A bit is the smallest unit of data a computer stores, holding either 0 or 1. The word bit is a contraction of binary digit.

How many bits make one byte?

One byte is a group of eight bits. A byte is the smallest block of storage that most systems address individually.

Define the term word as it applies to a processor.

A word is the number of bits a processor handles as a single unit. Word length is set by the width of the registers and the data bus.

Why does a larger word length usually give better performance?

A larger word length moves more bits between memory and the processor in one transfer. Larger words also allow a wider range of numbers to be held in one register.

How many different values can be represented by a group of n bits?

A group of n bits gives 2ⁿ different bit patterns. Eight bits therefore give 256 patterns, from 00000000 to 11111111.

State the largest unsigned denary value that can be held in one byte.

The largest unsigned value in one byte is 255. The bit pattern 11111111 gives that value, which is 2⁸ − 1.

Eduqas A-Level Computer Science A500QS

Data Structures: Arrays, Records and Hash Tables

Topic overview One-dimensional arrays and indexing Two- and three-dimensional arrays Manipulating arrays: insertion, deletion and searching Records and fields Arrays of records and record manipulation Hash tables, hashing and collisions Choosing and justifying a data structure

Stacks, Queues, Linked Lists and Trees

Topic overview Stacks: push, pop and the stack pointer Implementing a stack in an array Queues: enqueue, dequeue and pointers Circular queues and priority queues Linked lists: nodes, pointers and the free list Binary trees: nodes, roots and leaves Traversing linked lists and trees

Boolean Logic and Simplification

Topic overview AND, OR and NOT truth tables XOR, NAND and NOR truth tables Truth tables for combined Boolean expressions Boolean identities and rules De Morgan's laws Simplifying Boolean expressions Logical operators in programs, masking and encryption

Algorithms, Pseudo-Code and Programming Constructs

Topic overview Algorithms and how they are defined Pseudo-code conventions Flowcharts and flowchart symbols Sequence and selection Repetition: count-controlled and condition-controlled loops Counts, totals and rogue values Tracing, altering and writing algorithms

Variables, Scope, Parameters and Identifiers

Topic overview Variables and constants Self-documenting identifiers Annotation and program layout Scope of variables: local and global Lifetime of variables Procedure calling, parameters and return values Call by value and call by reference

Recursion and Modular Programming

Topic overview Recursion and the base case How recursive calls use the stack Recursive algorithms: factorial and Fibonacci Recursion compared with iteration Integer division with DIV and MOD Standard functions and standard modules User defined subprograms and modular design

Sorting Algorithms

Topic overview Why a variety of sorting algorithms is needed Bubble sort Insertion sort Quicksort Comparisons, exchanges and passes Storage space and sorting efficiency Writing and altering sort algorithms

Searching and Shortest-Path Algorithms

Topic overview Linear search Binary search Comparing linear and binary search Graphs, weights and the shortest-path problem Dijkstra's shortest-path algorithm Tracing a shortest-path algorithm by hand Choosing the right searching technique

Big O Notation and Algorithm Efficiency

Topic overview What Big O notation measures The common complexity classes Time complexity of the sorting algorithms Space complexity and sorting in place Time complexity of linear and binary search Deriving the complexity of a given algorithm Comparing algorithms that do the same task

Validation, Verification and Testing

Topic overview Validation and verification compared Types of validation check Implementing validation in an algorithm Verification techniques Validation and verification of data in databases Choosing test data Dry running, trace tables and identifying errors

Data Compression

Topic overview What data compression is and why it is used Lossless compression Lossy compression Run-length encoding Dictionary and Huffman coding Measuring compression: ratio and saving percentage Choosing a compression method

Programming Paradigms and Computer Languages

Topic overview Programming paradigms and where each is used Procedural programming Event-driven and visual programming Mark-up languages Object-oriented programming: objects, classes and methods Ambiguity in natural language and the standardisation of languages Backus-Naur form and syntax diagrams High-level and low-level languages, and choosing one

Systems Analysis, Maintenance and Documentation

Topic overview Waterfall, Agile and approaches to systems development The feasibility study, budgets and time scales Methods of investigation Abstraction, decomposition and data flow diagrams Selecting suitable hardware and software Acceptance testing and methods of changeover Perfective, adaptive and corrective maintenance Backup and recovery procedures User and maintenance documentation

