Module 5: Number Systems
Module 5: Number SystemsInstructor MaterialsIntroduction to Networks v7.0(ITN)
What to Expect in this Module§ To facilitate learning, the following features within the GUI may be included in this module:FeatureAnimationsVideosCheck YourUnderstanding(CYU)DescriptionExpose learners to new skills and concepts.Expose learners to new skills and concepts.Per topic online quiz to help learners gauge content understanding.Interactive ActivitiesA variety of formats to help learners gauge content understanding.Syntax CheckerSmall simulations that expose learners to Cisco command line to practiceconfiguration skills.PT ActivitySimulation and modeling activities designed to explore, acquire, reinforce, andexpand skills. 2016 Cisco and/or its affiliates. All rights reserved. Cisco Confidential3
What to Expect in this Module (Cont.)§ To facilitate learning, the following features may be included in this module:FeatureDescriptionHands-On LabsLabs designed for working with physical equipment.Class ActivitiesThese are found on the Instructor Resources page. Class Activities aredesigned to facilitate learning, class discussion, and collaboration.Module QuizzesSelf-assessments that integrate concepts and skills learned throughout theseries of topics presented in the module.Module SummaryBriefly recaps module content. 2016 Cisco and/or its affiliates. All rights reserved. Cisco Confidential4
Module 5: Number SystemsIntroduction to Networks v7.0(ITN)
Module ObjectivesModule Title: Number SystemsModule Objective: Calculate numbers between decimal, binary, and hexadecimal systems.Topic TitleBinary Number SystemTopic ObjectiveCalculate numbers between decimal and binarysystems.Hexadecimal Number SystemCalculate numbers between decimal andhexadecimal systems. 2016 Cisco and/or its affiliates. All rights reserved. Cisco Confidential9
5.1 Binary Number System 2016 Cisco and/or its affiliates. All rights reserved. Cisco Confidential10
Binary Number SystemBinary and IPv4 Addresses Binary numbering system consists of 1s and 0s, called bitsDecimal numbering system consists of digits 0 through 9Hosts, 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. 2016 Cisco and/or its affiliates. All rights reserved. Cisco Confidential11
Binary Number SystemVideo – Convert Between Binary and Decimal NumberingSystemsThis video will cover the following: Positional notation reviewPowers of 10 reviewDecimal – base 10 numbering reviewBinary – base 2 numbering reviewConvert an P address in binary to decimal numbering 2016 Cisco and/or its affiliates. All rights reserved. Cisco Confidential12
Binary Number SystemBinary 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.ThousandsHundredsTensOnesPositional Value10001001010Decimal Number (1234)1234(101)(100)Calculate1 x 10002 x 1003 x 104x1101Add them up 1000 200 30 4Radix10101010Position in Number321Calculate(103)(102)Position Value1000100Result1,234 2016 Cisco and/or its affiliates. All rights reserved. Cisco Confidential13
Binary Number SystemBinary Positional Notation (Cont.)The binary positional notation system operates as shown in the tables below.Radix22222222Position in )(20)Position Value1286432168421Positional Value1286432168421Binary Number 0x20x1Add Them Up 128 64 0 0 0 0 0 0Result192 2016 Cisco and/or its affiliates. All rights reserved. Cisco Confidential14
Binary Number SystemConvert Binary to DecimalConvert 11000000.10101000.00001011.00001010 to decimal.Positional Value1286432168421Binary Number 0x20x1Add Them Up 128 64 0 0 0 0 0 0Binary Number 0x20x1Add Them Up 128 0 32 0 8 0 0 0Binary Number 1x21x1Add Them Up 0 0 0 0 8 0 2 1Binary Number 1x20x1Add Them Up 0 0 0 0 8 0 2 0192168192.168.11.101110 2016 Cisco and/or its affiliates. All rights reserved. Cisco Confidential15
Binary Number SystemDecimal to Binary ConversionThe binary positional value table is useful in converting a dotted decimal IPv4 address tobinary. Start in the 128 position (the mostsignificant bit). Is the decimal number ofthe octet (n) equal to or greater than128?If no, record a binary 0 in the 128positional value and move to the 64positional value.If yes, record a binary 1 in the 128positional value, subtract 128 from thedecimal number, and move to the 64positional value.Repeat these steps through the 1positional value. 2016 Cisco and/or its affiliates. All rights reserved. Cisco Confidential16
Binary Number SystemDecimal to Binary Conversion Example Convert decimal 168 to binaryIs 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 onIs 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 onIs 8 8?- Equal. Enter 1 in 8 position and subtract 8 (8-8 0)No values left. Enter 0 in remaining binary positions128643216842110101000Decimal 168 is written as 10101000 in binary 2016 Cisco and/or its affiliates. All rights reserved. Cisco Confidential17
