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Quiz about Not so Horrible Hexadecimal
Quiz about Not so Horrible Hexadecimal

Not so Horrible Hexadecimal! Trivia Quiz


This is a quiz about the hexadecimal number system, which is used by computer programmers and in computers.

A multiple-choice quiz by DanielPoulson. Estimated time: 4 mins.
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Time
4 mins
Type
Multiple Choice
Quiz #
281,714
Updated
Nov 23 22
# Qns
10
Difficulty
Average
Avg Score
7 / 10
Plays
244
- -
Question 1 of 10
1. Yesterday I finished reading a book with "1AF" pages. Today I started reading a book with "17B" pages. What is the total number of pages for both books? Answers are in the decimal, or base ten system. All numbers in the question are in the hexadecimal system. Hint


Question 2 of 10
2. The "Renault Laguna 2.0T auto Dynamique S" develops "A8" bhp. The "Ford Mondeo 2.0 TDCI 130 PS Estate Auto" develops "80" bhp. Is the "Renault" more powerful? All numbers in the question are in the hexadecimal system.


Question 3 of 10
3. If a diamond ring costs "5A4" pounds and I have "5DC" pounds, how much change will I receive, if I pay that amount for the ring? All numbers in the question are in the hexadecimal system. All answers are in the decimal, or base ten system. Hint


Question 4 of 10
4. If a collector had 1,241 stamps and bought 17 more, how many stamps would he have? All possible answers are in hexadecimal, all numbers in the question are in decimal, or base ten. Hint


Question 5 of 10
5. If a shop sold a dress for 1,916 pounds and made a profit of 375 pounds, how much did they buy the dress for? All possible answers are in hexadecimal, all numbers in the question are in decimal. Hint


Question 6 of 10
6. If a train network provides 30 trains every hour, how many trains will have begun the journey after 4 hours? All possible answers are in hexadecimal and all of the numbers in the question are in decimal, or base ten. Hint


Question 7 of 10
7. If, after tax, a person earns "7D0" pounds in a month, how much does the person earn in a year. All possible answers are in hexadecimal, as is the number in the question. Hint


Question 8 of 10
8. If this person gets a promotion and earns "7530" pounds a year, how much does the person in a month? All possible answers are in hexadecimal, as is the number in the question. Hint


Question 9 of 10
9. If a footballer had scored "76" goals in his career, but in his last season scored "14" more, how many goals would he have scored overall? All possible answers are in hexadecimal, as are the numbers in the question. Hint


Question 10 of 10
10. To end with, I think that we should have a slightly tricky question. Could you please tell me what the hexadecimal number "FADE" is in decimal? Hint



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Quiz Answer Key and Fun Facts
1. Yesterday I finished reading a book with "1AF" pages. Today I started reading a book with "17B" pages. What is the total number of pages for both books? Answers are in the decimal, or base ten system. All numbers in the question are in the hexadecimal system.

Answer: 810

The hexadecimal number system is used by computer programmers for communication with the machine, in order to perform various tasks. It is also used in various means of coding for tasks. It's simply one type of numerical system. Our decimal system is in base ten, hexadecimal is in base sixteen. This means that each place value in our system is the next power of ten in the sequence. In hexadecimal, each place value is the next power of sixteen. With the decimal system the place values are as follows:

1 (10^0)
10 (10^1)
100 (10^2)
1,000 (10^3) etc.

With the hexadecimal system, the place values are as follows:

1 (16^0)
16 (16^1)
256 (16^2)
4,096 (16^3)

Binary, the number system used by most computers to operate, is base two, which means that the place values are as follows:

1 (2^0)
2 (2^1)
4 (2^2)
8 (2^3)

Therefore, binary numbers are much longer, as each place value is much lower. There is one problem with hexadecimal numbers, however. That is that we would run out of digits. When we want to say that we have ten lots of a place value, we cannot use "10", as that we mean that we have 1 lot of the NEXT place value and 0 lots of the current one. This is demonstrated by the fact that if we wanted to say that we have ten lots of 1, writing "10" would mean that we would have:

16s:1
1s:0,

as the "1" is representing the next place value. Therefore, we use letters.

A = "10"
B = "11"
C = "12"
D = "13"
E = "14"
F = "15"

Then "10" represents "16", as we have:

16s:1
1s:0

16 + 0 = 16.

