Networking Basics

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Converting 8-bit binary numbers to decimal numbers

This page will teach you how to convert binary numbers to decimal numbers.

Here is an example:

Convert the binary number 01110000 to a decimal number.


NOTE:
Work from right to left. Remember that anything raised to the 0 power is 1.

0 x 20 = 0

0 x 2^1 = 0

0 x 2^2 = 0

0 x 2^3 = 0

1 x 2^4 = 16

1 x 2^5 = 32

1 x 2^6 = 64

0 x 2^7 = 0

__________

= 112

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Four-octet dotted decimal representation of 32-bit binary numbers

This page will explain how binary numbers are represented in dotted decimal notation.

Currently, addresses assigned to computers on the Internet are 32-bit binary numbers. To make it easier to work with these addresses, the 32-bit binary number is broken into a series of decimal numbers. First the binary number is split into four groups of eight binary digits. Then each group of eight bits, or octet, is converted into its decimal equivalent. This conversion can be performed as shown on the previous page.

When written, the complete binary number is represented as four groups of decimal digits separated by periods. This is called dotted decimal notation and provides a compact and easy way to refer to 32-bit addresses. This representation is used frequently later in this course, so it is necessary to understand it. For dotted decimal to binary conversions, remember that each group of one to three decimal digits represents a group of eight binary digits. If the decimal number that is being converted is less than 128, zeros will be needed to be added to the left of the equivalent binary number until there are a total of eight bits.

Try the following conversions for practice:

Convert 200.114.6.51 to its 32-bit binary equivalent.

Convert 10000000 01011101 00001111 10101010 to its dotted decimal equivalent.

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Hexadecimal

This page will teach you about the hexadecimal number system. You will also learn how hexadecimal is used to represent binary and decimal numbers.

The hexadecimal or Base 16 number system is commonly used to represent binary numbers in a more readable form. Computers perform computations in binary. However, there are several instances when the binary output of a computer is expressed in hexadecimal to make it easier to read.

The configuration register in routers often requires hexadecimal to binary and binary to hexadecimal conversions. routers have a configuration register that is 16 bits long. The 16-bit binary number can be represented as a four-digit hexadecimal number. For example, 0010000100000010 in binary equals 2102 in hexadecimal. A hexadecimal number is often indicated with a 0x. For example, the hexadecimal number 2102 would be written as 0x2102.

Like the binary and decimal systems, the hexadecimal system is based on the use of symbols, powers, and positions. The symbols that hexadecimal uses are the digits 0 through 9 and the letters A through F.

All combinations of four binary digits can be represented with one hexadecimal symbol. These values require one or two decimal symbols. Two hexadecimal digits can efficiently represent any combination of eight binary digits. The decimal representation of an eight-bit binary number will require either two or three decimal digits. Since one hexadecimal digit always represents four binary digits, hexadecimal symbols are easier to use than decimal symbols when working with large binary numbers. Using hexadecimal representation also reduces the confusion of reading long strings of binary numbers and the amount of space it takes to write binary numbers. Remember that 0x may be used to indicate a hexadecimal value. The hexadecimal number 5D might be written as 0x5D.

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Boolean or binary logic

This page will introduce Boolean logic and explain how it is used.

Boolean logic is based on digital circuitry that accepts one or two incoming voltages. Based on the input voltages, output voltage is generated. For computers the voltage difference is represented as an ON or OFF state. These two states are associated with a binary 1 or 0.

Boolean logic is a binary logic that allows two numbers to be compared and makes a choice based on the numbers. These choices are the logical AND, OR, and NOT. With the exception of the NOT, Boolean operations have the same function. They accept two numbers, which are 1 and 0, and generate a result based on the logic rule.

The NOT operation takes the value that is presented and inverts it. A 1 becomes a 0 and a 0 becomes a 1. Remember that the logic gates are electronic devices built specifically for this purpose. The logic rule that they follow is whatever the input is, the output is the opposite.

The AND operation compares two input values. If both values are 1, the logic gate generates a 1 as the output. Otherwise it outputs a 0. There are four combinations of input values. Three of these combinations generate a 0, and one combination generates a 1.

The OR operation also takes two input values. If at least one of the input values is 1, the output value is 1. Again there are four combinations of input values. Three combinations generate a 1 and the fourth generates a 0.

The two networking operations that use Boolean logic are subnetwork and wildcard masking. The masking operations are used to filter addresses. The addresses identify the devices on the network and can be grouped together or controlled by other network operations.

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IP addresses and network masks

This page will explain the relationship between IP addresses and network masks.

When IP addresses are assigned to computers, some of the bits on the left side of the 32-bit IP number represent a network. The number of bits designated depends on the address class. The bits left over in the 32-bit IP address identify a particular computer on the network. A computer is referred to as a host. The IP address of a computer consists of a network and a host part.

