**Decimal Numbers System**

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, **‘4,378’** has four digits. It is understood that in the number **‘4,378’** the **‘8’** is filling the **“1s place,”** while the **‘7’** is filling the **“10s place,”** the **‘3’** is filling the **“100s place”**, and the **‘4’** is filling the **“1,000s place”**. So you could express things this way if you wanted to be explicit:

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:

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.

**Binary Number System**

Computers happen to operate using the base-2 number system, also known as the **binary number system** and therefore use binary digits in place of decimal digits. The word **bit** is a shortening of the words “**Binary digit**.” Whereas decimal digits have **10** possible values ranging from **0** to **9**, bits have only two possible values: **0** and **1**. Therefore, a binary number is composed of only **0s** and **1s**, like this: **1110**. How do you figure out what the value of the binary number **1110** is? You do it in the same way we did it above for **4378**, but you use a **base of 2** instead of a **base of 10**. So:

You can see that in binary numbers, each bit holds the value of increasing powers of **2**. That makes counting in binary pretty easy. Starting at **0** and going through **21**, counting in decimal and binary looks like this :

When you look at this sequence, **0** and **1** are the same for decimal and binary number systems. At the number **2**, you see carrying first take place in the binary system. If a bit is **1**, and you add **1** to it, the bit becomes **0** and the next bit becomes **1**. In the transition from **15** to **16** this effect rolls over through **4** bits, turning **1111** into **10000**. Bits are rarely seen alone in computers. They are almost always bundled together into **8-bit** collections, and these collections are called **bytes**. With **8 bits** in a **byte**, you can represent **256** values ranging from **0** to **255.**