Now, the first thing which we must do is convert our number into the lovely base ten. or decimal system, which we all know and love. Our first number is 1AF, so we have:

256s:1
16s:A (remember that A = "10")
1s:F (remember that F = "15")

256 x 1 = 256.

16 x 10 (or A) = 160.

1 x 15 (or F) = 15.

256 + 160 + 15 = 431.

Our second number is 17B, so we have:

256s:1
16s:7
1s:B (remember that B = "11")

256 x 1 = 256.

16 x 7 = 112.

1 x 11 (or B) = 11

256 + 112 + 11 = 379.

431 + 379 = 810.
2. The "Renault Laguna 2.0T auto Dynamique S" develops "A8" bhp. The "Ford Mondeo 2.0 TDCI 130 PS Estate Auto" develops "80" bhp. Is the "Renault" more powerful? All numbers in the question are in the hexadecimal system.

Answer: Yes

Because the Hexadecimal number system is reasonably uncommon, I need to repeat the explanation given in the previous question for anybody who is playing this quiz in an environment other than that of the original quiz. Those playing the actual quiz may skip the part in the quotation marks, as this is repeated throughout. Otherwise, proceed:

START: "The hexadecimal number system is used by computer programmers for communication with the machine, in order to perform various tasks. It is also used in various means of coding for tasks. It's simply one type of numerical system. Our decimal system is in base ten, hexadecimal is in base sixteen. This means that each place value in our system is the next power of ten in the sequence. In hexadecimal, each place value is the next power of sixteen. With the decimal system the place values are as follows:

1 (10^0)
10 (10^1)
100 (10^2)
1,000 (10^3) etc.

With the hexadecimal system, the place values are as follows:

1 (16^0)
16 (16^1)
256 (16^2)
4,096 (16^3)

Binary, the number system used by most computers to operate, is base two, which means that the place values are as follows:

1 (2^0)
2 (2^1)
4 (2^2)
8 (2^3)

Therefore, binary numbers are much longer, as each place value is much lower. There is one problem with hexadecimal numbers, however. That is that we would run out of digits. When we want to say that we have ten lots of a place value, we cannot use "10", as that we mean that we have 1 lot of the NEXT place value and 0 lots of the current one. This is demonstrated by the fact that if we wanted to say that we have ten lots of 1, writing "10" would mean that we would have:

16s:1
1s:0,

as the "1" is representing the next place value. Therefore, we use letters.

A = "10"
B = "11"
C = "12"
D = "13"
E = "14"
F = "15"

Then "10" represents "16", as we have:

16s:1
1s:0

16 + 0 = 16." END.

Because the vast majority of us are not computer systems, we will struggle to do this question without first converting the numbers into the base ten, or decimal system. Our first number is "A8", which means that we have:

16s:A (remember that A = "10")
1s:8

16 x 10 (or A) = 160

1 x 8 = 8

160 + 8 = 168.

Our second number is "80", so we have:

16s:8
1s:0

16 x 8 = 128

1 x 0 = 0

128 + 0 = 128.

168 is bigger that 128, so the "Renault" is more powerful.
3. If a diamond ring costs "5A4" pounds and I have "5DC" pounds, how much change will I receive, if I pay that amount for the ring? All numbers in the question are in the hexadecimal system. All answers are in the decimal, or base ten system.

Answer: 56 pounds

Because the Hexadecimal number system is reasonably uncommon, I need to repeat the explanation given in the previous question for anybody who is playing this quiz in an environment other than that of the original quiz. Those playing the actual quiz may skip the part in the quotation marks, as this is repeated throughout. Otherwise, proceed:

START: "The hexadecimal number system is used by computer programmers for communication with the machine, in order to perform various tasks. It is also used in various means of coding for tasks. It's simply one type of numerical system. Our decimal system is in base ten, hexadecimal is in base sixteen. This means that each place value in our system is the next power of ten in the sequence. In hexadecimal, each place value is the next power of sixteen. With the decimal system the place values are as follows:

1 (10^0)
10 (10^1)
100 (10^2)
1,000 (10^3) etc.

