Process
WJEC A-Level Computer Science 601-5345-3
Hardware: Architecture, Memory and Storage
Networks and Data Transmission
Logic Gates and Boolean Algebra
Data Representation and Data Types
Data Structures
Organisation of Data: Files and Records
Database Systems
The Operating System
Algorithms and Programs
Principles of Programming
Systems Analysis
Software Engineering and Program Construction
Topic overviewIntegrated development environments and their purposeEditors, syntax highlighting and code entry toolsDebugging tools: breakpoints, stepping and watchesTranslation, source code and object codeLexical analysis and the symbol tableSyntax and semantic analysisCode generation and optimisation
Types of Software System
Practical Programming
Data Security and Integrity
Computing, Society and the Law
Topic overviewSocial and economic change from computingComputers and the nature of employmentThe digital divide and cultural changeEnvironmental cost of computingData protection and freedom of information lawThe Computer Misuse Act 1990 and computer crimeCopyright, surveillance and professional codes
Advanced Data Structures and Logic
Recursion, Sorting and Searching
Programming Paradigms and Translators
Topic overviewFunctional, declarative and imperative paradigmsClasses, methods and object-oriented designStandardisation of computer languagesAmbiguity in natural language and unambiguous notationBackus-Naur form and syntax diagramsCompilers, interpreters and assemblersTranslation and execution errors
System Design and Human-Computer Interaction
Software Engineering Tools and Professional Practice
Topic overviewSoftware tools for the software engineering processSoftware packages in systems analysis and specificationSoftware packages in systems designTesting tools and testing strategiesProgram version managementProgram libraries and project management toolsCodes of conduct and professional behaviour
Advanced Architecture and Assembly Language
Communication Networks and File Organisation
Number Representation and Floating Point
Databases and Distributed Systems
Topic overviewConsistency, redundancy and data independenceRelational organisation and normalisationRestructuring data into third normal formEntity relationship modellingQuery languages and SQLValidation, verification and the DBMSBig Data, data warehousing and miningDistributed systems and distributed databases
Operating System Management
Software Systems and Applications
Data Security, Cryptography and Attack
Number Representation and Floating Point
- 7 subtopics
- 21 things to know
- A2 Unit 4
What Number Representation and Floating Point covers
Number Representation and Floating Point is examined in A2 Unit 4, Computer Architecture, Data, Communication and Applications. It covers binary arithmetic, sign and magnitude representation, two's complement, floating point representation, converting between real numbers and floating point, truncation, rounding and accuracy and shifts, overflow and underflow.
Where it is assessed
A2 Unit 4
Computer Architecture, Data, Communication and Applications.
Check the WJEC specification ↗The 7 subtopics
Each one has its own page.
- Binary arithmeticRecall questions on the four rules of binary addition and the carry, worked 8-bit additions, converting between binary, denary and hexadecimal, subtraction by two's complement, and multiplication and division by shifting.Open →
- Sign and magnitude representationRecall questions on how the sign bit works, representing −20 and reading 10000111, the range and why it is one value narrower, the two zeros and why they cost, why plain addition fails, and why two's complement displaced it.Open →
- Two's complementRecall questions on invert-and-add-one, representing −5 and −100, reading 11111011 and 11010110, the 8-bit and 16-bit ranges, why the negative range is one larger, the negative place value of the top bit, subtraction, and sign extension.Open →
- Floating point representationTwo parts of a floating point number, fixed point representation and normalised floating point number.Open →
- Converting between real numbers and floating pointRecall questions on normalising 0.5, 0.75, 6 and −0.5 into mantissa and exponent, reading a value back from a stored pair, which way the exponent moves as the point moves, why 0.1 cannot be held exactly, and how a negative exponent is represented.Open →
- Truncation, rounding and accuracyAbsolute error, relative error and accumulated error.Open →
- Shifts, overflow and underflowLogical shift, arithmetic shift and circular shift.Open →
What you need to know
Answer each one before you reveal it.
Your recallNot started
Key term
What does truncation do, how does its error behave over many operations, how does rounding differ, and what is that error?
Key term
How does sign and magnitude represent a negative number, and what does that arrangement cost?
Key term
State the four rules of binary addition for a single column.
Key term
State the method for finding the two's complement of a binary number.
Key term
What are the two parts of a floating point number?
Key term
Express 0.5 as a normalised mantissa and exponent.
Key term
What is the result of adding 1 + 1 + 1 in one column?
Key term
How does sign and magnitude represent a negative number?
Key term
State the range of an 8-bit two's complement number.
Key term
What does the exponent represent?
Key term
Give the 8-bit two's complement mantissa and 8-bit exponent for 0.5.
Key term
What is truncation?
Key term
What is a logical shift?
Key term
Why is hexadecimal used as shorthand for binary?
Key term
State the range of an 8-bit sign and magnitude number.
Key term
State the range of a 16-bit two's complement number.
Key term
Why is the form called floating point?
Key term
Express 6 in normalised floating point form.
Key term
Which introduces more error on average, truncation or rounding, and why?
Key term
Apply a logical shift left of two places to 00000110 and give the denary result.
Take Number Representation and Floating Point further
The same content, four other ways.
Questions from this topic
Each one with the model answer underneath.
- 1
State the four rules of binary addition for a single column.
Model answer
0+0 = 0, 0+1 = 1, 1+0 = 1, and 1+1 = 0 with a carry of 1 into the next column.
- 2
What is the result of adding 1 + 1 + 1 in one column?
Model answer
1, with a carry of 1 into the next column.
- 3
Add the 8-bit values 00101101 and 00010011.
Model answer
01000000.
- 4
Add the 8-bit values 01011010 and 00100110.
Model answer
10000000.
- 5
Convert 10110110₂ to denary.
Model answer
182.
- 6
Convert 213 to an 8-bit binary value.
Model answer
11010101.
What is inside Levo
Six ways to work the same material.
Number Representation and Floating Point revision questions
- What does Number Representation and Floating Point cover in WJEC A-Level Computer Science?
- 7 subtopics: binary arithmetic, sign and magnitude representation, two's complement, floating point representation, converting between real numbers and floating point, truncation, rounding and accuracy and shifts, overflow and underflow. Each one has its own page with questions and model answers.
- How is Number Representation and Floating Point organised?
- By the WJEC 601-5345-3 specification, subtopic by subtopic, so it matches the order you are taught it in.
Every question in Number Representation and Floating Point, 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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