# Answers to Appendix C Extra Practice Problems

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1 APPENDIX C ANSWERS Answers to Appendix C Extra Practice Problems This document contains the answers and explanations for the problems posed in Appendix C, Extra Practice, of the book. The problems in Appendix C are organized based on the chapters in the book that explain the processes and math formulas used to solve the problems. This document uses that same organization, for easier reference. Answers to Chapter 1 Practice Problems Like most types of math problems, practicing the process can help. This section lists several practice problems for converting numbers between different formats. The four types of problems related to Chapter 1, and posed in this appendix, are as follows: Converting an 8-bit binary number to a decimal number Converting a decimal number to an 8-bit binary number Converting an 8-bit binary number to a hexadecimal number Converting a hexadecimal number to an 8-bit binary number Answers to Converting an 8-bit Binary Number to a Decimal Number Table W-1 lists the answers to the binary-to-decimal conversion problems listed in Table C-2 of Appendix C of the book. Following that, the answers are explained in more detail. Table W-1 Answers to Binary-to-Decimal Conversion Problems Problem Number Binary Decimal Value

2 2 Networking Basics CCNA 1 Companion Guide The process for converting from an 8-bit binary number to decimal, as covered in Chapter 1 of the book, is relatively straightforward. It is repeated here: How To Step 1 Write the powers of 2, in decimal, in the top row of a table, similar to Table W-2. Step 2 On the second line, write the binary number that is to be converted, lining up each binary digit under the powers of 2. Step 3 Multiply each pair of numbers (the numbers in the same column) together. Step 4 Add the eight products from Step 3. Table W-2 shows the details of the process for Problem 1. Table W-2 Answer to Problem 1: Converting to Decimal Value Associated with That Digit or Column The number itself Product of two numbers in same column Sum of all products 85 The first step in the four-step conversion process is always to write the powers of 2, as shown in the top row of Table W-2. Then, in Step 2, the binary number is recorded in the second row. At that point, the last two steps are simple arithmetic: you multiply the two numbers in each column together (Step 3) and then add those eight numbers together (Step 4). In this case, the answer is 85. Tables W-3 through W-7 show the details of the conversion for binary-to-decimal Problems 2 through 6. Table W-3 Answer to Problem 2: Converting to Decimal Value Associated with That Digit or Column The number itself Product of two numbers in same column Sum of all products 170

4 4 Networking Basics CCNA 1 Companion Guide Answers to Converting a Decimal Number to an 8-bit Binary Number Table W-8 lists the answers to the decimal-to-binary conversion problems listed in Table C-3 of Appendix C of the book. Following that, the answers are explained in more detail. Table W-8 Answers to Decimal-to-Binary Conversion Problems Problem Number Decimal Value Binary Chapter 1 of the book covers the process of converting from decimal to 8-bit binary numbers. The process listed in Chapter 1 is repeated here for reference, after which the answers are provided. Begin by writing down eight powers of 2, starting with 128 on the left, and ending with 1 on the right, similar to Table W-9. The blank lines below the powers of 2 are placeholders in which you will record the binary digits. Table W-9 Table for Converting Decimal to 8-bit Binary Power of Binary Digits Beginning with 128 and moving toward 1, follow these steps eight times, once for each power of 2: Step 1 How To If the decimal number is greater than or equal to the power of 2, do the following: A. Record a 1 as the binary digit under the power of 2. B. Subtract the power of 2 from the decimal number, which results in a number called the remainder. C. Use the remainder for the next step/power of 2. Step 2 If the decimal number is less than the power of 2, do the following: A. Record a 0 as the binary digit under the power of 2. B. Move to the next power of 2 and use the same remainder as in this step.

