Introduction
This revision zone looks at the ‘Hexadecimal Number System’.
Specifically:
– How the hexadecimal number system works
– The reasons why computer scientists may make use of this number system
– How to convert between binary and hexadecimal numbers
1: Read to Understand
Begin the revision process by reading the presentation…
2: Make some revision notes
3: Reinforce your understanding
Interactive Flash Cards
[qdeck align=”center” style=”width: 100%; border: 4px solid #306EFF;” card_back=”white”]
[h]
Hexadecimal Numbers
[q]What is a major drawback of writing binary numbers?
[a]One problem is that very quickly, a fairly small number like 258 (3 digits long) becomes the massive binary number of 100000010 (9 digits!)
[q]What is the hexadecimal number system?
[a]The hexadecimal number system is base 16. This means that its place values increase in the following manner:
Therefore the number 101 in hexadecimal is 257.
[q]Because the second column is 16, we have to count to 15 in the 1s column before we can place a 1 in the 16s column
…but in all number systems, placing two digits in one column is not allowed. How does the hexadecimal number system overcome this?
[a]The hexadecimal number system uses letters to represent 10, 11, 12, 13, 14 and 15.
[q]What is the hexadecimal number 13 in denary?
[a]
[q]What is the hexadecimal number 47 in denary?
[a]
[q]What is the hexadecimal number A1 in denary?
[a]
[q]What is the hexadecimal number AB in denary?
[a]
[q]What is the hexadecimal number 9D in denary?
[a]
[q]What is the denary number 50 converted into hexadecimal?
[a]
[q]What is the denary number 172 converted into hexadecimal?
[a]
[q]What is the denary number 101 converted into hexadecimal?
[a]
[q]What is the denary number 68 converted into hexadecimal?
[a]
[q]The question that many people ask is ‘why do computer scientists use hexadecimal?’
One reasons is that Hexadecimal uses fewer digits to represent values compared to binary – but so do denary numbers!?
So why do computer scientists use Hexadecimal?
[a]It is because it is easy to convert between Hex and Binary!
[q]How do you convert a binary number into hexadecimal?
[a]To convert binary into hexadecimal:
– split the number into nibbles
– work out value of each nibble (use AF if value is 1015)
– join the separate values to form the hexadecimal number.
[q]Convert the binary number 10000011 into hexadecimal?
[a]
[q]Convert the binary number 11111001 into hexadecimal?
[a]
[q]Convert the binary number 11010111 into hexadecimal?
[a]
[q]Convert the binary number 11101010 into hexadecimal?
[a]
[q]Convert the hexadecimal number BC into binary?
[a]
[q]Convert the hexadecimal number 4B into binary?
[a]
[q]Convert the hexadecimal number 2F into binary?
[a]
[q]Convert the hexadecimal number 7A into binary?
[a]
[/qdeck]
Printable Flash Cards
Download and print out these ‘Flash Cards’ – use them to reinforce your understanding!
Ensure you print these double sided, ‘flipped on short edge’ so that the front and back of each card match up!
The Hexadecimal Number System – 22 Flashcards
4: Assess your understanding
Assessment 1
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Question 1 of 10
1. Question
The hexadecimal number system is a…
Correct
Denary is base 10. Column values from right to left go 1, 10, 100 etc (10^0, 10^1, 10^2 etc)
Binary is base 2. Column values from right to left go 1, 2, 4, 8 etc (2^0, 2^1, 2^2 etc)
Hexadecimal is base 16. Column values from right to left go 1, 16, 256 etc (16^0, 16^1, 16^2 etc)Incorrect
Denary is base 10. Column values from right to left go 1, 10, 100 etc (10^0, 10^1, 10^2 etc)
Binary is base 2. Column values from right to left go 1, 2, 4, 8 etc (2^0, 2^1, 2^2 etc)
Hexadecimal is base 16. Column values from right to left go 1, 16, 256 etc (16^0, 16^1, 16^2 etc) 
Question 2 of 10
2. Question
What is the value of the hexadecimal number 16, in denary?
Correct
Incorrect

Question 3 of 10
3. Question
What is the value of B in hexadecimal?
Correct
Remember, in hexadecimal, you count up to 15 in each column. But, you can’t have more than one digit in a column, so in hexadecimal, we use the letter A for 10, B for 11, C for 12, D for 13, E for 14 and F for 15.
Incorrect
Remember, in hexadecimal, you count up to 15 in each column. But, you can’t have more than one digit in a column, so in hexadecimal, we use the letter A for 10, B for 11, C for 12, D for 13, E for 14 and F for 15.