System Design and Human-Computer Interaction

Topic overview Approaches to communicating with a computer Types of user interface Natural language interfaces Ambiguity in spoken input Designing an interface for its users The design review Evaluating a computer-based solution

Software Engineering Tools and Translators

Topic overview Software tools for the software engineering process Software packages in analysis, specification, design and testing Integrated development environments Debugging tools Program version management Compilers, interpreters and assemblers The stages of compilation Translation errors and execution errors

Computing, Society and the Law

Topic overview Social and economic change from computing Moral and ethical consequences Cultural change and the digital divide Codes of conduct and professional behaviour The effect of computers on employment Data protection and privacy law Computer misuse, copyright and freedom of information

Computer Architecture, the Processor and Assembly Language

Topic overview Hardware elements and how they are connected Von Neumann architecture and the stored program concept The processor: control unit, ALU and registers Types of memory: RAM, ROM and virtual memory Cache memory and locality of reference The fetch-execute cycle and its registers Parallel processing and the limits to parallelisation Assembly language and executing a program

Input, Output and Secondary Storage

Topic overview Input devices and how data is captured Output devices and how results are presented Choosing input and output devices for a situation Voice input, dictation and voice print recognition Magnetic, optical and solid state storage Comparing secondary storage for a purpose Disc organisation, fragmentation and defragmentation

Networks, Protocols and the Internet

Topic overview Networks, LANs and WANs Network topologies and connection hardware Networking standards and the layered model IP addressing, TCP and UDP Application protocols: HTTP, FTP, SMTP, IMAP and DHCP Handshaking and establishing a connection Wireless hardware and wireless technologies The internet and connected mobile devices

Data Transmission and Network Performance

Topic overview Serial and parallel transmission Simplex, half duplex and full duplex Multiplexing and sharing a channel Circuit, message and packet switching Packets, headers and packet contents Network collisions and collision detection Routing traffic on a network Calculating transfer rates and lowest cost routes

Number Systems and Binary Arithmetic

Topic overview Bits, bytes and words Binary and denary place value Hexadecimal notation Storing characters and numbers in binary Binary addition and subtraction Two's complement and sign and magnitude Logical and arithmetic shifts Overflow and underflow

Data Types, Characters and Floating Point

Topic overview Primitive data types Storage requirements for each data type ASCII and standardised character sets Unicode and multilingual encoding Floating point form: mantissa and exponent Converting between real numbers and floating point Integer and floating point compared Truncation, rounding and accuracy

Files, Records and File Organisation

Topic overview The purpose of files in data processing Files, records and fields Fixed and variable length fields and records Master files and transaction files Serial and sequential file access Indexed sequential access and multi-level indexes Direct access and hashing algorithms Overflow handling and file reorganisation File security, backups, generations and archiving

Databases, Normalisation and Entity Modelling

Topic overview Data consistency, redundancy and independence Relational databases and other database models Primary keys, foreign keys and indexes First normal form Second normal form Third normal form Entity relationship modelling User views and turning data into information

SQL, Big Data and Distributed Systems

Topic overview Query languages and the purpose of SQL Creating tables: CREATE TABLE, data types and keys Retrieving data with SELECT, FROM and WHERE Comparison operators, IN, AND, OR and sub-queries Sorting, grouping and aggregate functions Inserting, updating, deleting and joining data The DBMS, the data dictionary and distributed databases Big Data, data warehousing, data mining and predictive analytics

The Operating System and Its Modes

Topic overview The need for an operating system and the role of the kernel Managing peripherals, processes and memory protection The user interface and the layers between user and hardware Directory structures and file attributes Utility software Batch processing, real time control and real time transaction systems Types of operating system: single-user, multi-user, multi-tasking and multi-programming Designing an interface for different users and environments

Interrupts, Memory Management and Scheduling

Topic overview What causes an interrupt Interrupt handling and the interrupt service routine Interrupt priorities and how they are allocated Partitioning main memory Methods of data transfer between processor and devices Buffers and double buffering High level scheduling, processor and device allocation Process states, time-slicing, polling and threading

Types of Software System

Topic overview Open source, bespoke and off-the-shelf software Safety-critical systems Computers in weather forecasting Computer aided design and computer generated graphics Robotics and automation Control systems Expert systems The internet, intranets and search engines

Data Security, Cryptography and Attack

Topic overview Online updating and the integrity of shared files Dangers of holding personal data Clerical procedures, access levels, passwords and write protection Cryptography: its purpose, and symmetric and asymmetric keys Hashing, digital signatures and certificates Caesar and Vernam ciphers and comparing cipher strength Biometric technologies and their limitations Threats, damage and contingency planning Malicious software, hacking and penetration testing

Number Systems and Binary Arithmetic

8 subtopics
24 things to know
Component 2

What Number Systems and Binary Arithmetic covers

Number Systems and Binary Arithmetic is examined in Component 2, Computer Architecture, Data, Communication and Applications. It covers bits, bytes and words, binary and denary place value, hexadecimal notation, storing characters and numbers in binary, binary addition and subtraction, two's complement and sign and magnitude, logical and arithmetic shifts and overflow and underflow.

