Binary Math
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Mastering Binary Math Cisco certification candidates, from the CCNA to the CCIE, must master binary math. This includes basic conversions, such as binary-to-decimal and decimal-to-binary, as well as more advanced scenarios involving subnetting and VLSM. There’s another conversion that might rear its ugly head on your Cisco exam, though, and that involves hexadecimal numbering. Newcomers to hexadecimal numbering are often confused as to how a letter of the alphabet can possibly represent a number. Worse, they may be intimidated – after all, there must be some incredibly complicated formula involved with representing the decimal 11 with the letter “b”, right? Wrong. The numbering system we use every day, decimal, concerns itself with units of ten. Although we rarely stop to think of it this way, if you read a decimal number from right to left, the number indicates how many units of one, ten, and one hundred we have. That is, the number “15” is five units of one and one unit of ten. The number “289” is nine units of one, eight units of ten, and two units of one hundred. Simple enough!
The decimal “15” The decimal “289”
Units Of 100 0 2
Units Of 10 1 8
Units Of 1 5 9
Hex numbers are read much the same way, except the units here are units of 16. The number “15” in hex is read as having five units of one and one unit of sixteen. The number “289” in hex is nine units of one, eight units of sixteen, and two units of 256 (16 x 16).
The hex numeral “15” The hex numeral “289”
Units Of 256 0 2
Units Of 16 1 8
Units Of 1 5 9
Since hex uses units of sixteen, how can we possibly represent a value of 10, 11, 12, 13, 14, or 15? We do so with letters. The decimal “10” is represented in hex with the letter “a”; the decimal 11 with “b”; the decimal “12” with “c”, “13” with “d”, “14” with “e”, and finally, “15” with “f”. (Remember that a MAC address of “ffff.ffff.ffff” is a Layer 2 broadcast.) Practice Your Conversions for Exam Success Now that you know where the letters fall into place in the hexadecimal numbering world, you’ll have little trouble converting hex to decimal and decimal to hex – if you practice. How would you convert the decimal 27 to hex? You can see that there is one unit of 16 in this decimal; that leaves 11 units of one. This is represented in hex with “1b” – one unit of sixteen, 11 units of one. Work From Left To Right To Perform Decimal – Hexadecimal Conversions.
Decimal Number “27”
Units of 256 0
Chris Bryant, CCIE™ #12933 www.thebryantadvantage.com Free CCNA and CCNP tutorials!
Units of 16 1
Units of 1 B (11)
Hexadecimal Value 1b
Page 1
Mastering Binary Math Converting the decimal 322 to hex is no problem. There is one unit of 256; that leaves 66. There are four units of 16 in 66; that leaves 2, or two units of one. The hex equivalent of the decimal 322 is the hex figure 142 – one unit of 256, four units of 32, and 2 units of 2.
Decimal Number “322”
Units of 256 1
Units of 16 4
Units of 1 2
Hexadecimal Value 142
Hex-to-decimal conversions are even simpler. Given the hex number 144, what is the decimal equivalent? We have one unit of 256, four units of 16, and four units of 4. This gives us the decimal figure 324. Units of 256 1
Hexadecimal Number “144”
Units of 16 4
Units of 1 4
Decimal Value 256 + 64 + 4 = 324
What about the hex figure c2? We now know that the letter “c” represents the decimal number “12”. This means we have 12 units of 16, and two units of 2. This gives us the decimal figure 194.
Hexadecimal Number “c2”
Units of 256 0
Units of 16 12
Units of 1 2
Decimal Value 192 + 2 = 194
Tips for Exam Day Practice your binary and hexadecimal conversions over and over again before you take your CCNA exams. Binary math questions come in many different forms; make sure you have practiced all of them before exam day. The number one reason CCNA candidates fail their exam is that they’re not prepared for the different types of binary math questions they’re going to be asked, and that they aren’t ready for hexadecimal questions at all. As you can see, hexadecimal conversions are actually simple. though!
