Networking Basics

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Bits and bytes

This page will explain what bits and bytes are.

A binary 0 might be represented by 0 volts of electricity.

A binary 1 might be represented by +5 volts of electricity.

Computers are designed to use groupings of eight bits. This grouping of eight bits is referred to as a byte. In a computer, one byte represents a single addressable storage location. These storage locations represent a value or single character of data, such as an ASCII code. The total number of combinations of the eight switches being turned on and off is 256. The value range of a byte is from 0 to 255. So a byte is an important concept to understand when working with computers and networks.

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Base 10 number system

Numbering systems consist of symbols and rules for their use. This page will discuss the most commonly used number system, which is decimal, or Base 10.

Base 10 uses the ten symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. These symbols, can be combined to represent all possible numeric values.

The decimal number system is based on powers of 10. Each column position of a value, from right to left, is multiplied by the base number 10 raised to a power, which is the exponent. The power that 10 is raised to depends on its position to the left of the decimal point. When a decimal number is read from right to left, the first or rightmost position represents 100, which equals 1. The second position represents 101, which equals 10. The third position represents 102, which equals 100. The seventh position to the left represents 106, which equals 1,000,000. This is true no matter how many columns the number has.

Here is an example:

2134 =
(2x10^3) + (1x10^2) + (3x10^1) + (4x10^0)

This review of the decimal system will help you understand the Base 2 and Base 16 number systems. These systems use the same methods as the decimal system.

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Base 2 number system


This page will discuss the number system that computers use to recognize and process data, which is binary, or Base 2.
The binary system uses only two symbols, which are 0 and 1. The position of each digit from right to left in a binary number represents the base number 2 raised to a power or exponent. These place values are, from right to left, 20, 21, 22, 23, 24, 25, 26, and 27, or 1, 2, 4, 8, 16, 32, 64, and 128 respectively.

Here is an example:

101102 =
(1 x 2^4 = 16) + (0 x 2^3 = 0) + (1 x 2^2 = 4) + (1 x 2^1 = 2) + (0 x 2^0 = 0) = 22 (16 + 0 + 4 + 2 + 0)

This example shows that the binary number 10110 is equal to the decimal number 22.

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Converting decimal numbers to 8-bit binary numbers


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


Conversion exercise:

Use the example below to convert the decimal number 168 to a binary number:

128 is less than 168 so the left most bit in the binary number is a 1. 168 - 128 = 40.
64 is not less than or equal to 40 so the second bit from the left is a 0.
32 is less than 40 so the third bit from the left is a 1. 40 - 32 = 8.
16 is not less than or equal to 8 so the fourth bit from the left is a 0.
8 is equal to 8 so the fifth bit from the left is a 1. 8 - 8 = 0. Therefore, the bits to the right are all 0.

This example shows that the decimal number 168 is equal to the binary number 10101000.

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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.