Binary Number System

Calculate numbers between decimal and binary systems.

Binary and IPv4 Addresses

• Binary numbering system consists of 1s and 0s, called bits
• Decimal numbering system consists of digits 0 through 9
• Hosts, servers, and network equipment using binary addressing to identify each other.
• Each address is made up of a string of 32 bits, divided into four sections called octets.
• Each octet contains 8 bits (or 1 byte) separated by a dot.
• For ease of use by people, this dotted notation is converted to dotted decimal.

Binary Positional Notation

• Positional notation means that a digit represents different values depending on the “position” the digit occupies in the sequence of numbers.
• The decimal positional notation system operates as shown in the tables below.

• The binary positional notation system operates as shown in the tables below.

Convert Binary to Decimal

• Example: Convert 11000000.10101000.00001011.00001010 to decimal.

=> 192.168.11.10

Decimal to Binary Conversion

The binary positional value table is useful in converting a dotted decimal IPv4 address to binary.

• Start in the 128 position (the most significant bit). Is the decimal number of the octet (n) equal to or greater than 128?
• If no, record a binary 0 in the 128 positional value and move to the 64 positional value.
• If yes, record a binary 1 in the 128 positional value, subtract 128 from the decimal number, and move to the 64 positional value.
• Repeat these steps through the 1 positional value.

Decimal to Binary Conversion Example

Example: Convert decimal 168 to binary

• Is 168 > 128? Yes, enter 1 in 128 position and subtract 128 (168-128=40)
• Is 40 > 64? No, enter 0 in 64 position and move on
• Is 40 > 32? Yes, enter 1 in 32 position and subtract 32 (40-32=8)
• Is 8 > 16? No, enter 0 in 16 position and move on Is 8 > 8? Equal.
• Enter 1 in 8 position and subtract 8 (8-8=0) No values left.
• Enter 0 in remaining binary positions

Decimal 168 is written as 10101000 in binary

IPv4 Addresses

Routers and computers only understand binary, while humans work in decimal. It is important for you to gain a thorough understanding of these two numbering systems and how they are used in networking.

Other related topics

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