You have to practice them,
You don’t have time to learn how to do in on exam day. You’ve got to be ready before you go into the exam room, and the only way to be ready is a lot of practice. Finally, make sure you read the question carefully. You’ve got hex, decimal, and binary numbers to concern yourself with on your CCNA and CCNP exams. Make sure you give Cisco the answer in the format they’re looking for. I have written 20 practice questions that will help you practice your hexadecimal conversion skills. Once you practice with these questions, and know exactly how each answer was arrived at, you’ll have no problem with hexadecimal conversions on your Cisco exams. Best of luck! To your success, Chris Bryant, CCIE™ #12933
Chris Bryant, CCIE™ #12933 www.thebryantadvantage.com Free CCNA and CCNP tutorials!
Page 2
Mastering Binary Math 1. Convert the following hexadecimal number to decimal: 1c 2. Convert the following hexadecimal number to decimal: f1 3. Convert the following hexadecimal number to decimal: 2a9 4. Convert the following hexadecimal number to decimal: 14b 5. Convert the following hexadecimal number to decimal: 3e4 6. Convert the following decimal number to hexadecimal: 13 7. Convert the following decimal number to hexadecimal: 784 8. Convert the following decimal number to hexadecimal: 419 9. Convert the following decimal number to hexadecimal: 1903 10. Convert the following decimal number to hexadecimal: 345 11. Convert the following hex number to binary: 42 12. Convert the following hex number to binary: 12 13. Convert the following hex number to binary: a9 14. Convert the following hex number to binary: 3c 15. Convert the following hex number to binary: 74 16. Convert the following binary string to hex: 00110011 17. Convert the following binary string to hex: 11001111 18. Convert the following binary string to hex: 01011101 19. Convert the following binary string to hex: 10011101 20. 20.Convert the following binary string to hex: 11010101 Answers begin on the next page. No peeking!
Chris Bryant, CCIE™ #12933 www.thebryantadvantage.com Free CCNA and CCNP tutorials!
Page 3
Mastering Binary Math Before we go through the answers and how they were achieved, let's review the meaning of letters in hexadecimal numbering: A = 10, B = 11, C = 12, D = 13, E = 14, F = 15. (And remember that ffff.ffff.ffff is a Layer 2 broadcast!) Conversions involving hexadecimal numbers will use this chart: 256
16
1
_________________________________________________________________________ 1.
Convert the following hexadecimal number to decimal: 1c 256
16 1
1 c
There is one unit of 16 and twelve units of 1. 16 + 12 = 28. _________________________________________________________________________
2.
Convert the following hexadecimal number to decimal: f1
256
16 f
1 1
There are fifteen units of 16 and 1 unit of 1. 240 + 1 = 241 _________________________________________________________________________
3.
Convert the following hexadecimal number to decimal: 2a9 256 2
16 a
1 9
There are two units of 256, ten units of 16, and nine units of 1. 512 + 160 + 9 = 681 _________________________________________________________________________
Chris Bryant, CCIE™ #12933 www.thebryantadvantage.com Free CCNA and CCNP tutorials!
Page 4
Mastering Binary Math 4.
Convert the following hexadecimal number to decimal: 14b 256 1
16 4
1 b
There is one unit of 256, four units of 16, and 11 units of 1. 256 + 64 + 11 = 331 _________________________________________________________________________
5.
Convert the following hexadecimal number to decimal: 3e4 256 3
16 e
1 4
There are three units of 256, fourteen units of 16, and four units of 1. 768 + 224 + 4 = 996 _________________________________________________________________________ 6.
Convert the following decimal to hexadecimal: 13
When converting decimal to hex, work with the same chart from left to right. Are there any units of 256 in the decimal 13? No. 256 0
16
1
Are there any units of 16 in the decimal 13? No. 256 0
16 0
1
Are there any units of 1 in the decimal 13? Sure. Thirteen of them. Remember how we express the number "13" with a single hex character? 256 0
16 0
1 d
The answer is "d". It's not necessary to have any leading zeroes when expressing hex value. _________________________________________________________________________
7.
Convert the following decimal to hexadecimal: 784
Are there any units of 256 in the decimal 784? Yes, three of them, for a total of 768. Place a "3" in the 256 slot, and subtract 768 from 784. 256 3
Chris Bryant, CCIE™ #12933 www.thebryantadvantage.com Free CCNA and CCNP tutorials!
