State the digits used by decimal, binary and hexadecimal.

Decimal (base 10) uses 0 to 9. Binary (base 2) uses 0 and 1 only. Hexadecimal (base 16) uses 0 to 9 followed by A, B, C, D, E and F to stand for the values ten to fifteen.

Give the decimal value of each of the hexadecimal digits A to F.

A = 10, B = 11, C = 12, D = 13, E = 14, F = 15.

Why is it essential to state the base when writing a number down?

The same digits mean different values in different bases. 10 is ten in decimal, two in binary and sixteen in hexadecimal, and 11 is eleven, three and seventeen respectively. Without a stated base the value is ambiguous.

Convert 67₁₀ to binary.

1000011₂. Take the place values 64, 32, 16, 8, 4, 2, 1: 67 − 64 = 3, then 3 − 2 = 1, then 1 − 1 = 0, so the 64, 2 and 1 columns hold a 1 and the rest hold 0. In eight bits this is 01000011₂.

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

Number bases: decimal, binary and hexadecimal

3 things to know
Paper 2

Overview

Recall questions on what a base is, the digits each system uses, and converting between decimal, binary and hexadecimal in both directions.

What you need to know

Answer each one before you reveal it.

Your recallNot started

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.

Questions from this subtopic

Each one with the model answer underneath.

1
What is meant by the base of a number system?
Model answer
The base is the number of distinct digits the system uses, and it fixes the place values: each column is worth the base times the column to its right. Base 10 uses digits 0–9 with place values …, 100, 10, 1; base 2 uses 0 and 1 with place values …, 8, 4, 2, 1; base 16 uses sixteen digits with place values …, 256, 16, 1.
2
State the digits used by decimal, binary and hexadecimal.
Model answer
Decimal (base 10) uses 0 to 9. Binary (base 2) uses 0 and 1 only. Hexadecimal (base 16) uses 0 to 9 followed by A, B, C, D, E and F to stand for the values ten to fifteen.
3
Give the decimal value of each of the hexadecimal digits A to F.
Model answer
A = 10, B = 11, C = 12, D = 13, E = 14, F = 15.
4
How is the base of a number written down, and what do 67₁₀, 10011011₂ and AE₁₆ mean?
Model answer
The base is written as a subscript after the number. 67₁₀ is sixty-seven in base 10, 10011011₂ is a binary number, and AE₁₆ is a hexadecimal number. Writing the base removes any doubt about how the digits should be read.
5
Why is it essential to state the base when writing a number down?
Model answer
The same digits mean different values in different bases. 10 is ten in decimal, two in binary and sixteen in hexadecimal, and 11 is eleven, three and seventeen respectively. Without a stated base the value is ambiguous.
6
Convert 67₁₀ to binary.
Model answer
1000011₂. Take the place values 64, 32, 16, 8, 4, 2, 1: 67 − 64 = 3, then 3 − 2 = 1, then 1 − 1 = 0, so the 64, 2 and 1 columns hold a 1 and the rest hold 0. In eight bits this is 01000011₂.

See the rest and revise

Other ways to work this

The same content, four other ways.

What is inside Levo

Six ways to work the same material.

1Closed book

2Open book

3Closed book

The 3-step method, run for you

Answer cold, learn it, then prove it stuck. Levo tracks the jump between your first attempt and your last.

Fundamentals of Programming

Fundamentals of Data Structures

Fundamentals of Algorithms

Theory of Computation

Cram a whole paper in one sitting

Sort every topic into what you know and what you do not, then drill only the weak ones.

A driver is .

softwarehardwarestorage

Blank Blitz makes facts automatic

Rapid timed gap-fills on the terms and numbers you need to recall without thinking.

AThe integer 5 is 0101.

B0.75 is 1/2 + 1/4.

CThe fraction bits are 1100.

Build It gets the exam shape right

Assemble a full-mark answer from its marking points, in the order an examiner wants them.

Head means the first single element of a non-empty list.

TrueFalse

Test It catches misconceptions

Spot the fault in a statement. The traps are the mistakes students actually make.

721941163128510

Brain Breaks between sessions

Short focus games to reset attention, so the next set lands better than the last.

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.

Start revising, £5 a month See how the method works

Or £46 a year, about £3.83 a month. Cancel anytime.