Binary Number SystemIPv4 Addresses Routers and computers only understand binary, while humans work indecimal. It is important for you to gain a thorough understanding of thesetwo numbering systems and how they are used in networking. 2016 Cisco and/or its affiliates. All rights reserved. Cisco Confidential18
5.2 Hexadecimal NumberSystem 2016 Cisco and/or its affiliates. All rights reserved. Cisco Confidential19
Hexadecimal Number SystemHexadecimal and IPv6 Addresses To understand IPv6 addresses,you must be able to converthexadecimal to decimal andvice versa.Hexadecimal is a base sixteennumbering system, using thedigits 0 through 9 and letters Ato F.It is easier to express a valueas a single hexadecimal digitthan as four binary bit.Hexadecimal is used torepresent IPv6 addresses andMAC addresses. 2016 Cisco and/or its affiliates. All rights reserved. Cisco Confidential20
Hexadecimal Number SystemHexadecimal and IPv6 Addresses (Cont.) IPv6 addresses are 128 bits inlength. Every 4 bits isrepresented by a singlehexadecimal digit. That makesthe IPv6 address a total of 32hexadecimal values.The figure shows the preferredmethod of writing out an IPv6address, with each Xrepresenting four hexadecimalvalues.Each four hexadecimalcharacter group is referred toas a hextet. 2016 Cisco and/or its affiliates. All rights reserved. Cisco Confidential21
Hexadecimal Number SystemVideo – Converting Between Hexadecimal and DecimalNumbering SystemsThis video will cover the following: Characteristics of the Hexadecimal System Convert from Hexadecimal to Decimal Convert from Decimal to Hexadecimal 2016 Cisco and/or its affiliates. All rights reserved. Cisco Confidential22
Hexadecimal Number SystemDecimal to Hexadecimal ConversionsFollow the steps listed to convert decimal numbers to hexadecimal values: Convert the decimal number to 8-bit binary strings. Divide the binary strings in groups of four starting from the rightmost position. Convert each four binary numbers into their equivalent hexadecimal digit.For example, 168 converted into hex using the three-step process. 168 in binary is 10101000. 10101000 in two groups of four binary digits is 1010 and 1000. 1010 is hex A and 1000 is hex 8, so 168 is A8 in hexadecimal. 2016 Cisco and/or its affiliates. All rights reserved. Cisco Confidential23
Hexadecimal Number SystemHexadecimal to Decimal ConversionsFollow the steps listed to convert hexadecimal numbers to decimal values: Convert the hexadecimal number to 4-bit binary strings. Create 8-bit binary grouping starting from the rightmost position. Convert each 8-bit binary grouping into their equivalent decimal digit.For example, D2 converted into decimal using the three-step process: D2 in 4-bit binary strings is 1110 and 0010. 1110 and 0010 is 11100010 in an 8-bit grouping. 11100010 in binary is equivalent to 210 in decimal, so D2 is 210 is decimal 2016 Cisco and/or its affiliates. All rights reserved. Cisco Confidential24
5.3 Module Practice and Quiz 2016 Cisco and/or its affiliates. All rights reserved. Cisco Confidential25
Module Practice and QuizWhat did I learn in this module?Binary is a base two numbering system that consists of the numbers 0 and 1, called bits.Decimal is a base ten numbering system that consists of the numbers 0 through 9.Binary is what hosts, servers, and networking equipment uses to identify each other.Hexadecimal is a base sixteen numbering system that consists of the numbers 0 through 9 andthe letters A to F. Hexadecimal is used to represent IPv6 addresses and MAC addresses. IPv6 addresses are 128 bits long, and every 4 bits is represented by a hexadecimal digit for a totalof 32 hexadecimal digits. To convert hexadecimal to decimal, you must first convert the hexadecimal to binary, then convertthe binary to decimal. To convert decimal to hexadecimal, you must first convert the decimal to binary and then thebinary to hexadecimal. 2016 Cisco and/or its affiliates. All rights reserved. Cisco Confidential26
Module Quizzes Self-assessments that integrate concepts and skills learned throughout the series of topics presented in the module. Module Summary Briefly recaps module content. What to Expect in this Module (Cont.) §To facilitate learning, the following
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WinDbg Commands . 0:000 k . Module!FunctionD Module!FunctionC 130 Module!FunctionB 220 Module!FunctionA 110 . User Stack for TID 102. Module!FunctionA Module!FunctionB Module!FunctionC Saves return address Module!FunctionA 110 Saves return address Module!FunctionB 220 Module!FunctionD Saves return address Module!FunctionC 130 Resumes from address
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