16
1
Page 5
Mastering Binary Math 784 - 768 = 16 Obviously, there's one unit of 16 in 16. Since there is no remainder, we can place a "0" in the remaining slots. 256 3
16 1
1 0
The final result is the hex number "310". _________________________________________________________________________
8.
Convert the following decimal to hexadecimal: 419
Are there any units of 256 in the decimal 419? Yes, one, with a remainder of 163.
256 1
16
1
Are there any units of 16 in the decimal 163? Yes, ten of them, with a remainder of three. 256 1
16 a
1
Three units of one take care of the remainder, and the hex number "1a3" is the answer. 256 1
16 a
1 3
_________________________________________________________________________ 9.
Convert the following decimal to hexadecimal: 1903
Are there any units of 256 in the decimal 1903? Yes, seven of them, totaling 1792. This leaves a remainder of 111. 256 7
16
1
Are there any units of 16 in the decimal 111? Yes, six of them, with a remainder of 15. 256 7
16 6
1
By using the letter "f" to represent 15 units of 1, the final answer "76f" is achieved. 256 7
16 6
1 f
_________________________________________________________________________
Chris Bryant, CCIE™ #12933 www.thebryantadvantage.com Free CCNA and CCNP tutorials!
Page 6
Mastering Binary Math 10. Convert the following decimal to hexadecimal: 345 Are there any units of 256 in 345? Sure, one, with a remainder of 89. 256 1
16
1
Are there any units of 16 in 89? Yes, five of them, with a remainder of 9. 256 1
16 5
1
Nine units of nine give us the hex number "159". 256 1
16 5
1 9
_________________________________________________________________________
11. Convert the following hex number to binary: 42 First, convert the hex number to decimal. We know "42" in hex means we have four units of 16 and two units of 1. Since 64 + 2 = 66, we have our decimal. Now we've got to convert that decimal into binary. Here's our chart showing how to convert the decimal 66 into binary:
66
128 0
64 1
32 0
16 0
8 0
4 0
2 1
1 0
The correct answer: 01000010 _________________________________________________________________________
12. Convert the following hex number to binary: 12 First, convert the hex number to decimal. The hex number "12" indicates one unit of sixteen and two units of one; in decimal, this is 18. Now to convert that decimal into binary. Use the same chart we used in Question 11:
18
128 0
64 0
32 0
16 1
8 0
4 0
2 1
1 0
The correct answer: 00010010 _________________________________________________________________________
Chris Bryant, CCIE™ #12933 www.thebryantadvantage.com Free CCNA and CCNP tutorials!
Page 7
Mastering Binary Math 13. Convert the following hex number to binary: a9 First, convert the hex number to decimal. Since "a" equals 10 in hex, we have 10 units of 16 and nine units of 1. 160 + 9 = 169 Now convert the decimal 169 to binary:
169
128 1
64 0
32 1
16 0
8 1
4 0
2 0
1 1
The correct answer: 10101001 _________________________________________________________________________
14. Convert the following hex number to binary: 3c First, convert the hex number to decimal. We have three units of 16 and 12 units of 1 (c = 12), giving us a total of 60 (48 + 12). Convert the decimal 60 into binary:
60
128 0
64 0
32 1
16 1
8 1
4 1
2 0
1 0
The correct answer: 00111100 _________________________________________________________________________ 15. Convert the following hex number to binary: 74 First, convert the hex number to decimal. We have seven units of 16 and four units of 1, resulting in the decimal 116 (112 + 4). Convert the decimal 116 into binary:
116
128 0
64 1
32 1
16 1
8 0
4 1
2 0
1 0
The correct answer: 01110100 _________________________________________________________________________ The next five questions dealt with converting binary to hex. We're going to use much the same method in solving these questions, but this point bears repeating: Make sure to answer the question in the format that Cisco is asking for on your exams. _________________________________________________________________________
Chris Bryant, CCIE™ #12933 www.thebryantadvantage.com Free CCNA and CCNP tutorials!
