1. (return of the…) Data blast
2.1.4 Digital Representation

2. Go… 1 2 3

3. Candidates should be able to:
define the terms bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte
1 bit = 1 binary digit
– represents an electrical signal being on or off.
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4. Candidates should be able to:
define the terms bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte
4 bits = 1 nibble.
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5. Candidates should be able to:
define the terms bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte
8 bits = 1 byte
Stands for "by eight"?
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6. Candidates should be able to:
define the terms bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte
(kilo = 1000)
1024 bytes = 1 kilobyte
(mega = million)
1024 kilobytes = 1 megabyte
1024 megabytes = 1 gigabyte
(giga = billion)
1024 gigabytes = 1 terabyte
(tera = trillion)
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7. Candidates should be able to:
understand that data needs to be converted into a binary format to be processed by a computer.
Computers work by processing electrical signals.
Electrical signals can be either on or off
Text, images, sound and instructions all
need to be converted into binary so
that computers can understand the
information
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8. Candidates should be able to:
convert positive denary whole numbers (0-255) into 8-bit binary numbers and vice versa 1
Convert the following binary number to denary.
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9. Candidates should be able to:
convert positive denary whole numbers (0-255) into 8-bit binary numbers and vice versa
128 64 32 16 8 4 2 1
Write the column headings above each number
Start with “1” and double each time.
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10. Candidates should be able to:
convert positive denary whole numbers (0-255) into 8-bit binary numbers and vice versa
128 64 32 16 8 4 2 1
Write down all the numbers with a “1” below them
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11. Candidates should be able to:
convert positive denary whole numbers (0-255) into 8-bit binary numbers and vice versa
Add them up…
178
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12. Converting from denary to binary
Convert the following denary number to binary.
178

13. Horbury Academy ICT and Business Studies
Step 1
Write out the column headings…
178
128 64 32 16 8 4 2 1
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14. Horbury Academy ICT and Business Studies
Step 2
Find the biggest number that will fit…
178
128 64 32 16 8 4 2 1
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15. Horbury Academy ICT and Business Studies
Step 3
Write a “1” below that number…
178
128 64 32 16 8 4 2 1
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16. Horbury Academy ICT and Business Studies
Step 4
Take away the column heading from our number 50 is now our target number
178 – 128 = 50
128 64 32 16 8 4 2 1
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17. Horbury Academy ICT and Business Studies
Step 5
Work through the columns. 50
128 64 32 16 8 4 2 1
Is the column heading (64)
Bigger than our target number (50)
Yes? – write a zero
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18. Horbury Academy ICT and Business Studies
Step 6
Work through the columns. 50
128 64 32 16 8 4 2 1
Is the column heading (32)
Bigger than our target number (50)
No? – write a one
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19. Horbury Academy ICT and Business Studies
Step 7
Work out the next target…
50 – 32 = 18
128 64 32 16 8 4 2 1
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20. Horbury Academy ICT and Business Studies
Step 7
Continue!
128 64 32 16 8 4 2 1 18
18 is bigger than 16
128 64 32 16 8 4 2 1 2
2 is not bigger than 8
128 64 32 16 8 4 2 1 2
2 is not bigger than 4
128 64 32 16 8 4 2 1 2
2 is equal to 2
128 64 32 16 8 4 2 1
Write a 0!
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21. Adding two binary numbers 1 1 1 1
Just like normal, start on the right…
…for the exam, the first nibble will
probably not have any "carries"
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22. Adding two binary numbers
0 + 1 = 1
(no carries) 1 1 1 1 1
The second nibble may have some carries
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23. Adding two binary numbers
1 + 1 = 10
(so write 0, and carry 1) 1 1 1 1 1 1
The second nibble may have some carries
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24. Adding two binary numbers
1 + 1 (+ carry) = 11
(so write 1, and carry 1) 1 1 1 1 1 1 1 1
The second nibble may have some carries
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25. Adding two binary numbers
0 + 1 (+ carry) = 10
(so write 0, and carry 1) 1 1 1 1 1 1 1 1 1
The second nibble may have some carries
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26. Adding two binary numbers 1 1 1 1 1 1 1 1 1 1
This leaves the carried 1, which goes into
the 9th column
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27. Adding two binary numbers 1 1 1 1 1 1 1 1 1 1
This would produce an error as we can only store 8 bits in a byte.
You will usually be asked to explain this.
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28. Horbury Academy ICT and Business Studies
Hex
As well as binary, we often use Hexadecimal in computing.
Hexadecimal use the numbers 0 to 9 and then the letter A to F
A B C D E F
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29. Horbury Academy ICT and Business Studies
Convert denary to hex…
165 (denary)
= A5 (hex)
Divide by 16
165/16 = 10 remainder 5
A in hex
5 in hex
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30. Horbury Academy ICT and Business Studies
Convert hex to denary…
CD (hex)
= 205 (denary)
Convert to denary CD
C = 12
D = 13
Multiply by 16
12 x 16 = 192
…add 13
= 205
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31. How to convert binary to hex…
Step 1 – write down the binary numbers 1 to 16…
0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
1010
1011
1100
1101
1110
1111
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32. How to convert binary to hex…
Step 2 – Write the Hex numbers next to them…
0000
0001
0010
0011 1 2 3
0100
0101
0110
0111 4 5 6 7
1000
1001
1010
1011 8 9 A B
1100
1101
1110
1111 C D E F
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33. Horbury Academy ICT and Business Studies
Convert binary to hex
Split your number in two nibbles…
0110
1011
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34. Horbury Academy ICT and Business Studies
Convert binary to hex
Convert each nibble into hex…
0110
1011 6 B
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35. Why do we use Hexadecimal?
Binary numbers get very long very quickly – for example 1023 is
This means that they are difficult to remember and it is easy to make mistakes when you enter them
This is why we use hex:
= 3FF
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