in a file viewer.

You might hear an advertisement that says, "This computer has a **32-bit** Pentium processor with 64 **megabytes** of RAM and 2.1 **gigabytes** of hard disk space." And many HowStuffWorks articles talk about bytes (for example, How CDs Work). In this article, we will discuss bits and bytes so that you have a complete understanding.

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### Decimal Numbers

The easiest way to understand bits is to compare them to something you know: **digits**. A digit is a single place that can hold numerical values between 0 and 9. Digits are normally combined together in groups to create larger numbers. For example, 6,357 has four digits. It is understood that in the number 6,357, the 7 is filling the "1s place," while the 5 is filling the 10s place, the 3 is filling the 100s place and the 6 is filling the 1,000s place. So you could express things this way if you wanted to be explicit:

(6 * 1000) + (3 * 100) + (5 * 10) + (7 * 1) = 6000 + 300 + 50 + 7 = 6357

Another way to express it would be to use **powers of 10**. Assuming that we are going to represent the concept of "raised to the power of" with the "^" symbol (so "10 squared" is written as "10^2"), another way to express it is like this:

(6 * 10^3) + (3 * 10^2) + (5 * 10^1) + (7 * 10^0) = 6000 + 300 + 50 + 7 = 6357

What you can see from this expression is that each digit is a **placeholder** for the next higher power of 10, starting in the first digit with 10 raised to the power of zero.

That should all feel pretty comfortable — we work with decimal digits every day. The neat thing about number systems is that there is nothing that forces you to have 10 different values in a digit. Our **base-10** number system likely grew up because we have 10 fingers, but if we happened to evolve to have eight fingers instead, we would probably have a base-8 number system. You can have base-anything number systems. In fact, there are lots of good reasons to use different bases in different situations.

Computers happen to operate using the base-2 number system, also known as the **binary number system** (just like the base-10 number system is known as the decimal number system). Find out why and how that works in the next section.