2.1.1, 2.1.2, 2.1.3Binary representation and unsigned binary–denary conversion
Edexcel GCSE Computer Science (1CP2) · Data › Binary
Practise Binary representation and unsigned binary–denary conversion. 12 exam-style questions plus unlimited generated ones on this subtopic, at up to four difficulty levels, with full mark schemes and a progress tracker. Free, no account needed.
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Give two things, other than numbers, that computers represent in binary.
Any two from: text, images, sound, video, program instructions.
State how many different combinations of on and off are possible for the 5 switches.
32
Three 8-bit unsigned binary integers are stored: A: 1001 0110 B: 0110 1001 C: 1000 1111 Convert B to denary.
105
State the number of different values that can be represented using 10 bits.
1024
Sample questions
Written for this site in the style of Edexcel exam questions. They are not taken from real past papers.
Question 1Easy4 marks
Computers use binary to represent data and program instructions.
(a) State why computers use binary.[1]
(b) Give two things, other than numbers, that computers represent in binary.[2]
(c) Identify the number of different binary patterns that can be made using 4 bits.[1]
4
8
15
16
Show the answer and mark scheme
(a)Answer: Their circuits are made of switches (transistors) that have only two states, on and off, which can represent 1 and 0.
computers are built from (billions of) switches / transistors / circuits that have only two states (on and off), which can represent 1 and 0
(b)Answer: Any two from: text, images, sound, video, program instructions.
text / characters
images / graphics
sound
video
program instructions
(c)Answer: 16
Question 2Medium4 marks
A weather station records the direction of the wind. At first, it records the direction as one of the 16 points of the compass, such as N, NNE and NE.
(a) State the minimum number of bits needed to give each of the 16 compass points a unique binary code.[1]
(b) The station is upgraded so that it records the direction to the nearest whole degree, from 0° to 359°. Calculate the minimum number of bits needed to store the direction. Show your working.[2]
(c) Give one disadvantage of using more bits than are needed to store each value.[1]
360 different values are needed and 28 = 256 is not enough
29 = 512 is enough, so 9 (bits)
(c)Answer: It wastes storage space and increases the amount of data to transmit.
it wastes storage space / memory / makes files larger / means more data has to be transmitted (so it takes longer)
Question 3Hard5 marks
(a) Explain why computers use binary rather than denary to represent data.[2]
(b) A student says, 'If you double the number of bits used to store an unsigned integer, you double the largest number that can be stored.' Explain whether the student is correct. Use examples in your answer.[3]
Show the answer and mark scheme
(a)Answer: Transistors have two states, so two voltage levels can be told apart reliably; representing ten different levels would be complex and error-prone.
computers are made of electronic switches / transistors that have two states (on / off)
it is much easier / more reliable to tell two voltage levels apart than ten / denary would need ten different states, making circuits more complex and errors more likely
(b)Answer: Incorrect. 4 bits give a maximum of 15; 8 bits give 255, not 30. Each extra bit doubles the number of values, so doubling the bits squares the number of values.
the student is incorrect
a correct example, e.g. 4 bits can store up to 15 but 8 bits can store up to 255, which is far more than double (30)
adding just one bit doubles the number of values that can be represented / doubling the number of bits squares the number of values (2n becomes 22n)