Page 8
Mastering Binary Math 16. Convert the following binary string to hex: 00110011 First, we'll convert the binary string to decimal: 128 0
64 0
32 1
16 1
8 0
4 0
2 1
1 1
Decimal 51
To finish answering the question, convert the decimal 51 to hex. Are there any units of 256 in the decimal 51? No. Are there any units of 16 in the decimal 51? Yes, three, for a total of 48 and a remainder of three. Three units of one give us the hex number "33". 256 0
16 3
1 3
_________________________________________________________________________ 17. Convert the following binary string to hex: 11001111 First, we'll convert the binary string to decimal: 128 1
64 1
32 0
16 0
8 1
4 1
2 1
1 1
Decimal 207
Now convert the decimal 207 to hex. Are there any units of 256 in the decimal 207? No. Are there any units of 16 in the decimal 207? Yes, twelve of them, for a total of 192 and a remainder of 15. Twelve is represented in hex with the letter "c". Fifteen units of one are expressed with the letter "f", giving us a hex number of "cf". 256 0
16 c
1 f
_________________________________________________________________________ 18. Convert the following binary string to hex: 01011101 First, convert the binary string to decimal:
128 0
64 1
32 0
16 1
8 1
4 1
2 0
1 1
Decimal 93
Now convert the decimal 93 to hex. There are no units of 256, obviously. How many units of 16 are there? Five, for a total of 80 and a remainder of 13. We express the number 13 in hex with the letter "d". The final result is the hex number "5d". 256 0
16 5
1 d
19. Convert the following binary string to hex: 10011101
Chris Bryant, CCIE™ #12933 www.thebryantadvantage.com Free CCNA and CCNP tutorials!
Page 9
Mastering Binary Math As always, convert the binary string to decimal first: 128 1
64 0
32 0
16 1
8 1
4 1
2 0
1 1
Decimal 157
Now convert the decimal 157 to hex. There are no units of 256. How many units of 16 are there in the decimal 157? Nine, for a total of 144 and a remainder of 13. You know to express the number 13 in hex with the letter "d", resulting in a hex number of “9d". 256 0
16 9
1 d
_________________________________________________________________________
20. Convert the following binary string to hex: 11010101 First, convert the binary string to decimal: 128 1
64 1
32 0
16 1
8 0
4 1
2 0
1 1
Decimal 213
Now convert the decimal 213 to hex. No units of 256, but how many of 16? Thirteen of them, with a total of 208 and a remainder of 5. Again, the number 13 in hex is represented with the letter "d", and the five units of one give us the hex number "d5". 256 0
Chris Bryant, CCIE™ #12933 www.thebryantadvantage.com Free CCNA and CCNP tutorials!
16 d
1 5
Page 10
The decimal “15” The decimal “289”
Units Of 100 0 2
Units Of 10 1 8
Units Of 1 5 9
Hex numbers are read much the same way, except the units here are units of 16. The number “15” in hex is read as having five units of one and one unit of sixteen. The number “289” in hex is nine units of one, eight units of sixteen, and two units of 256 (16 x 16).
The hex numeral “15” The hex numeral “289”
Units Of 256 0 2
Units Of 16 1 8
Units Of 1 5 9
Since hex uses units of sixteen, how can we possibly represent a value of 10, 11, 12, 13, 14, or 15? We do so with letters. The decimal “10” is represented in hex with the letter “a”; the decimal 11 with “b”; the decimal “12” with “c”, “13” with “d”, “14” with “e”, and finally, “15” with “f”. (Remember that a MAC address of “ffff.ffff.ffff” is a Layer 2 broadcast.) Practice Your Conversions for Exam Success Now that you know where the letters fall into place in the hexadecimal numbering world, you’ll have little trouble converting hex to decimal and decimal to hex – if you practice. How would you convert the decimal 27 to hex? You can see that there is one unit of 16 in this decimal; that leaves 11 units of one. This is represented in hex with “1b” – one unit of sixteen, 11 units of one. Work From Left To Right To Perform Decimal – Hexadecimal Conversions.
Decimal Number “27”
Units of 256 0
Chris Bryant, CCIE™ #12933 www.thebryantadvantage.com Free CCNA and CCNP tutorials!