With the hexadecimal system, the place values are as follows:

1 (16^0)
16 (16^1)
256 (16^2)
4,096 (16^3)

Binary, the number system used by most computers to operate, is base two, which means that the place values are as follows:

1 (2^0)
2 (2^1)
4 (2^2)
8 (2^3)

Therefore, binary numbers are much longer, as each place value is much lower. There is one problem with hexadecimal numbers, however. That is that we would run out of digits. When we want to say that we have ten lots of a place value, we cannot use "10", as that we mean that we have 1 lot of the NEXT place value and 0 lots of the current one. This is demonstrated by the fact that if we wanted to say that we have ten lots of 1, writing "10" would mean that we would have:

16s:1
1s:0,

as the "1" is representing the next place value. Therefore, we use letters.

A = "10"
B = "11"
C = "12"
D = "13"
E = "14"
F = "15"

Then "10" represents "16", as we have:

16s:1
1s:0

16 + 0 = 16." END.

The first thing which we should do is convert our hexadecimal numbers into the decimal, or base ten system. Our first number is 5A4, so we have:

256s:5
16s:A (remember that A = "10")
1s:4

256 x 5 = 1,280

16 x 10 (or A) = 160

1 x 4 = 4

1,280 + 160 + 4 = 1,444.

Our second number is 5DC, so we have:

256s:5
16s:D (remember that D = "13")
1s:C (remember that C = "12")

256 x 5 = 1,280

16 x 13 (or D) = 208

1 x 12 (or C) = 12

1,280 + 208 + 12 = 1,500.

1,500 - 1,444 = 56.
4. If a collector had 1,241 stamps and bought 17 more, how many stamps would he have? All possible answers are in hexadecimal, all numbers in the question are in decimal, or base ten.

Answer: 4EA

Because the Hexadecimal number system is reasonably uncommon, I need to repeat the explanation given in the previous question for anybody who is playing this quiz in an environment other than that of the original quiz. Those playing the actual quiz may skip the part in the quotation marks, as this is repeated throughout. Otherwise, proceed:

START: "The hexadecimal number system is used by computer programmers for communication with the machine, in order to perform various tasks. It is also used in various means of coding for tasks. It's simply one type of numerical system. Our decimal system is in base ten, hexadecimal is in base sixteen. This means that each place value in our system is the next power of ten in the sequence. In hexadecimal, each place value is the next power of sixteen. With the decimal system the place values are as follows:

1 (10^0)
10 (10^1)
100 (10^2)
1,000 (10^3) etc.

With the hexadecimal system, the place values are as follows:

1 (16^0)
16 (16^1)
256 (16^2)
4,096 (16^3)

Binary, the number system used by most computers to operate, is base two, which means that the place values are as follows:

1 (2^0)
2 (2^1)
4 (2^2)
8 (2^3)

Therefore, binary numbers are much longer, as each place value is much lower. There is one problem with hexadecimal numbers, however. That is that we would run out of digits. When we want to say that we have ten lots of a place value, we cannot use "10", as that we mean that we have 1 lot of the NEXT place value and 0 lots of the current one. This is demonstrated by the fact that if we wanted to say that we have ten lots of 1, writing "10" would mean that we would have:

16s:1
1s:0,

as the "1" is representing the next place value. Therefore, we use letters.

A = "10"
B = "11"
C = "12"
D = "13"
E = "14"
F = "15"

Then "10" represents "16", as we have:

16s:1
1s:0

16 + 0 = 16." END.

To begin with, we need to add up our two numbers, 1,241 + 17 = 1,258.

Our next step must be to convert 1,258 into a hexadecimal number. We know that our place values are:

1 (16^0)
16 (16^1)
256 (16^2)
4,096 (16^3)

and from this we can work out how many digits we will need. 4,096 is much too big, so we will need three digits, as 256 is not nearly too big. However, it is too small, so we need to work out how many 256s we will need. In order to do this we must divide 1,258 by 256 and that will tell us how many we will need. 1,258 divided by 256 = 4, with a remainder of 234. This means that we will need 4 lots of 256, however, we still need an extra 234. This we obtain from the next two digits, but we can't obtain it from the first, as we would then exceed our target number. The next place value is 16, so we divide the remainder, 234, by 16. 234 divided by 16 = 14, with a remainder of ten. Therefore, we have 14 lots of 16, or E lots of 16 and the remainder of ten lots of 1. This is because we obtain our remaining ten from the last place value, 1. So we have 10 lots of 1, or A lots of 1. Therefore, our number is 4EA.
5. If a shop sold a dress for 1,916 pounds and made a profit of 375 pounds, how much did they buy the dress for? All possible answers are in hexadecimal, all numbers in the question are in decimal.

