As you can see on the above screen shot the place holders are using the power of 2. Starting at the right side the place holder begins with 1, going left the next place holder after the one is 2 which is 2 to the power of 1. After the 2 is the place holder 4 which is 2 to the power of 2 which is 4.

So a quick calculation of all the place holders from left to right looks like this.

1, 2×1=2, 2×2=4, 2×4=8, 2×8=16, 2×16=32, 2×32=64, 2×64=128 and so on.

Now we will convert Binary to Decimal. Here is an example:

00011010

So looking at matching the place holders will look like this

0x128 +0x64 + 0x32 + 1×16 + 1×8 0x4 + 1×2 + 0x1 = 26

To make it clearer

0 + 0 + 0 +16 + 8 + 0 + 2 + 0 = 26

To calculate even quicker we only have to see which place holder is on and add those numbers. Here is another example.

10000011 8^th     place holder = 128
10000011 2^nd       place holder = 2
10000011 1^st         place holder = 1

128 + 2 + 1 =131

A few more examples

10101010 = 170
11111000 = 230
01010101 = 75

Decimal to Binary * important for the Exam and to be a successful to be a network Engineer

So if we want to convert a decimal number to Binary we need to determine which place holders need to be on or off.

The following screenshot demonstrates how we convert 210 to Binary