Where it is assessed

Component 2

Computer Architecture, Data, Communication and Applications.

Check the Eduqas specification ↗

The 8 subtopics

Each one has its own page.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Key term

Define a bit and a byte.

Numbers

How many patterns does a group of bits give, and what is the largest value one byte can hold?

Key term

What is the base of the binary number system?

Key term

What is the base of the hexadecimal number system?

Key term

How does a computer store a character such as the letter A?

Key term

State the rules of single-column binary addition.

Key term

How is a negative number written in sign and magnitude form?

Key term

What is a logical shift?

Key term

Define overflow.

Key term

State the place values of the eight columns in an 8-bit binary number.

Key term

State the denary values of the hexadecimal digits A to F.

Key term

State the ASCII code for lower case a in denary and in hexadecimal.

Key term

Add binary 00101100 and 00010011, giving an 8-bit answer.

Key term

Write −45 in 8-bit sign and magnitude.

Key term

Apply a logical left shift of two places to 00010110.

Key term

Define underflow.

Key term

What is a bit?

Key term

Convert binary 11010110 to denary.

Key term

Why is hexadecimal a convenient shorthand for binary?

Key term

Why is the character 7 not the same as the number 7 inside a computer?

Key term

Add binary 01001101 and 00110110 in an 8-bit register and state the denary result.

Key term

State the range of 8-bit sign and magnitude representation.

Key term

Apply a logical right shift of one place to 10011010.

Key term

How does overflow show itself when adding two positive two's complement numbers?

Take Number Systems and Binary Arithmetic further

The same content, four other ways.

Commonly confused

Pairs that lose marks when they are blurred together.

Two's complement vs Sign and magnitude
Two's complement: giving the top bit a place value of −128 in eight bits, so 10101101 is −83. Sign and magnitude: treating the top bit as a flag only, so the same pattern is −45.
Carry out vs Overflow
Carry out: a bit leaving the top column, which is discarded in two's complement subtraction. Overflow: the signed answer itself is wrong.
Logical shift vs Arithmetic shift
Logical shift: a shift bringing in a 0, which can turn a negative value positive. Arithmetic shift: a shift copying the sign bit, which preserves the sign.

Questions from this topic

Each one with the model answer underneath.

1
What is a bit?
Model answer
A bit is the smallest unit of data a computer stores, holding either 0 or 1. The word bit is a contraction of binary digit.
2
How many bits make one byte?
Model answer
One byte is a group of eight bits. A byte is the smallest block of storage that most systems address individually.
3
Define the term word as it applies to a processor.
Model answer
A word is the number of bits a processor handles as a single unit. Word length is set by the width of the registers and the data bus.
4
Why does a larger word length usually give better performance?
Model answer
A larger word length moves more bits between memory and the processor in one transfer. Larger words also allow a wider range of numbers to be held in one register.
5
How many different values can be represented by a group of n bits?
Model answer
A group of n bits gives 2ⁿ different bit patterns. Eight bits therefore give 256 patterns, from 00000000 to 11111111.
6
State the largest unsigned denary value that can be held in one byte.
Model answer
The largest unsigned value in one byte is 255. The bit pattern 11111111 gives that value, which is 2⁸ − 1.

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Data Structures: Arrays, Records and Hash Tables

Stacks, Queues, Linked Lists and Trees

Boolean Logic and Simplification

Algorithms, Pseudo-Code and Programming Constructs

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Number Systems and Binary Arithmetic revision questions

What does Number Systems and Binary Arithmetic cover in Eduqas A-Level Computer Science?: 8 subtopics: bits, bytes and words, binary and denary place value, hexadecimal notation, storing characters and numbers in binary, binary addition and subtraction, two's complement and sign and magnitude, logical and arithmetic shifts and overflow and underflow. Each one has its own page with questions and model answers.
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