Units of 16 1
Units of 1 B (11)
Hexadecimal Value 1b
Page 1
Mastering Binary Math Converting the decimal 322 to hex is no problem. There is one unit of 256; that leaves 66. There are four units of 16 in 66; that leaves 2, or two units of one. The hex equivalent of the decimal 322 is the hex figure 142 – one unit of 256, four units of 32, and 2 units of 2.
Decimal Number “322”
Units of 256 1
Units of 16 4
Units of 1 2
Hexadecimal Value 142
Hex-to-decimal conversions are even simpler. Given the hex number 144, what is the decimal equivalent? We have one unit of 256, four units of 16, and four units of 4. This gives us the decimal figure 324. Units of 256 1
Hexadecimal Number “144”
Units of 16 4
Units of 1 4
Decimal Value 256 + 64 + 4 = 324
What about the hex figure c2? We now know that the letter “c” represents the decimal number “12”. This means we have 12 units of 16, and two units of 2. This gives us the decimal figure 194.
Hexadecimal Number “c2”
Units of 256 0
Units of 16 12
Units of 1 2
Decimal Value 192 + 2 = 194
Tips for Exam Day Practice your binary and hexadecimal conversions over and over again before you take your CCNA exams. Binary math questions come in many different forms; make sure you have practiced all of them before exam day. The number one reason CCNA candidates fail their exam is that they’re not prepared for the different types of binary math questions they’re going to be asked, and that they aren’t ready for hexadecimal questions at all. As you can see, hexadecimal conversions are actually simple. though!
You have to practice them,
You don’t have time to learn how to do in on exam day. You’ve got to be ready before you go into the exam room, and the only way to be ready is a lot of practice. Finally, make sure you read the question carefully. You’ve got hex, decimal, and binary numbers to concern yourself with on your CCNA and CCNP exams. Make sure you give Cisco the answer in the format they’re looking for. I have written 20 practice questions that will help you practice your hexadecimal conversion skills. Once you practice with these questions, and know exactly how each answer was arrived at, you’ll have no problem with hexadecimal conversions on your Cisco exams. Best of luck! To your success, Chris Bryant, CCIE™ #12933
Chris Bryant, CCIE™ #12933 www.thebryantadvantage.com Free CCNA and CCNP tutorials!
Page 2
Mastering Binary Math 1. Convert the following hexadecimal number to decimal: 1c 2. Convert the following hexadecimal number to decimal: f1 3. Convert the following hexadecimal number to decimal: 2a9 4. Convert the following hexadecimal number to decimal: 14b 5. Convert the following hexadecimal number to decimal: 3e4 6. Convert the following decimal number to hexadecimal: 13 7. Convert the following decimal number to hexadecimal: 784 8. Convert the following decimal number to hexadecimal: 419 9. Convert the following decimal number to hexadecimal: 1903 10. Convert the following decimal number to hexadecimal: 345 11. Convert the following hex number to binary: 42 12. Convert the following hex number to binary: 12 13. Convert the following hex number to binary: a9 14. Convert the following hex number to binary: 3c 15. Convert the following hex number to binary: 74 16. Convert the following binary string to hex: 00110011 17. Convert the following binary string to hex: 11001111 18. Convert the following binary string to hex: 01011101 19. Convert the following binary string to hex: 10011101 20. 20.Convert the following binary string to hex: 11010101 Answers begin on the next page. No peeking!
Chris Bryant, CCIE™ #12933 www.thebryantadvantage.com Free CCNA and CCNP tutorials!
Page 3
Mastering Binary Math Before we go through the answers and how they were achieved, let's review the meaning of letters in hexadecimal numbering: A = 10, B = 11, C = 12, D = 13, E = 14, F = 15. (And remember that ffff.ffff.ffff is a Layer 2 broadcast!) Conversions involving hexadecimal numbers will use this chart: 256
16
1
_________________________________________________________________________ 1.
Convert the following hexadecimal number to decimal: 1c 256
16 1
1 c
There is one unit of 16 and twelve units of 1. 16 + 12 = 28. _________________________________________________________________________
2.
Convert the following hexadecimal number to decimal: f1
256
16 f
1 1
There are fifteen units of 16 and 1 unit of 1. 240 + 1 = 241 _________________________________________________________________________
3.