To inform a computer how the 32-bit IP address has been split, a second 32-bit number called a subnetwork mask is used. This mask is a guide that determines how the IP address is interpreted. It indicates how many of the bits are used to identify the network of the computer. The subnetwork mask sequentially fills in the 1s from the left side of the mask. A subnet mask will always be all 1s until the network address is identified and then it will be all 0s to the end of the mask. The bits in the subnet mask that are 0 identify the computer or host.

Some examples of subnet masks are as follows:

11111111000000000000000000000000
written in dotted decimal as 255.0.0.0

11111111111111110000000000000000
written in dotted decimal as 255.255.0.0

In the first example, the first eight bits from the left represent the network portion of the address, and the last 24 bits represent the host portion of the address. In the second example the first 16 bits represent the network portion of the address, and the last 16 bits represent the host portion of the address.

The IP address 10.34.23.134
in binary form is 00001010.00100010.00010111.10000110.

A Boolean AND of the IP address 10.34.23.134 and the subnet mask 255.0.0.0 produces the network address of this host:

00001010.00100010.00010111.10000110
11111111.00000000.00000000.00000000
00001010.00000000.00000000.00000000

The dotted decimal conversion is 10.0.0.0 which is the network portion of the IP address when the 255.0.0.0 mask is used.

A Boolean AND of the IP address 10.34.23.134 and the subnet mask 255.255.0.0 produces the network address of this host:

00001010.00100010.00010111.10000110
11111111.11111111.00000000.00000000
00001010.00100010.00000000.00000000

The dotted decimal conversion is 10.34.0.0 which is the network portion of the IP address when the 255.255.0.0 mask is used.

This is a brief illustration of the effect that a network mask has on an IP address. The importance of masking will become much clearer as more work with IP addresses is done. For right now it is only important that the concept of the mask is understood.

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Summary

Decimal representation of IP addresses and network masksThis page summarizes the topics discussed in this module.

A connection to a computer network can be broken down into the physical connection, the logical connection, and the applications that interpret the data and display the information. Establishment and maintenance of the physical connection requires knowledge of PC components and peripherals. Connectivity to the Internet requires an adapter card, which may be a modem or a network interface card (NIC).

In the early 1960s modems were introduced to provide connectivity to a central computer. Today, access methods have progressed to services that provide constant, high-speed access.

The logical connection uses standards called protocols. The Transmission Control Protocol/Internet Protocol (TCP/IP) suite is the primary group of protocols used on the Internet. TCP/IP can be configured on a workstation using operating system tools. The ping utility can be used to test connectivity.

A web browser is software that is installed on the PC to gain access to the Internet and local web pages. Occasionally a browser may require plug-in applications. These applications work in conjunction with the browser to launch the program required to view special or proprietary files.

Computers recognize and process data using the binary, or Base 2, numbering system. Often the binary output of a computer is expressed in hexadecimal to make it easier to read. The ablility to convert decimal numbers to binary numbers is valuable when converting dotted decimal IP addresses to machine-readable binary format. Conversion of hexadecimal numbers to binary, and binary numbers to hexadecimal, is a common task when dealing with the configuration register in routers.

Boolean logic is a binary logic that allows two numbers to be compared and a choice generated based on the two numbers. Two networking operations that use Boolean logic are subnetting and wildcard masking.

The 32-bit binary addresses used on the Internet are referred to as Internet Protocol (IP) addresses.

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Networking Terminology

Data networks


This page will discuss the evolution of data networks.

Data networks developed as a result of business applications that were written for microcomputers. The microcomputers were not connected so there was no efficient way to share data among them. It was not efficient or cost-effective for businesses to use floppy disks to share data. Sneakernet created multiple copies of the data. Each time a file was modified it would have to be shared again with all other people who needed that file. If two people modified the file and then tried to share it, one of the sets of changes would be lost. Businesses needed a solution that would successfully address the following three problems:

How to avoid duplication of equipment and resources
How to communicate efficiently
How to set up and manage a network

Businesses realized that computer networking could increase productivity and save money. Networks were added and expanded almost as rapidly as new network technologies and products were introduced. The early development of networking was disorganized. However, a tremendous expansion occurred in the early 1980s.

In the mid-1980s, the network technologies that emerged were created with a variety of hardware and software implementations. Each company that created network hardware and software used its own company standards. These individual standards were developed because of competition with other companies. As a result, many of the network technologies were incompatible with each other. It became increasingly difficult for networks that used different specifications to communicate with each other. Network equipment often had to be replaced to implement new technologies.

One early solution was the creation of local-area network (LAN) standards. LAN standards provided an open set of guidelines that companies used to create network hardware and software. As a result, the equipment from different companies became compatible. This allowed for stability in LAN implementations.

In a LAN system, each department of the company is a kind of electronic island. As the use of computers in businesses grew, LANs became insufficient.

A new technology was necessary to share information efficiently and quickly within a company and between businesses. The solution was the creation of metropolitan-area networks (MANs) and wide-area networks (WANs). Because WANs could connect user networks over large geographic areas, it was possible for businesses to communicate with each other across great distances.