Question 4 of 10
4. Question
What is the hex value of B4 in denary?
Correct
Incorrect

Question 5 of 10
5. Question
What is the denary value of 14 in Hexadecimal?
Correct
Remember, in hexadecimal, you count up to 15 in each column. But, you can’t have more than one digit in a column, so in hexadecimal, we use the letter A for 10, B for 11, C for 12, D for 13, E for 14 and F for 15.
Incorrect
Remember, in hexadecimal, you count up to 15 in each column. But, you can’t have more than one digit in a column, so in hexadecimal, we use the letter A for 10, B for 11, C for 12, D for 13, E for 14 and F for 15.

Question 6 of 10
6. Question
What is the denary value of 51 in Hexadecimal?
Correct
51 is made up of 3 lots of 16, with a remainder of 3.
So, 51 is 33 in hexadecimal.
Remember, when converting from denary to hex, see how many times 16 fits into the number first (this answer will go in your first column) then see what the remainder is (this answer will go in your second column).Incorrect
51 is made up of 3 lots of 16, with a remainder of 3.
So, 51 is 33 in hexadecimal.
Remember, when converting from denary to hex, see how many times 16 fits into the number first (this answer will go in your first column) then see what the remainder is (this answer will go in your second column). 
Question 7 of 10
7. Question
What is the denary value 164 in Hexadecimal?
Correct
The tip here is to recognise that 164 is close to 160, which of course is 10 lots of 16. So you can immediately notice that 16 fits into 164, 10 times. Then finding the remainder is easy…it is just 4.
So the answer is A4 (10 (or A) lots of 16, plus 4)Incorrect
The tip here is to recognise that 164 is close to 160, which of course is 10 lots of 16. So you can immediately notice that 16 fits into 164, 10 times. Then finding the remainder is easy…it is just 4.
So the answer is A4 (10 (or A) lots of 16, plus 4) 
Question 8 of 10
8. Question
What is 1100 + 1100?
Correct
Incorrect

Question 9 of 10
9. Question
What is 11001101 + 10001111?
Correct
Incorrect

Question 10 of 10
10. Question
What is the problem with the obtaining a 9 bit answer from the addition of two bytes?
Correct
Remember, traditionally 8bit CPUs had registers that could only hold 8 bit binary numbers, so when 9 bit binary numbers were calculated, they couldn’t handle the extra bit and so an overflow error resulted.
Incorrect
Remember, traditionally 8bit CPUs had registers that could only hold 8 bit binary numbers, so when 9 bit binary numbers were calculated, they couldn’t handle the extra bit and so an overflow error resulted.
Assessment 2
Quizsummary
0 of 10 questions completed
Questions:
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Take this test to assess your knowledge and understanding of hexadecimal and binary conversions.
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Aaand relax, its over! Now take a look at your result and spend further time revising any areas of the test that you got incorrect.
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 Answered
 Review

Question 1 of 10
1. Question
What is the ‘BASE’ of the binary number system?
Correct
Denary is base 10. Column values from right to left go 1, 10, 100 etc (10^0, 10^1, 10^2 etc)
Hexadecimal is base 16. Column values from right to left go 1, 16, 256 etc (16^0, 16^1, 16^2 etc)
Binary is base 2. Column values from right to left go 1, 2, 4, 8 etc (2^0, 2^1, 2^2 etc)Incorrect
Denary is base 10. Column values from right to left go 1, 10, 100 etc (10^0, 10^1, 10^2 etc)
Hexadecimal is base 16. Column values from right to left go 1, 16, 256 etc (16^0, 16^1, 16^2 etc)
Binary is base 2. Column values from right to left go 1, 2, 4, 8 etc (2^0, 2^1, 2^2 etc) 
Question 2 of 10
2. Question
What is the ‘BASE’ of the hexadecimal number system?
Correct
Denary is base 10. Column values from right to left go 1, 10, 100 etc (10^0, 10^1, 10^2 etc)
Binary is base 2. Column values from right to left go 1, 2, 4, 8 etc (2^0, 2^1, 2^2 etc)
Hexadecimal is base 16. Column values from right to left go 1, 16, 256 etc (16^0, 16^1, 16^2 etc)Incorrect
Denary is base 10. Column values from right to left go 1, 10, 100 etc (10^0, 10^1, 10^2 etc)
Binary is base 2. Column values from right to left go 1, 2, 4, 8 etc (2^0, 2^1, 2^2 etc)
Hexadecimal is base 16. Column values from right to left go 1, 16, 256 etc (16^0, 16^1, 16^2 etc) 
Question 3 of 10
3. Question
What is the Hex number ‘A’, in binary?
Correct
Remember, in hexadecimal, you count up to 15 in each column. But, you can’t have more than on digit in a column, so in hexadecimal, we use the letter A for 10, B for 11, C for 12, D for 13, E for 14 and F for 15.
Then you need to convert your denary number to binary, so 10 becomes 1010, as its 1 lot of 8 plus 1 lot of 2.Incorrect
Remember, in hexadecimal, you count up to 15 in each column. But, you can’t have more than on digit in a column, so in hexadecimal, we use the letter A for 10, B for 11, C for 12, D for 13, E for 14 and F for 15.
Then you need to convert your denary number to binary, so 10 becomes 1010, as its 1 lot of 8 plus 1 lot of 2. 
Question 4 of 10
4. Question
What is the Hex number ’12’, in binary?
Correct
To convert from hex to binary is easy! Just split the hex number into its individual digits and then convert those digits into nibbles.
For example the 1 converts to 0001 and the 2 converts to 0010, then we join the answers to produce 00010010 (or simply 10010).
Incorrect
To convert from hex to binary is easy! Just split the hex number into its individual digits and then convert those digits into nibbles.
For example the 1 converts to 0001 and the 2 converts to 0010, then we join the answers to produce 00010010 (or simply 10010).