Answer: 605

Because the Hexadecimal number system is reasonably uncommon, I need to repeat the explanation given in the previous question for anybody who is playing this quiz in an environment other than that of the original quiz. Those playing the actual quiz may skip the part in the quotation marks, as this is repeated throughout. Otherwise, proceed:

START: "The hexadecimal number system is used by computer programmers for communication with the machine, in order to perform various tasks. It is also used in various means of coding for tasks. It's simply one type of numerical system. Our decimal system is in base ten, hexadecimal is in base sixteen. This means that each place value in our system is the next power of ten in the sequence. In hexadecimal, each place value is the next power of sixteen. With the decimal system the place values are as follows:

1 (10^0)
10 (10^1)
100 (10^2)
1,000 (10^3) etc.

With the hexadecimal system, the place values are as follows:

1 (16^0)
16 (16^1)
256 (16^2)
4,096 (16^3)

Binary, the number system used by most computers to operate, is base two, which means that the place values are as follows:

1 (2^0)
2 (2^1)
4 (2^2)
8 (2^3)

Therefore, binary numbers are much longer, as each place value is much lower. There is one problem with hexadecimal numbers, however. That is that we would run out of digits. When we want to say that we have ten lots of a place value, we cannot use "10", as that we mean that we have 1 lot of the NEXT place value and 0 lots of the current one. This is demonstrated by the fact that if we wanted to say that we have ten lots of 1, writing "10" would mean that we would have:

16s:1
1s:0,

as the "1" is representing the next place value. Therefore, we use letters.

A = "10"
B = "11"
C = "12"
D = "13"
E = "14"
F = "15"

Then "10" represents "16", as we have:

16s:1
1s:0

16 + 0 = 16." END.

In order to work out how much the dress was bought for, we must take 375 from 1,916. 1,916 - 375 = 1,541.

Having worked that out, we must convert 1,541 to hexadecimal. We know that our place values are:

1 (16^0)
16 (16^1)
256 (16^2)
4,096 (16^3)

and this can be used to calculate how many digits we will need. We will need three digits, as 4,096, the place value of the fourth digit, is far too big. However, the place value of the third digit, 256, is not. It is not big enough, however, so we must work out how many 256s we need. To do this, we must divide 1,541 by 256. 1,541 divided by 256 = 6, with a remainder of 5. We can obtain the 5 from the next two digits. 5 is far smaller than 16, so we need 0 lots of 16, we just need 5 lots of 1. So we have 605.
6. If a train network provides 30 trains every hour, how many trains will have begun the journey after 4 hours? All possible answers are in hexadecimal and all of the numbers in the question are in decimal, or base ten.

Answer: 78

Because the Hexadecimal number system is reasonably uncommon, I need to repeat the explanation given in the previous question for anybody who is playing this quiz in an environment other than that of the original quiz. Those playing the actual quiz may skip the part in the quotation marks, as this is repeated throughout. Otherwise, proceed:

START: "The hexadecimal number system is used by computer programmers for communication with the machine, in order to perform various tasks. It is also used in various means of coding for tasks. It's simply one type of numerical system. Our decimal system is in base ten, hexadecimal is in base sixteen. This means that each place value in our system is the next power of ten in the sequence. In hexadecimal, each place value is the next power of sixteen. With the decimal system the place values are as follows:

1 (10^0)
10 (10^1)
100 (10^2)
1,000 (10^3) etc.

With the hexadecimal system, the place values are as follows:

1 (16^0)
16 (16^1)
256 (16^2)
4,096 (16^3)

Binary, the number system used by most computers to operate, is base two, which means that the place values are as follows:

1 (2^0)
2 (2^1)
4 (2^2)
8 (2^3)

Therefore, binary numbers are much longer, as each place value is much lower. There is one problem with hexadecimal numbers, however. That is that we would run out of digits. When we want to say that we have ten lots of a place value, we cannot use "10", as that we mean that we have 1 lot of the NEXT place value and 0 lots of the current one. This is demonstrated by the fact that if we wanted to say that we have ten lots of 1, writing "10" would mean that we would have:

16s:1
1s:0,

as the "1" is representing the next place value. Therefore, we use letters.

