Understanding the Binary System

The secret of the binary system?

The first thing to know is that you read binary numbers from right to left. The second thing you need to understand is that each digit is based on a power of the number 2. Check this out:

2 to the power of 0 equals 1
2 to the power of 1 equals 2
2 to the power of 2 equals 4
2 to the power of 3 equals 8
2 to the power of 4 equals 16
2 to the power of 5 equals 32
2 to the power of 6 equals 64
2 to the power of 7 equals 128
…

See the pattern? Now let’s take these numbers to use them as a template while remembering that binary numbers are read from right to left:

Now let’s use this template on that ugly binary number from our earlier example. At the top is our template, at the bottom is our binary number:

Now we use simple multiplication and addition. If the binary number is a 1, it means this digit is “on” or “true” and we add the corresponding number from the template, if it is a 0, it means the digit is “off” or “false”, and we do not add the corresponding number from the template.

In our example, the digits for 128, 32, 8, 4 and 2 are true, so we add

128 + 32 + 8 + 4 + 2 = 174

You could also express it as

128*1 + 64*0 + 32*1 + 16*0 + 8*1 + 4*1 + 2*1 + 1*0 = 174

This means our binary number 10101110 is the number 174 in the decimal system.

Page 1: What is the binary system
Page 2: This page
Page 3: Bits vs bytes, some terminology
Page 4: Bus width