5 Appendix C Answers 5 Answer to Problem 1: Converting 255 to Binary Table W-10 shows the results of the preceding process for the first problem, which is to convert decimal 255 to 8-bit binary. 255 is a popular number with IP addressing, so many people simply memorize that 255 is in binary. Table W-10 Answer to Problem 1: Converting 255 to Binary Power of Binary Digits _ _ The decision points at each step are as follows: Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 The decimal number (255) is greater than 128, so a 1 was recorded in the 128 column, and = 127. The remaining decimal number (127) is greater than or equal to 64, so a 1 was recorded in the 64 column, and = 63. The remaining decimal number (63) is greater than or equal to 32, so a 1 was recorded in the 32 column, and = 31. The remaining decimal number (31) is greater than or equal to 16, so a 1 was recorded in the 16 column, and = 15. The remaining decimal number (15) is greater than or equal to 8, so a 1 was recorded in the 8 column, and 15 8 = 7. The remaining decimal number (7) is greater than or equal to 4, so a 1 was recorded in the 4 column, and 7 4 = 3. The remaining decimal number (3) is greater than or equal to 2, so a 1 was recorded in the 2 column, and 3 2 = 1. The remaining decimal number (1) is greater than or equal to 1, so a 1 was recorded in the 1 column. (The final bit of math, 1 1 = 0, isn t really needed at this point.) Answer to Problem 2: Converting 128 to Binary Table W-11 shows the answer for decimal-to-binary conversion Problem 2. Table W-11 Answer to Problem 2: Converting 128 to Binary Power of Binary Digits _ _

6 6 Networking Basics CCNA 1 Companion Guide The decision points at each step are as follows: Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 The decimal number (128) is greater than or equal to 128, so a 1 was recorded in the 128 column, and = 0. The remaining decimal number (0) is not greater than or equal to 64, so a 0 was recorded in the 64 column. The remaining decimal number (0) is not greater than or equal to 32, so a 0 was recorded in the 32 column. The remaining decimal number (0) is not greater than or equal to 16, so a 0 was recorded in the 16 column. The remaining decimal number (0) is not greater than or equal to 8, so a 0 was recorded in the 8 column. The remaining decimal number (0) is not greater than or equal to 4, so a 0 was recorded in the 4 column. The remaining decimal number (0) is not greater than or equal to 2, so a 0 was recorded in the 2 column. The remaining decimal number (0) is not greater than or equal to 1, so a 0 was recorded in the 1 column. Answer to Problem 3: Converting 200 to Binary Table W-12 shows the answer for decimal-to-binary conversion Problem 3. Table W-12 Answer to Problem 3: Converting 200 to Binary Power of Binary Digits _ _ The decision points at each step are as follows: Step 1 Step 2 Step 3 Step 4 The decimal number (200) is greater than or equal to 128, so a 1 was recorded in the 128 column, and = 72. The remaining decimal number (72) is greater than or equal to 64, so a 1 was recorded in the 64 column, and = 8. The remaining decimal number (8) is not greater than or equal to 32, so a 0 was recorded in the 32 column. The remaining decimal number (8) is not greater than or equal to 16, so a 0 was recorded in the 16 column.

7 Appendix C Answers 7 Step 5 Step 6 Step 7 Step 8 The remaining decimal number (8) is greater than or equal to 8, so a 1 was recorded in the 8 column, and 8 8 = 0. The remaining decimal number (0) is not greater than or equal to 4, so a 0 was recorded in the 4 column. The remaining decimal number (0) is not greater than or equal to 2, so a 0 was recorded in the 2 column. The remaining decimal number (0) is not greater than or equal to 1, so a 0 was recorded in the 1 column. Answer to Problem 4: Converting 9 to Binary Table W-13 shows the answer for decimal-to-binary conversion Problem 4. Table W-13 Answer to Problem 4: Converting 9 to Binary Power of Binary Digits _ _ The decision points at each step are as follows: Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 The decimal number (9) is not greater than or equal to 128, so a 0 was recorded in the 128 column. The remaining decimal number (9) is not greater than or equal to 64, so a 0 was recorded in the 64 column. The remaining decimal number (9) is not greater than or equal to 32, so a 0 was recorded in the 32 column. The remaining decimal number (9) is not greater than or equal to 16, so a 0 was recorded in the 16 column. The remaining decimal number (9) is greater than or equal to 8, so a 1 was recorded in the 8 column, and 9 8 = 1. The remaining decimal number (1) is not greater than or equal to 4, so a 0 was recorded in the 4 column. The remaining decimal number (1) is not greater than or equal to 2, so a 0 was recorded in the 2 column. The remaining decimal number (1) is greater than or equal to 1, so a 1 was recorded in the 1 column. (The final bit of math, 1 1 = 0, isn t really needed at this point.)

