Key term
AQA AS-Level Computer Science 7517
Fundamentals of Programming
Topic overviewData typesProgramming concepts and program structureArithmetic operationsRelational Operations, Constants and VariablesBoolean operationsString-handling operationsRandom numbers and exception handlingSubroutines, parameters and return valuesVariable scope and stack framesProgramming paradigms and the procedural approach
Fundamentals of Data Structures
Theory of Computation
Topic overviewLogic Problems and Algorithm ConstructsPseudo-Code, Hand-Tracing and Program CorrectnessRepresentational Abstraction, Generalisation and Information HidingProcedural and Functional AbstractionData Abstraction and Problem ReductionDecomposition and CompositionAutomation and Finite State Machines
Fundamentals of Data Representation
Topic overviewNumber systems and the sets of numbersNumber bases: decimal, binary and hexadecimalBits, bytes and units of informationUnsigned binary and binary arithmeticSigned binary using two's complementFixed point and floating point representationCharacter coding systemsError checking and correctionBit patterns, analogue and digitalBitmapped graphicsDigital representation of soundMIDI and Data CompressionEncryption
Fundamentals of Computer Systems
Fundamentals of Computer Organisation and Architecture
Topic overviewInternal components, buses and von Neumann and Harvard architecturesThe Stored Program Concept and the ProcessorThe Fetch-Execute cycleThe processor instruction setAddressing modesMachine-Code OperationsShifts, Halting and Assembly Language ProgramsFactors affecting processor performanceInput and output devicesSecondary storage devices
Fundamentals of Communication and Networking
Consequences of Uses of Computing
Systematic Approach to Problem Solving
Fundamentals of Data Representation
- 13 subtopics
- 41 things to know
- Paper 2
What Fundamentals of Data Representation covers
Number bases and binary arithmetic, two's complement, fixed and floating point, rounding error, character codes, error checking, images, sound and encryption. Examined on Paper 2.
Where it is assessed
Paper 2
The written theory exam, 2 hours 30 minutes and 40% of the A-level.
Check the AQA specification ↗The 13 subtopics
Each one has its own page. AQA AS Computer Science students sit this topic in the first year.
- Number systems and the sets of numbersRecall questions on the sets ℕ, ℤ, ℚ and ℝ, why every integer is rational, whether a recurring decimal is rational, and ordinal against cardinal numbers.Open →
- Number bases: decimal, binary and hexadecimalRecall questions on what a base is, the digits each system uses, and converting between decimal, binary and hexadecimal in both directions.Open →
- Bits, bytes and units of informationRecall questions on how many values n bits can hold, choosing the smallest workable number of bits, and the binary prefixes against the decimal ones.Open →
- Unsigned binary and binary arithmeticRecall questions on the range of an n-bit unsigned number, converting in both directions, adding and multiplying in binary, and recognising overflow.Open →
- Signed binary using two's complementRecall questions on what the most significant bit contributes, the invert-and-add-one and copy-and-invert methods, the range formula, and subtraction by addition.Open →
- Fixed point and floating point representationRecall questions on place values after the binary point, representing a given decimal in a fixed point format, and how the mantissa and exponent divide the work.Open →
- Character coding systemsRecall questions on ASCII and Unicode, why letters are coded in alphabetical order, converting between case, and why a character code is not a numeric value.Open →
- Error checking and correctionRecall questions on parity bits, majority voting, checksums and check digits, what each detects, and which of them can correct an error rather than only spot one.Open →
- Bit patterns, analogue and digitalRecall questions on how one bit pattern can mean many things, analogue against digital data and signals, sampling, and the error quantisation introduces.Open →
- Bitmapped graphicsRecall questions on pixels, resolution and colour depth, how many colours a given depth allows, and calculating the storage an image needs.Open →
- Digital representation of soundRecall questions on sampling rate and sample resolution, the Nyquist theorem and the CD sampling rate, and calculating the size of a sound file.Open →
- MIDI and Data CompressionRecall questions on the purpose of MIDI, its event messages and files, and on lossy and lossless compression and run length encoding.Open →
- EncryptionRecall questions on the Caesar and Vernam ciphers, frequency analysis, why the one-time pad alone is unbreakable, and symmetric against asymmetric keys.Open →
What you need to know
Answer each one before you reveal it.
Your recallNot started
Key term
Is a recurring decimal such as 0.333… rational? Justify your answer.
Numbers
For the well-ordered set S = {'a', 'b', 'c', 'd'}, give the ordinal number of each element?
Numbers
What is meant by the base of a number system?
Key term
How is the base of a number written down, and what do 67₁₀, 10011011₂ and AE₁₆ mean?
Key term
Describe the repeated division method for converting a decimal number to hexadecimal.
Numbers
State the names, symbols and powers of 10 of the four decimal prefixes.
Key term
A drive is advertised as 500 GB but the operating system reports about 465 units. Explain what has happened.
Key term
Add 1011 and 0110 as unsigned 4-bit numbers. What goes wrong?
Key term
What is the effect of shifting an unsigned binary number one place to the right?
Key term
In a two's complement number, what does the most significant bit tell you?
Key term
In eight-bit two's complement, what are −1 and −128, and why is the range lopsided?
Key term
Convert +45 and −45 to 8-bit two's complement.