A = "10"
B = "11"
C = "12"
D = "13"
E = "14"
F = "15"

Then "10" represents "16", as we have:

16s:1
1s:0

16 + 0 = 16." END.

Our first step must be to multiply 30 by 4 and 30 x 4 = 120. Now that we have the answer, we must convert it into hexadecimal. We know that our place values are:

1 (16^0)
16 (16^1)
256 (16^2)
4,096 (16^3)

and from this we can calculate how many digits will be required. Two digits will be required, as the place value for the third digit, 256, is much too large. The place value for the second digit, 16, however, is not. It is not big enough, though, so we must work out exactly how many lots of 16 will be required. In order to do this, we must divide our number, 120, by 16. 120 divided by 16 = 7, with a remainder of 8. Therefore, we have 7 lots of 16 and 8 lots of 1, the next place value. So our number is 78.
7. If, after tax, a person earns "7D0" pounds in a month, how much does the person earn in a year. All possible answers are in hexadecimal, as is the number in the question.

Answer: "5DC0" pounds

Because the Hexadecimal number system is reasonably uncommon, I need to repeat the explanation given in the previous question for anybody who is playing this quiz in an environment other than that of the original quiz. Those playing the actual quiz may skip the part in the quotation marks, as this is repeated throughout. Otherwise, proceed:

START: "The hexadecimal number system is used by computer programmers for communication with the machine, in order to perform various tasks. It is also used in various means of coding for tasks. It's simply one type of numerical system. Our decimal system is in base ten, hexadecimal is in base sixteen. This means that each place value in our system is the next power of ten in the sequence. In hexadecimal, each place value is the next power of sixteen. With the decimal system the place values are as follows:

1 (10^0)
10 (10^1)
100 (10^2)
1,000 (10^3) etc.

With the hexadecimal system, the place values are as follows:

1 (16^0)
16 (16^1)
256 (16^2)
4,096 (16^3)

Binary, the number system used by most computers to operate, is base two, which means that the place values are as follows:

1 (2^0)
2 (2^1)
4 (2^2)
8 (2^3)

Therefore, binary numbers are much longer, as each place value is much lower. There is one problem with hexadecimal numbers, however. That is that we would run out of digits. When we want to say that we have ten lots of a place value, we cannot use "10", as that we mean that we have 1 lot of the NEXT place value and 0 lots of the current one. This is demonstrated by the fact that if we wanted to say that we have ten lots of 1, writing "10" would mean that we would have:

16s:1
1s:0,

as the "1" is representing the next place value. Therefore, we use letters.

A = "10"
B = "11"
C = "12"
D = "13"
E = "14"
F = "15"

Then "10" represents "16", as we have:

16s:1
1s:0

16 + 0 = 16." END.

The first thing that we should do is convert the hexadecimal number into a nice, easy decimal number. Our number is 7D0, so we have:

256s:7
16s:D (remember that D = "13")
1s:0

256 x 7 = 1,792

16 x 13 (or D) = 208

1 x 0 = 0

1,792 + 208 + 0 = 2,000.

There are 12 months in a year, so we do 2,000 multiplied by 12, and 2,000 x 12 = 24,000.

Now that we have our answer, we must convert it into hexadecimal. The place values are as follows:

1 (16^0)
16 (16^1)
256 (16^2)
4,096 (16^3)
65,536 (16^4)

and from these we can decide how many digits we are going to need. We will need 4 digits, as the place value for the fifth digit, 65,536, is far too high. Conversely, the place value for the fourth digit, 4,096, is definitely not. It is much too low, however, so we will need a number of 4,096s, but how many? To work this out, we must divide our number, 24,000, by 4,096. 24,000 divided by 4,096 = 5, with a remainder of 3,520. We will get this from our other digits. Our next place value is 256, but how many 256s do we need? Well, we divide our remainder, 3,520, by 256 and 3,520 divided by 256 = 13, with a remainder of 192. So we have 5 lots of 4,096 and 13 lots of 256. Which means that we actually have D lots of 13. But we still have a remainder of 192. Therefore, we must divide 192 by the next place value, 16. 192 divided by 16 = 12, with no remainder. So we have 12 lots of 16, or C lots of 16 and 0 lots of 1. Which means that our answer is "5DC0".
8. If this person gets a promotion and earns "7530" pounds a year, how much does the person in a month? All possible answers are in hexadecimal, as is the number in the question.