Question 5 of 10
5. Question
What is the Hex number ‘2B’, in binary?
Correct
To convert from hex to binary is easy! Just split the hex number into its individual digits and then convert those digits into nibbles.
For example the 2 converts to 0010 and the B (which is 11) converts to 1011, then we join the answers to produce 00101011 (or simply 101011).
Incorrect
To convert from hex to binary is easy! Just split the hex number into its individual digits and then convert those digits into nibbles.
For example the 2 converts to 0010 and the B (which is 11) converts to 1011, then we join the answers to produce 00101011 (or simply 101011).

Question 6 of 10
6. Question
What is the binary number 01101100 in Hex?
Correct
To convert from binary to hex is also easy! Just split the binary number into nibbles and then convert the nibbles into hex digits, then join the hex digits together to form the hexadecimal number.
For example the 01101100 splits into the nibbles 0110 and 1100. 0110 converts to 6 (1 lot of 4 plus 1 lot of 2) and 1100 converts to 12 which is a C in hex (1 lot of 8 plus 1 lot of 4), then we join the digits together to produce 6C.
Incorrect
To convert from binary to hex is also easy! Just split the binary number into nibbles and then convert the nibbles into hex digits, then join the hex digits together to form the hexadecimal number.
For example the 01101100 splits into the nibbles 0110 and 1100. 0110 converts to 6 (1 lot of 4 plus 1 lot of 2) and 1100 converts to 12 which is a C in hex (1 lot of 8 plus 1 lot of 4), then we join the digits together to produce 6C.

Question 7 of 10
7. Question
Convert the Binary number 01011010 into Hex?
Correct
To convert from binary to hex is also easy! Just split the binary number into nibbles and then convert the nibbles into hex digits, then join the hex digits together to form the hexadecimal number.
For example the 01011010 splits into the nibbles 0101 and 1010. 0101 converts to 5 (1 lot of 4 plus 1 lot of 1) and 1010 converts to 10 which is a A in hex (1 lot of 8 plus 1 lot of 2), then we join the digits together to produce 5A.
Incorrect
To convert from binary to hex is also easy! Just split the binary number into nibbles and then convert the nibbles into hex digits, then join the hex digits together to form the hexadecimal number.
For example the 01011010 splits into the nibbles 0101 and 1010. 0101 converts to 5 (1 lot of 4 plus 1 lot of 1) and 1010 converts to 10 which is a A in hex (1 lot of 8 plus 1 lot of 2), then we join the digits together to produce 5A.

Question 8 of 10
8. Question
What is the greatest number that can be held in a single digit of Hex?
Correct
There are 15 different hex digits, each representing the numbers from 1 to 15 (e.g. 1=1…..15=F).
The greatest number held in a single digit of hex is therefore 15!Incorrect
There are 15 different hex digits, each representing the numbers from 1 to 15 (e.g. 1=1…..15=F).
The greatest number held in a single digit of hex is therefore 15! 
Question 9 of 10
9. Question
What is the greatest number that can be held in two digits of Hex?
Correct
The biggest number that can be represented with 2 digits of hex is FF.
FF is 15 lots of 16 plus 15 lots of 1.
This works out as 255.
Incorrect
The biggest number that can be represented with 2 digits of hex is FF.
FF is 15 lots of 16 plus 15 lots of 1.
This works out as 255.

Question 10 of 10
10. Question
How many bits are required to store a single digit of Hex?
Correct
The largest number that can be stored in a single digit of hex is 15 (which is F).
15 in hexadecimal is 1111 in binary.
Therefore 4 digits are required to store a single hex digit.Incorrect
The largest number that can be stored in a single digit of hex is 15 (which is F).
15 in hexadecimal is 1111 in binary.
Therefore 4 digits are required to store a single hex digit.