Convert the following hexadecimal number to decimal: 2a9 256 2
16 a
1 9
There are two units of 256, ten units of 16, and nine units of 1. 512 + 160 + 9 = 681 _________________________________________________________________________
Chris Bryant, CCIE™ #12933 www.thebryantadvantage.com Free CCNA and CCNP tutorials!
Page 4
Mastering Binary Math 4.
Convert the following hexadecimal number to decimal: 14b 256 1
16 4
1 b
There is one unit of 256, four units of 16, and 11 units of 1. 256 + 64 + 11 = 331 _________________________________________________________________________
5.
Convert the following hexadecimal number to decimal: 3e4 256 3
16 e
1 4
There are three units of 256, fourteen units of 16, and four units of 1. 768 + 224 + 4 = 996 _________________________________________________________________________ 6.
Convert the following decimal to hexadecimal: 13
When converting decimal to hex, work with the same chart from left to right. Are there any units of 256 in the decimal 13? No. 256 0
16
1
Are there any units of 16 in the decimal 13? No. 256 0
16 0
1
Are there any units of 1 in the decimal 13? Sure. Thirteen of them. Remember how we express the number "13" with a single hex character? 256 0
16 0
1 d
The answer is "d". It's not necessary to have any leading zeroes when expressing hex value. _________________________________________________________________________
7.
Convert the following decimal to hexadecimal: 784
Are there any units of 256 in the decimal 784? Yes, three of them, for a total of 768. Place a "3" in the 256 slot, and subtract 768 from 784. 256 3
Chris Bryant, CCIE™ #12933 www.thebryantadvantage.com Free CCNA and CCNP tutorials!
16
1
Page 5
Mastering Binary Math 784 - 768 = 16 Obviously, there's one unit of 16 in 16. Since there is no remainder, we can place a "0" in the remaining slots. 256 3
16 1
1 0
The final result is the hex number "310". _________________________________________________________________________
8.
Convert the following decimal to hexadecimal: 419
Are there any units of 256 in the decimal 419? Yes, one, with a remainder of 163.
256 1
16
1
Are there any units of 16 in the decimal 163? Yes, ten of them, with a remainder of three. 256 1
16 a
1
Three units of one take care of the remainder, and the hex number "1a3" is the answer. 256 1
16 a
1 3
_________________________________________________________________________ 9.
Convert the following decimal to hexadecimal: 1903
Are there any units of 256 in the decimal 1903? Yes, seven of them, totaling 1792. This leaves a remainder of 111. 256 7
16
1
Are there any units of 16 in the decimal 111? Yes, six of them, with a remainder of 15. 256 7
16 6
1
By using the letter "f" to represent 15 units of 1, the final answer "76f" is achieved. 256 7
16 6
1 f
_________________________________________________________________________
Chris Bryant, CCIE™ #12933 www.thebryantadvantage.com Free CCNA and CCNP tutorials!
Page 6
Mastering Binary Math 10. Convert the following decimal to hexadecimal: 345 Are there any units of 256 in 345? Sure, one, with a remainder of 89. 256 1
16
1
Are there any units of 16 in 89? Yes, five of them, with a remainder of 9. 256 1
16 5
1
Nine units of nine give us the hex number "159". 256 1
16 5
1 9
_________________________________________________________________________
11. Convert the following hex number to binary: 42 First, convert the hex number to decimal. We know "42" in hex means we have four units of 16 and two units of 1. Since 64 + 2 = 66, we have our decimal. Now we've got to convert that decimal into binary. Here's our chart showing how to convert the decimal 66 into binary:
66
128 0
64 1
32 0
16 0
8 0
4 0
2 1
1 0
The correct answer: 01000010 _________________________________________________________________________
12. Convert the following hex number to binary: 12 First, convert the hex number to decimal. The hex number "12" indicates one unit of sixteen and two units of one; in decimal, this is 18. Now to convert that decimal into binary. Use the same chart we used in Question 11:
18
128 0
64 0
32 0
16 1
8 0
4 0
2 1
1 0
The correct answer: 00010010 _________________________________________________________________________
Chris Bryant, CCIE™ #12933 www.thebryantadvantage.com Free CCNA and CCNP tutorials!