8 8 Networking Basics CCNA 1 Companion Guide Answer to Problem 5: Converting 100 to Binary Table W-14 shows the answer for decimal-to-binary conversion Problem 5. Table W-14 Answer to Problem 5: Converting 100 to Binary Power of Binary Digits _ _ The decision points at each step are as follows: Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 The decimal number (100) is not greater than or equal to 128, so a 0 was recorded in the 128 column. The remaining decimal number (100) is greater than or equal to 64, so a 1 was recorded in the 64 column, and = 36. The remaining decimal number (36) is greater than or equal to 32, so a 1 was recorded in the 32 column, and = 4. The remaining decimal number (4) is not greater than or equal to 16, so a 0 was recorded in the 16 column. The remaining decimal number (4) is not greater than or equal to 8, so a 0 was recorded in the 8 column. The remaining decimal number (4) is greater than or equal to 4, so a 1 was recorded in the 4 column, and 4 4 = 0. The remaining decimal number (0) is not greater than or equal to 2, so a 0 was recorded in the 2 column. The remaining decimal number (0) is not greater than or equal to 1, so a 0 was recorded in the 1 column. Answer to Problem 6: Converting 248 to Binary Table W-15 shows the answer for decimal-to-binary conversion Problem 6. Table W-15 Answer to Problem 6: Converting 248 to Binary Power of Binary Digits _ _ The decision points at each step are as follows: Step 1 The decimal number (248) is greater than 128, so a 1 was recorded in the 128 column, and = 120.

9 Appendix C Answers 9 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 The remaining decimal number (120) is greater than or equal to 64, so a 1 was recorded in the 64 column, and = 56. The remaining decimal number (56) is greater than or equal to 32, so a 1 was recorded in the 32 column, and = 24. The remaining decimal number (24) is greater than or equal to 16, so a 1 was recorded in the 16 column, and = 8. The remaining decimal number (8) is greater than or equal to 8, so a 1 was recorded in the 8 column, and 8 8 = 0. The remaining decimal number (0) is not greater than or equal to 4, so a 0 was recorded in the 4 column. The remaining decimal number (0) is not greater than or equal to 2, so a 0 was recorded in the 2 column. The remaining decimal number (0) is not greater than or equal to 1, so a 0 was recorded in the 1 column. Answers to Converting an 8-bit Binary Number to a Hexadecimal Number Table W-16 lists the answers to the binary-to-hexadecimal conversion problems listed in Table C-4 of Appendix C of the book. Following that, the answers are explained in more detail. Table W-16 Answers to Binary-to-Hexadecimal Conversion Problems Problem 8-bit Binary 2-digit Hex Number Number Number AA E F F C0 The process to convert between binary and hex, and vice versa, is relatively simple if you use a conversion chart, as presented in Chapter 1. Table W-17 lists all 16 hexadecimal digits and the 4-digit binary numbers they represent.

10 10 Networking Basics CCNA 1 Companion Guide Table W-17 Binary and Hexadecimal Conversion Chart Hexadecimal Binary Decimal Digit Equivalent Equivalent A B C D E F To perform the conversion, take each set of 4 binary digits and look up the corresponding hexadecimal values. For example, has two sets of 4 binary digits: 0101 and Each set of 4 bits corresponds to hex digit 5, so the hex value is 55. Table W-18 breaks down the logic used to find the answers to all six binary-to-hexadecimal conversion problems listed in Table C-4 of Appendix C.

