Name:
Data Representation in Computers
The OCR Specification says that you should be able to:
Units
• define the terms bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte
• understand that data needs to be converted into a binary format to be processed
by a computer
Numbers
• convert positive denary whole numbers (0-255) into 8-bit binary numbers and
vice versa
• add two 8-bit binary integers and explain overflow errors which may occur
• convert positive denary integers (0-255) into 2-digit hexadecimal numbers and
vice versa
• convert between binary and hexadecimal equivalents of the same number
• explain the use of hexadecimal numbers to represent binary numbers
Characters
• explain the use of binary codes to represent characters
• explain the term character set
• describe with examples (for example ASCII and Unicode) the relationship
between the number of bits per character in a character set and the number of
characters which can be represented
Images
• explain the representation of an image as a series of pixels represented in binary
• explain the need for metadata to be included in the file such as height, width and
colour depth
• discuss the effect of colour depth and resolution on the size of an image file
Sound
• explain how sound can be sampled and stored in digital form
• explain how sampling intervals and other considerations affect the size of a
sound file and the quality of its playback
Instructions
• explain how instructions are coded as bit patterns
• explain how the computer distinguishes between instructions and data
Past Paper Exam questions
Jan 2011
1. (a) Calculate the denary value of the 8-bit binary number 10010111. You must
show your working.
……………………………………………………………………………………
……………………………………………………………………………………
……………………………………………………………………………………
[2]
(b) Add the following two 8-bit binary numbers and explain the result. You must
show your working.
……………………………………………………………………………………
……………………………………………………………………………………
……………………………………………………………………………………
[3]
2. (a) Explain how ASCII is used to represent text in a computer system.
……………………………………………………………………………………
……………………………………………………………………………………
……………………………………………………………………………………
……………………………………………………………………………………
[3]
(b) State what is meant by the character set of a computer.
……………………………………………………………………………………
……………………………………………………………………………………
[1]
(c) Unicode is also used to represent text in a computer system. Explain the
difference between the character sets of Unicode and ASCII.
……………………………………………………………………………………
……………………………………………………………………………………
……………………………………………………………………………………
……………………………………………………………………………………
[2]
June 2011
3. (a) Convert the hexadecimal number 6A to denary. You must show your working.
……………………………………………………………………………………
……………………………………………………………………………………
[2]
(b) Convert the hexadecimal number 6A to binary.
……………………………………………………………………………………
……………………………………………………………………………………
[2]
(c) Convert the binary number 00111101 to hexadecimal.
……………………………………………………………………………………
……………………………………………………………………………………
……………………………………………………………………………………
[2]
(d) Explain why hexadecimal numbers are often used to represent binary numbers.
……………………………………………………………………………………
……………………………………………………………………………………
……………………………………………………………………………………
[2]
Jan 2012
4.
Bytes, Kilobytes and Megabytes are units used for the amount of data stored
in a computer.
(a) State which of these units is most appropriate for the following items of
data.
A one page text document:
……………………………………………………………………………………
……………………………………………………………………………………
A ten minute movie clip:
……………………………………………………………………………………
……………………………………………………………………………………
A person’s surname:
……………………………………………………………………………………
……………………………………………………………………………………
[3]
(b) A computer has a hard disk of 2 Terabytes. How much is this in Gigabytes?
You must show your working.
…………………………………………………………………………………………………………
…………………………………………………………………………………………………………
…………………………………………………………………………………………………………
…………………………………………………………………………………………………………
[2]
5. Peter takes a picture of himself and his friends to put on a social networking
site. The picture is converted into pixels and stored as a bitmap file.
(a) Tick one box in each row to show whether or not each of the following items
must be included in the bitmap file.
[5]
(b) (i) What is meant by the resolution of the picture?
……………………………………………………………………………………
……………………………………………………………………………………
[1]
(ii) How does the resolution affect the size of the bitmap file?
……………………………………………………………………………………
……………………………………………………………………………………
……………………………………………………………………………………
[2]
June 2012
6 (a) Convert the denary number 55 to an 8 bit binary number.
……………………………………………………………………………………
……………………………………………………………………………………
……………………………………………………………………………………
[2]
(b) Convert the denary number 55 to hexadecimal.
……………………………………………………………………………………
……………………………………………………………………………………
……………………………………………………………………………………
……………………………………………………………………………………
[2]
Jan 2013
7 (a) Add the following bytes.
[2]
(b) State the problem that will occur if a computer is to store the result as a byte.
……………………………………………………………………………………
……………………………………………………………………………………
[1]
8. When recording a sound file on a computer, the sound needs to be sampled.
(i) Describe how sampling is used when storing sound.
……………………………………………………………………………………
……………………………………………………………………………………
……………………………………………………………………………………
……………………………………………………………………………………
[2]
(ii) Explain the effect of the sampling interval on the size and quality of the sound
file recorded.
……………………………………………………………………………………
……………………………………………………………………………………
……………………………………………………………………………………
……………………………………………………………………………………
……………………………………………………………………………………
[3]
9 (a) Explain why data is stored in computers in a binary format.
……………………………………………………………………………………
……………………………………………………………………………………
……………………………………………………………………………………
……………………………………………………………………………………
[2]
(b) In the ASCII character set, the character codes for the first three capital letters
are given below.
(ii) State how the ASCII character set is used to represent text i a computer.
……………………………………………………………………………………
……………………………………………………………………………………
[1]
(ii) Convert the word CAB into binary using the ASCII character set.
……………………………………………………………………………………
……………………………………………………………………………………
[1]
(iii) Explain why the ASCII character set is not suitable for representing text in all
the languages of the world.
……………………………………………………………………………………
……………………………………………………………………………………
……………………………………………………………………………………
……………………………………………………………………………………
[2]
June 2013
2. Bob’s computer has 512 kilobytes of ROM and 8 gigabytes of RAM.
State how many bytes are in a kilobyte and a gigabyte.
a kilobyte.................................................................................................................
a gigabyte................................................................................................................
[2]
5 Numbers can be represented in denary, binary or hexadecimal.
(a) (i) Convert the binary number 01101001 to denary, showing your working.
……………………………………………………………………………………
……………………………………………………………………………………
……………………………………………………………………………………
……………………………………………………………………………………
[2]
(ii) Convert the denary number 154 to binary.
……………………………………………………………………………………
……………………………………………………………………………………
……………………………………………………………………………………
……………………………………………………………………………………
[2]
(b) The security code for an alarm system is a long binary number which begins
10001111100101111011 ...
The technicians prefer to use hexadecimal to enter the security code.
(i) When the number is converted into hexadecimal, the first two digits are 8F as
shown below
Complete the gaps to show the next three digits.
Binary:
1000
1111
Hexadecimal:
8
F
1001
0111
1011
[3]
(ii) Explain why the technicians prefer to use hexadecimal.
……………………………………………………………………………………
……………………………………………………………………………………
……………………………………………………………………………………
……………………………………………………………………………………
[2]