OCR GCSE Computer Science Teaching and Learning Resources
Chapter 16: Data representation, conversion
and arithmetic
ANSWERS TO QUESTIONS IN THE STUDENT’S BOOK
Page 154
1. Convert 18, 41, 135 and 221 in denary to binary.
Answer
18 = 10010
41 = 101001
135 = 10000111
221 = 11011101
Question
2. Convert 1101, 11101, 10101010 and 11111101 from binary into denary.
Answer
1101 = 13
11101 = 29
10101010 = 170
11111101 = 253
Question
3. How many kilobytes are there in 3 terabytes?
Answer
3 000 000 000 or three billion
Question
4. How many megabytes are there in 2 petabytes?
Answer
2 000 000 000 or two billion
OCR GCSE Computer Science
© Hodder & Stoughton Limited 2016
OCR GCSE Computer Science Teaching and Learning Resources
Question
5. Add the following binary numbers, showing your workings:
a) 1101 + 10001
b) 10011 + 11111
c) 11000111 + 11101
Answer
a)
1101
+ 10001
= 11110
1
Answer: 11110
b)
10011
+ 11111
= 110010
1111
Answer: 110010
c)
11000111
+ 11101
=11100100
11111
Answer: 11100100
Question
6. Convert the following binary numbers to hexadecimal:
a) 10000011
b) 10101100
c) 00111110
d) 11111111
Answer
a) 83
b) AC
c) 3E
d) FF
OCR GCSE Computer Science
© Hodder & Stoughton Limited 2016
OCR GCSE Computer Science Teaching and Learning Resources
Question
7. Convert the following hexadecimal numbers to binary and to denary:
a) 3B
b) AE
c) 23
d) 5C
Answer
a) 00111011
59
b) 10101110
174
c) 00100011
35
d) 01011100
92
Page 157
Question
8. What is meant by the character set of a computer?
Answer
The character set of a computer is the set of all characters and symbols available to
the computer.
Question
9. Explain how ASCII represents the character set of a computer.
Answer
The characters and symbols are mapped to a number represented in binary in 7 bits
and can define 128 separate characters; extended to 8 bits and 256 characters.
Question
10. What happens if you sort the list ‘Apple, grape, cherry, Damson’ in a program
using ASCII or Unicode to represent the character set?
Answer
It is sorted as Apple, Damson, cherry, grape because the lower case letters have larger
ASCII values than upper case ones.
Question
11. Explain the difference between using an ASCII character set and a Unicode
character set.
OCR GCSE Computer Science
© Hodder & Stoughton Limited 2016
OCR GCSE Computer Science Teaching and Learning Resources
Answer
ASCII can only represent 128 or 256 characters, meaning many symbols and foreign
language characters are not available. Unicode uses several code pages to represent
the chosen language symbols and there are several billion possibilities.
Page 161
Question
12. How does the resolution of an image affect the size of the file?
Answer
The higher the resolution, the larger the file needed to store the image.
Question
13. What do we mean by image size?
Answer
The number of pixels used for the image (length × width).
Question
14. What metadata is stored with an image file?
Answer
For example: resolution, colour depth, image size (accept any other reasonable data)
Question
15. If an image has its colour depth decreased, what is the effect?
Answer
The image will have fewer colours available to it
Question
16. How many colours can be represented using a 4-bit colour depth?
Answer
24 or 16 colours
Page 164
Question
17. Why are there so few tracks on a typical audio CD?
OCR GCSE Computer Science
© Hodder & Stoughton Limited 2016
OCR GCSE Computer Science Teaching and Learning Resources
Answer
A typical music CD is sampled at a very high rate (1411.2kbps) to provide superior
audio quality, but at the expense of much larger file sizes than many MP3 files.
Question
18. How does the sample rate affect the quality of the playback for an MP3 sound
track?
Answer
The sample rate is the number of samples taken per unit of time, so fewer samples
will reduce the match between the sampled sound and the original sound, leading to
poorer quality.
Question
19. What effect does a high bit rate have on the number of sound files that can be
stored on a CD?
Answer
With a high bit rate, more data is stored for each unit of time and the file used to store
the sampled sound is therefore much larger, meaning fewer data can be stored in the
same amount of storage space.
Page 167
Question
20. What is file compression?
Answer
File compression is where the data in a file is compressed to make it smaller, e.g. so
the data can be sent over the internet.
Question
21. Describe the difference between lossy and lossless compression.
Answer
Lossy compression removes some of the data, modifying the original data so that it
cannot be restored to its original detail.
Lossless compression removes redundant and repeated data, whilst keeping track of
these changes so that this data can be restored in its original detail.
OCR GCSE Computer Science
© Hodder & Stoughton Limited 2016
OCR GCSE Computer Science Teaching and Learning Resources
Question
22. Explain why compression must be lossless when sending a computer program
as an email attachment.
Answer
Computer programs will only work if none of the detail is removed or cannot be
restored, hence lossless compression must be used if sending as an email attachment.
Question
23. Describe one advantage and one disadvantage of storing music as MP3 files.
Answer
DISADVANTAGE
MP3 uses lossy compression, meaning some of the detail is lost and the quality
compromised. However, much of the data lost is considered redundant, e.g.
frequencies above the normal range of human hearing.
ADVANTAGE
Storing data as MP3 files means more data can be stored in the same storage space,
which is especially useful for music stored on portable devices.
Question
24. Explain the importance of compressing image and video files when
transmitting them over the internet.
Answer
Image files can be quite large and when many of these are combined to form a video,
the file soon becomes extremely large and often too large to send over the internet.
Removing redundant data and reducing the resolution or image size or colour depth
can make a significant difference, enabling data to be transmitted over the internet in
a reasonable time frame. Video streamed over the internet would require very large
buffers and there would be significant delays if the data were not compressed.
OCR GCSE Computer Science
© Hodder & Stoughton Limited 2016