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
Types of Software System
Practical Programming
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Computing, Society and the Law
Advanced Data Structures and Logic
Recursion, Sorting and Searching
Programming Paradigms and Translators
System Design and Human-Computer Interaction
Software Engineering Tools and Professional Practice
Advanced Architecture and Assembly Language
Communication Networks and File Organisation
Number Representation and Floating Point
Databases and Distributed Systems
Operating System Management
Software Systems and Applications
Data Security, Cryptography and Attack
Number Representation and Floating Point
Converting between real numbers and floating point
- 3 things to know
- A2 Unit 4
Overview
Recall 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.
What you need to know
Answer each one before you reveal it.
Give the 8-bit two's complement mantissa and 8-bit exponent for 0.5.
Express 6 in normalised floating point form.
Questions from this subtopic
Each one with the model answer underneath.
- 1
Express 0.5 as a normalised mantissa and exponent.
Model answer
A mantissa of 0.1 and an exponent of 0.
- 2
Give the 8-bit two's complement mantissa and 8-bit exponent for 0.5.
Model answer
Mantissa 01000000, exponent 00000000.
- 3
Express 6 in normalised floating point form.
Model answer
0.11 × 2³, so a mantissa of 0.11 and an exponent of 3.
- 4
Give the 8-bit mantissa and 8-bit exponent for 6.
Model answer
Mantissa 01100000, exponent 00000011.
- 5
Express 0.75 in normalised floating point form.
Model answer
0.11 × 2⁰, so a mantissa of 0.11 and an exponent of 0.
- 6
What real number is held by mantissa 01010000 with exponent 00000010?
Model answer
2.5, since 0.101 × 2² is 10.1 in binary.
Other ways to work this
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