Answer: "9C4" pounds

Because the Hexadecimal number system is reasonably uncommon, I need to repeat the explanation given in the previous question for anybody who is playing this quiz in an environment other than that of the original quiz. Those playing the actual quiz may skip the part in the quotation marks, as this is repeated throughout. Otherwise, proceed:

START: "The hexadecimal number system is used by computer programmers for communication with the machine, in order to perform various tasks. It is also used in various means of coding for tasks. It's simply one type of numerical system. Our decimal system is in base ten, hexadecimal is in base sixteen. This means that each place value in our system is the next power of ten in the sequence. In hexadecimal, each place value is the next power of sixteen. With the decimal system the place values are as follows:

1 (10^0)
10 (10^1)
100 (10^2)
1,000 (10^3) etc.

With the hexadecimal system, the place values are as follows:

1 (16^0)
16 (16^1)
256 (16^2)
4,096 (16^3)

Binary, the number system used by most computers to operate, is base two, which means that the place values are as follows:

1 (2^0)
2 (2^1)
4 (2^2)
8 (2^3)

Therefore, binary numbers are much longer, as each place value is much lower. There is one problem with hexadecimal numbers, however. That is that we would run out of digits. When we want to say that we have ten lots of a place value, we cannot use "10", as that we mean that we have 1 lot of the NEXT place value and 0 lots of the current one. This is demonstrated by the fact that if we wanted to say that we have ten lots of 1, writing "10" would mean that we would have:

16s:1
1s:0,

as the "1" is representing the next place value. Therefore, we use letters.

A = "10"
B = "11"
C = "12"
D = "13"
E = "14"
F = "15"

Then "10" represents "16", as we have:

16s:1
1s:0

16 + 0 = 16." END.

Our first step must be to convert our number, 7530, into decimal. 7530 means that we have:

4,096s:7
256s:5
16s:3
1s:0

4,096 x 7 = 28,672

256 x 5 = 1,280

16 x 3 = 48

1 x 0 = 0

28,672 + 1,280 + 48 + 0 = 30,000.

There are twelve months in one year, so we must divide 30,000 by 12 and 30,000 divided by 12 = 2,500. Now that we know how the person earns in a month, we must convert the answer to hexadecimal. The place values are as follows:

1 (16^0)
16 (16^1)
256 (16^2)
4,096 (16^3)

and from these we can decide how many digits will be required. We can see that we will need 3 digits, as 4,096, the place value for the fourth digit, is rather larger than 2,500. The place value for the third digit, 256, is not. It is too small, however, so we will need more than one. To work out how many more than one we will need, we must divide 2,500 by 256, which will give us the amount of 256s that can fit into 2,500. 2,500 divided by 256 = 9, with a remainder of 196. We will make the 196 from the remaining digits. The next place value is 16. Therefore, we must do 196 divided by 16. 196 divided by 16 = 12, with a remainder of 4, which will give us 4 lots of 1. 1 is the next place value and 4 divided by 1 = 4. So we have:

256s:9
16s:12, but 12 = C, so we actually have C lots of 16
1s:4.

Therefore, the answer is "9C4".
9. If a footballer had scored "76" goals in his career, but in his last season scored "14" more, how many goals would he have scored overall? All possible answers are in hexadecimal, as are the numbers in the question.

Answer: 8A

Because the Hexadecimal number system is reasonably uncommon, I need to repeat the explanation given in the previous question for anybody who is playing this quiz in an environment other than that of the original quiz. Those playing the actual quiz may skip the part in the quotation marks, as this is repeated throughout. Otherwise, proceed:

START: "The hexadecimal number system is used by computer programmers for communication with the machine, in order to perform various tasks. It is also used in various means of coding for tasks. It's simply one type of numerical system. Our decimal system is in base ten, hexadecimal is in base sixteen. This means that each place value in our system is the next power of ten in the sequence. In hexadecimal, each place value is the next power of sixteen. With the decimal system the place values are as follows:

1 (10^0)
10 (10^1)
100 (10^2)
1,000 (10^3) etc.