12 12 Networking Basics CCNA 1 Companion Guide Table W-20 Binary and Hexadecimal Conversion Chart Hexadecimal Binary Decimal Digit Equivalent Equivalent A B C D E F To perform the conversion, take each hexadecimal digit and substitute the 4-bit binary code from the conversion chart. For example, F0 has 2 hex digits. The F corresponds to binary 1111, and the 0 corresponds to binary Table W-21 breaks down the logic used to find the answers to all six hexadecimal-to-binary conversion problems listed in Appendix C.

23 Appendix C Answers 23 Figure W-4 Answer to Problem 2 for Determining the Number of Required Subnets Legend: Subnet Figure W-5 Answer to Problem 3 for Determining the Number of Required Subnets Server1 Legend: Subnet Server2 SW6 SW1 Server3 R1 R2 R3 R4 SW3

24 24 Networking Basics CCNA 1 Companion Guide Figure W-6 has three routers with two LAN interfaces plus a WAN interface. R2, R3, and R4 each have two LAN interfaces connected to two different LAN switches. So, each of these three routers connects to two LAN broadcast domains, requiring six subnets. R1 on the left connects to a single LAN broadcast domain, requiring a single subnet. Finally, the three WAN point-to-point links each require a subnet, so for this problem, ten subnets are required. Figure W-6 Answer to Problem 4 for Determining the Number of Required Subnets R2 R1 R3 Legend: Subnet R4 Answers to Determining the Required Number of Subnet and Host Bits Table W-30 lists the answers for the problems stated in Table C-11 of Appendix C. Following Table W-30, the text explains the answers. Table W-30 Answers to Determining the Number of Subnet and Host Bits Required Problem Classful Maximum Maximum Minimum Number Minimum Number Network Number of Number of Required Number of Subnets of Hosts per Subnet Subnet Bits Required Being Needed Needed Host Bits Subnetted

25 Appendix C Answers 25 The minimum number of subnet bits required is s, where s is the smallest number that makes the following formula true: 2 s 2 => the number of required subnets Similarly, the minimum number of host bits required is h, where h is the smallest number that makes the following formula true: 2 h 2 => the number of required hosts per subnet As a result, determining the answer to each problem relates specifically to either calculating or memorizing the powers of 2. Table W-31 lists the powers of 2 through Table W-31 The Powers of 2, 2 0 Through ,384 32,768 With the information in Table W-31, all you need to do is look at the requirements for the number of subnets and hosts and do some quick comparisons to find the number of required subnet and host bits. The following list describes the logic used to determine the answers in Table W-30. Problem 1 To create 4000 subnets, 11 subnet bits are not enough, because is only However, 12 subnet bits would be enough, because is 4094, which is larger than To support 4000 hosts per subnet, the same math applies, with 11 host bits not being enough, but 12 host bits supporting 4094 hosts per subnet, because is Problem 2 To create 200 subnets, 7 subnet bits are not enough, because is only 126. However, 8 subnet bits would be enough, because is 254, which is larger than 200. The same math applies to the process of deciding the number of host bits needed to support 200 hosts per subnet. Problem 3 To create 10 subnets, 3 subnet bits are not enough, because is only 6. However, 4 subnet bits would be enough, because is 14, which is larger than 10. The same math applies to the process of deciding the number of host bits needed to support 10 hosts per subnet. Problem 4 To create 200 subnets, 7 subnet bits are not enough, because is only 126. However, 8 subnet bits would be enough, because is 254, which is larger than 200. To support 100 hosts per subnet, 6 host bits are not enough, because is only 62. However, 7 host bits would be enough, because is 126, which is larger than 100. Problem 5 To create 50 subnets, 5 subnet bits are not enough, because is only 30. However, 6 subnet bits would be enough, because is 62, which is larger than 50. To support 2 hosts per subnet, 1 host bit is not enough, because is 0. However, 2 host bits would be enough, because is 2, which provides the exact number of hosts needed per subnet.

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