Key term
Represent 5.75 in binary using an unsigned fixed point format with 4 bits before the point and 4 after.
Numbers
For an unsigned fixed point format with 4 bits before the point and 4 after, what are the smallest step and the largest value?
Key term
Represent 6.5 in floating point with an 8-bit two's complement mantissa, point after the sign bit, and 4 bits for the power of two.
Key term
State the test for whether a mantissa is normalised, for both signs.
Key term
Explain why a mantissa of 1.1110000 is not normalised, and name the mistake students commonly make when normalising negative numbers.
Numbers
Why can the decimal value 0.1 never be represented exactly in binary, however many bits are used?
Numbers
Distinguish between the range and the precision of a number representation.
Numbers
Define overflow and describe the circumstances in which it occurs.
Key term
Why does the difference between a character code and a pure binary value matter in a program?
Evaluation
State one advantage and one disadvantage of Unicode compared with ASCII.
Numbers
The seven data bits 1010011 are to be sent. State the parity bit under even parity and under odd parity.
Evaluation
Describe how a checksum is used.
Evaluation
Describe how a check digit works.
Numbers
What is the difference between analogue data and digital data?
Process
How does an analogue to digital converter work?
Key term
Explain how a bitmap represents an image.
Numbers
What happens when a bitmapped image is enlarged, and why?
Key term
Explain why a vector graphic can be enlarged without any loss of quality.
Evaluation
State the advantages of bitmapped graphics over vector graphics.
Numbers
What is sample resolution, and what effect does it have?
Key term
Explain why a digital recording can never be a perfect copy of the original sound.
Key term
Describe what a MIDI file stores, and contrast it with a sampled sound file.
Evaluation
State the disadvantages of MIDI.
Numbers
Apply run length encoding to the string AAAAABBBCCCCCCCD.
Process
Explain the principle behind dictionary-based compression.
Process
Define encryption, and define the terms cipher, plaintext, ciphertext and key.
Key term
State the conditions the key must satisfy for a Vernam cipher.
Key term
Explain why the Vernam cipher is considered to have perfect security.
Take Fundamentals of Data Representation further
The same content, four other ways.
Commonly confused
Pairs that lose marks when they are blurred together.
Analogue data vs Digital data
Analogue data: values varying continuously across a range. Digital data: values represented using discrete symbols.
Lossless compression vs Lossy compression
Lossless compression: size reduction allowing exact reconstruction of the original. Lossy compression: size reduction permanently discarding selected information.
ASCII vs Unicode
ASCII: a 7-bit character code centred on English text. Unicode: a wider character standard covering many writing systems.
Questions from this topic
Each one with the model answer underneath.
- 1
What is a natural number, and what is the set ℕ?
Model answer
A natural number is a whole, non-negative number used for counting. The set of natural numbers is ℕ = {0, 1, 2, 3, …}. It includes zero, it has no upper limit, and it contains no negative numbers and no fractions.
- 2
Does the set ℕ include zero?
Model answer
Yes. ℕ is taken to be {0, 1, 2, 3, …}, so zero is a natural number. This matters when you are asked for the smallest natural number: the answer is 0, not 1.
- 3
Define an integer and state the set ℤ.
Model answer
An integer is a whole number, which may be positive, negative or zero. The set of integers is ℤ = {…, −3, −2, −1, 0, 1, 2, 3, …}. Every natural number is an integer, so ℕ is a subset of ℤ.
- 4
Give a number that belongs to ℤ but not to ℕ, and explain why.
Model answer
Any negative whole number, for example −4. It is a whole number so it is an integer, but ℕ contains only non-negative values, so −4 is not a natural number.
- 5
What is a rational number, and what is the set ℚ?
Model answer
A rational number is one that can be written as a fraction — a ratio a/b of two integers, where b is not zero. ℚ is the set of all such numbers, for example 3/4, −7/2 and 0.25.
- 6
Explain why every integer is also a rational number.
Model answer
Any integer can be written as a fraction with a denominator of 1. For example 7 = 7/1 and −3 = −3/1. Since both parts are integers and the denominator is not zero, the number satisfies the definition of a rational number, so ℤ is a subset of ℚ.
What is inside Levo
Six ways to work the same material.
Fundamentals of Data Representation revision questions
- Is Fundamentals of Data Representation examined at AS in AQA Computer Science?
- Yes. It sits in Paper 2, which you take in the first year, so it is on the AS paper as well as counting towards the full A level.
- What does Fundamentals of Data Representation cover in AQA AS-Level Computer Science?
- 13 subtopics: number systems and the sets of numbers, number bases: decimal, binary and hexadecimal, bits, bytes and units of information, unsigned binary and binary arithmetic, signed binary using two's complement, fixed point and floating point representation, character coding systems, error checking and correction, bit patterns, analogue and digital, bitmapped graphics, digital representation of sound, midi and data compression and encryption. Each one has its own page with questions and model answers.
- How is Fundamentals of Data Representation organised?
- By the AQA 7517 specification, subtopic by subtopic, so it matches the order you are taught it in.
Every question in Fundamentals of Data Representation, on a schedule.
Attempt a question from memory, write the correct version, then attempt it again. Levo records the jump between your first attempt and your last, and brings each question back on the day you are due to forget it.
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