With the hexadecimal system, the place values are as follows:

1 (16^0)
16 (16^1)
256 (16^2)
4,096 (16^3)

Binary, the number system used by most computers to operate, is base two, which means that the place values are as follows:

1 (2^0)
2 (2^1)
4 (2^2)
8 (2^3)

Therefore, binary numbers are much longer, as each place value is much lower. There is one problem with hexadecimal numbers, however. That is that we would run out of digits. When we want to say that we have ten lots of a place value, we cannot use "10", as that we mean that we have 1 lot of the NEXT place value and 0 lots of the current one. This is demonstrated by the fact that if we wanted to say that we have ten lots of 1, writing "10" would mean that we would have:

16s:1
1s:0,

as the "1" is representing the next place value. Therefore, we use letters.

A = "10"
B = "11"
C = "12"
D = "13"
E = "14"
F = "15"

Then "10" represents "16", as we have:

16s:1
1s:0

16 + 0 = 16." END.

The first thing which we must do is convert our hexadecimal numbers into decimal numbers. Our first number is 76, so we have:

16s:7
1s:6

16 x 7 = 112

1 x 6 = 6

112 + 6 = 118.

Our second number is 14, so we have:

16s:1
1s:4

16 x 1 = 16

1 x 4 = 4

16 + 4 = 20.

Now that we know what our numbers are, we must add them together. 118 + 20 = 138. Now that we know our answer, we have to convert it into hexadecimal. The place values are as follows:

1 (16^0)
16 (16^1)
256 (16^2)

and from this we can see that we will need a 2 digit number. This is because the place value for the third digit, 256, is too high. However, the place value for the second digit, 16, is not. We will need more than one though, to make 138. In order to decide how many, we must divide 138 by 16, which will give us the number of 16s in 138. 138 divided by 16 = 8 with a remainder of 10. We can make the ten from the last digit. This has a place value of 1, so we will 10 of those. However, in hexadecimal to denote ten, we must use the letter A. Therefore, our answer is 8A.
10. To end with, I think that we should have a slightly tricky question. Could you please tell me what the hexadecimal number "FADE" is in decimal?

Answer: 64,222

Because the Hexadecimal number system is reasonably uncommon, I need to repeat the explanation given in the previous question for anybody who is playing this quiz in an environment other than that of the original quiz. Those playing the actual quiz may skip the part in the quotation marks, as this is repeated throughout. Otherwise, proceed:

START: "The hexadecimal number system is used by computer programmers for communication with the machine, in order to perform various tasks. It is also used in various means of coding for tasks. It's simply one type of numerical system. Our decimal system is in base ten, hexadecimal is in base sixteen. This means that each place value in our system is the next power of ten in the sequence. In hexadecimal, each place value is the next power of sixteen. With the decimal system the place values are as follows:

1 (10^0)
10 (10^1)
100 (10^2)
1,000 (10^3) etc.

With the hexadecimal system, the place values are as follows:

1 (16^0)
16 (16^1)
256 (16^2)
4,096 (16^3)

Binary, the number system used by most computers to operate, is base two, which means that the place values are as follows:

1 (2^0)
2 (2^1)
4 (2^2)
8 (2^3)

Therefore, binary numbers are much longer, as each place value is much lower. There is one problem with hexadecimal numbers, however. That is that we would run out of digits. When we want to say that we have ten lots of a place value, we cannot use "10", as that we mean that we have 1 lot of the NEXT place value and 0 lots of the current one. This is demonstrated by the fact that if we wanted to say that we have ten lots of 1, writing "10" would mean that we would have:

16s:1
1s:0,

as the "1" is representing the next place value. Therefore, we use letters.

A = "10"
B = "11"
C = "12"
D = "13"
E = "14"
F = "15"

Then "10" represents "16", as we have:

16s:1
1s:0

16 + 0 = 16." END.

Our number is "FADE", so we have:

4,096s:F (remember that F = "15")
256s:A (remember that A = "10")
16s:D (remember that D = "13")
1s:E (remember that E = "14")

4,096 x 15 (or F) = 61,440
256 x 10 (or A) = 2,560
16 x 13 (or D) = 208
1 x 14 (or E) = 14

61,440 + 2,560 + 208 + 14 = 64,222.
Source: Author DanielPoulson

This quiz was reviewed by FunTrivia editor crisw before going online.
Any errors found in FunTrivia content are routinely corrected through our feedback system.
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