What is a bit, and why is it called the fundamental unit of information?

A bit is a single binary digit, which is either 0 or 1. It is the fundamental unit of information because it is the smallest amount of data that can be stored or transmitted — one choice between two possibilities. Every other quantity of data is built from bits.

A byte is a group of 8 bits. It is the usual unit in which storage is measured and is large enough to hold one character in ASCII, or an unsigned integer from 0 to 255.

How many different values can be represented with n bits?

2ⁿ different values. Each extra bit doubles the number of available patterns, because every existing pattern can be extended by either a 0 or a 1.

List all the patterns that 3 bits can take, and state how many there are.

There are 2³ = 8 patterns: 000, 001, 010, 011, 100, 101, 110 and 111.

How many different values can be stored in one byte?

2⁸ = 256 different values. Interpreted as unsigned binary these run from 0 to 255.

A system must give a unique code to 1000 different products. What is the smallest number of bits that will do, and why?

10 bits. Nine bits give 2⁹ = 512 codes, which is too few, while ten bits give 2¹⁰ = 1024 codes, which is enough with 24 spare. You must round up to the next whole bit, because you cannot use a fraction of a bit.

AQA A-Level Computer Science 7517

Fundamentals of Programming

Topic overview Data types Programming concepts and program structure Arithmetic operations Relational Operations, Constants and Variables Boolean operations String-handling operations Random numbers and exception handling Subroutines, parameters and return values Variable scope and stack frames Recursive techniques Programming paradigms and the procedural approach Classes, Objects, Inheritance and Polymorphism Aggregation, Composition, Class Diagrams and Design Principles

Fundamentals of Data Structures

Topic overview Data Structures and Abstract Data Types Static and Dynamic Data Structures Queues and Linear Queues Circular and Priority Queues Stacks Graphs Trees Hash tables Dictionaries Vectors and Their Notation Vector Arithmetic and Geometry

Fundamentals of Algorithms

Topic overview Graph traversal Tree traversal Reverse Polish notation Searching algorithms Sorting algorithms Optimisation algorithms

Theory of Computation

Topic overview Logic Problems and Algorithm Constructs Pseudo-Code, Hand-Tracing and Program Correctness Representational Abstraction, Generalisation and Information Hiding Procedural and Functional Abstraction Data Abstraction and Problem Reduction Decomposition and Composition Automation and Finite State Machines Sets and Set Notation Subsets and Set Operations Regular expressions and regular languages Backus-Naur Form and syntax diagrams Comparing Algorithms and Functions Order of complexity and Big-O notation Limits of computation, tractability and heuristics Computable problems and the Halting problem Turing machines

Fundamentals of Data Representation

Topic overview 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 Normalisation of floating point numbers Rounding errors, accuracy, range and precision Character coding systems Error checking and correction Bit patterns, analogue and digital Bitmapped graphics Vector graphics Digital representation of sound MIDI and Data Compression Encryption

Fundamentals of Computer Systems

Topic overview Hardware, Software and Its Classification System Software and the Operating System Translators and the Role of the Operating System Classification of programming languages Types of program translator Logic Gates and Their Truth Tables Logic Circuits and D-Type Flip-Flops Half-Adders and Full Adders Boolean algebra

Fundamentals of Computer Organisation and Architecture

Topic overview Internal components, buses and von Neumann and Harvard architectures The Stored Program Concept and the Processor The Fetch-Execute cycle The processor instruction set Addressing modes Machine-Code Operations Shifts, Halting and Assembly Language Programs Interrupts Factors affecting processor performance Input and output devices Secondary storage devices

Fundamentals of Communication and Networking

Topic overview Communication methods Communication basics Network Topology and Types of Networking Wireless networking The Internet and Packet Switching Routing, URLs and Domain Names Firewalls, Worms, Trojans and Viruses Encryption, Digital Signatures and Certificates TCP/IP Standard application layer protocols IP Address Structure and Subnet Masking IP Standards and Public and Private Addresses DHCP and Network Address Translation Client server model Thin- versus thick-client computing

Consequences of Uses of Computing

Topic overview The Four Kinds of Issue in Computing Legislation, Ethical Dilemmas and Case Studies

Systematic Approach to Problem Solving

Topic overview Analysis, Design and Implementation Testing and Evaluation

Fundamentals of Databases

Topic overview Conceptual data models and entity relationship modelling Relational databases Database design and normalisation techniques Structured Query Language (SQL)Client server databases

Big Data

Topic overview Volume, Velocity and Variety Why Big Data Resists Analysis Distributed Processing and Functional Programming Fact-Based Models and Graph Schemas

Fundamentals of Functional Programming

Topic overview Function Types, First-Class Objects and Function Application Partial Function Application and Composition Writing functional programs Lists in functional programming

Fundamentals of Data Representation

Bits, bytes and units of information

2 things to know
Paper 2

Overview

Recall questions on how many values n bits can hold, choosing the smallest workable number of bits, and the binary prefixes against the decimal ones.

What you need to know

Answer each one before you reveal it.

Your recallNot started

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.

Questions from this subtopic

Each one with the model answer underneath.

1
What is a bit, and why is it called the fundamental unit of information?
Model answer
A bit is a single binary digit, which is either 0 or 1. It is the fundamental unit of information because it is the smallest amount of data that can be stored or transmitted — one choice between two possibilities. Every other quantity of data is built from bits.
2
What is a byte?
Model answer
A byte is a group of 8 bits. It is the usual unit in which storage is measured and is large enough to hold one character in ASCII, or an unsigned integer from 0 to 255.
3
How many different values can be represented with n bits?
Model answer
2ⁿ different values. Each extra bit doubles the number of available patterns, because every existing pattern can be extended by either a 0 or a 1.
4
List all the patterns that 3 bits can take, and state how many there are.
Model answer
There are 2³ = 8 patterns: 000, 001, 010, 011, 100, 101, 110 and 111.
5
How many different values can be stored in one byte?
Model answer
2⁸ = 256 different values. Interpreted as unsigned binary these run from 0 to 255.
6
A system must give a unique code to 1000 different products. What is the smallest number of bits that will do, and why?
Model answer
10 bits. Nine bits give 2⁹ = 512 codes, which is too few, while ten bits give 2¹⁰ = 1024 codes, which is enough with 24 spare. You must round up to the next whole bit, because you cannot use a fraction of a bit.

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