Counting Binary Bits

Before we proceed on any class address we must first know how to count binary, the 8 bits for each group. IP address composed of four groups which are separated by a dotted decimal. For example, we will use the private address “192.168.1.1” then convert to binary number...

The result will be “11000000.10101000.00000001.00000001”. This is what our NIC (network interface card) does their job by reading the binary and handle important data-conversion to the network.

NIC – a PC device installed to each computer including the servers which provides connectivity between the PC and the network’s physical medium.

By reading the binary number it is hard to understand without calculation and knowing how to count the bits. In each bit represents a multiple of two (1, 2, 4, 8, 16, 32, 64, 128). However, we count the bits in opposite direction 128 to 1 because the first bit is 128.

See example below. 11000000 is equal to 192:



Binary Numbering System

In the binary numbering system, the radix is 2. Therefore, each position represents increasing powers of 2. In 8-bit binary numbers, the positions represent these quantities:

2^7 2^6 2^5 2^4 2^32^2 2^1 2^0

128 64 32 16 8 4 2 1

The base 2 numbering system only has two digits: 0 and 1.

When we interpret a byte as a decimal number, we have the quantity that position represents if the digit is a 1 and we do not have that quantity if the digit is a 0, as shown in the figure.

1 1 1 1 1 1 1 1

128 64 32 16 8 4 2 1

A 1 in each position means that we add the value for that position to the total. This is the addition when there is a 1 in each position of an octet. The total is 255.

128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255

A 0 in each position indicates that the value for that position is not added to the total. A 0 in every position yields a total of 0.

0 0 0 0 0 0 0 0

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



Notice in the figure that a different combination of ones and zeros will yield a different decimal value.