Page 7
Mastering Binary Math 13. Convert the following hex number to binary: a9 First, convert the hex number to decimal. Since "a" equals 10 in hex, we have 10 units of 16 and nine units of 1. 160 + 9 = 169 Now convert the decimal 169 to binary:
169
128 1
64 0
32 1
16 0
8 1
4 0
2 0
1 1
The correct answer: 10101001 _________________________________________________________________________
14. Convert the following hex number to binary: 3c First, convert the hex number to decimal. We have three units of 16 and 12 units of 1 (c = 12), giving us a total of 60 (48 + 12). Convert the decimal 60 into binary:
60
128 0
64 0
32 1
16 1
8 1
4 1
2 0
1 0
The correct answer: 00111100 _________________________________________________________________________ 15. Convert the following hex number to binary: 74 First, convert the hex number to decimal. We have seven units of 16 and four units of 1, resulting in the decimal 116 (112 + 4). Convert the decimal 116 into binary:
116
128 0
64 1
32 1
16 1
8 0
4 1
2 0
1 0
The correct answer: 01110100 _________________________________________________________________________ The next five questions dealt with converting binary to hex. We're going to use much the same method in solving these questions, but this point bears repeating: Make sure to answer the question in the format that Cisco is asking for on your exams. _________________________________________________________________________
Chris Bryant, CCIE™ #12933 www.thebryantadvantage.com Free CCNA and CCNP tutorials!
Page 8
Mastering Binary Math 16. Convert the following binary string to hex: 00110011 First, we'll convert the binary string to decimal: 128 0
64 0
32 1
16 1
8 0
4 0
2 1
1 1
Decimal 51
To finish answering the question, convert the decimal 51 to hex. Are there any units of 256 in the decimal 51? No. Are there any units of 16 in the decimal 51? Yes, three, for a total of 48 and a remainder of three. Three units of one give us the hex number "33". 256 0
16 3
1 3
_________________________________________________________________________ 17. Convert the following binary string to hex: 11001111 First, we'll convert the binary string to decimal: 128 1
64 1
32 0
16 0
8 1
4 1
2 1
1 1
Decimal 207
Now convert the decimal 207 to hex. Are there any units of 256 in the decimal 207? No. Are there any units of 16 in the decimal 207? Yes, twelve of them, for a total of 192 and a remainder of 15. Twelve is represented in hex with the letter "c". Fifteen units of one are expressed with the letter "f", giving us a hex number of "cf". 256 0
16 c
1 f
_________________________________________________________________________ 18. Convert the following binary string to hex: 01011101 First, convert the binary string to decimal:
128 0
64 1
32 0
16 1
8 1
4 1
2 0
1 1
Decimal 93
Now convert the decimal 93 to hex. There are no units of 256, obviously. How many units of 16 are there? Five, for a total of 80 and a remainder of 13. We express the number 13 in hex with the letter "d". The final result is the hex number "5d". 256 0
16 5
1 d
19. Convert the following binary string to hex: 10011101
Chris Bryant, CCIE™ #12933 www.thebryantadvantage.com Free CCNA and CCNP tutorials!
Page 9
Mastering Binary Math As always, convert the binary string to decimal first: 128 1
64 0
32 0
16 1
8 1
4 1
2 0
1 1
Decimal 157
Now convert the decimal 157 to hex. There are no units of 256. How many units of 16 are there in the decimal 157? Nine, for a total of 144 and a remainder of 13. You know to express the number 13 in hex with the letter "d", resulting in a hex number of “9d". 256 0
16 9
1 d
_________________________________________________________________________
20. Convert the following binary string to hex: 11010101 First, convert the binary string to decimal: 128 1
64 1
32 0
16 1
8 0
4 1
2 0
1 1
Decimal 213
Now convert the decimal 213 to hex. No units of 256, but how many of 16? Thirteen of them, with a total of 208 and a remainder of 5. Again, the number 13 in hex is represented with the letter "d", and the five units of one give us the hex number "d5". 256 0
Chris Bryant, CCIE™ #12933 www.thebryantadvantage.com Free CCNA and CCNP tutorials!
16 d
1 5
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