Be familiar with the concept of a natural number and the set ℕ of natural numbers (including zero).

ℕ = {0, 1, 2, 3, …}

Be familiar with the concept of an integer and the set ℤ of integers.

ℤ = { …, -3, -2, -1, 0, 1, 2, 3, … }

Be familiar with the concept of a rational number and the set ℚ of rational numbers, and that this set includes the integers.

ℚ is the set of numbers that can be written as fractions (ratios of integers). Since a number such as 7 can be written as 7/1, all integers are rational numbers.

Be familiar with the concept of an irrational number.

An irrational number is one that cannot be written as a fraction, for example √2.

Be familiar with the concept of a real number and the set ℝ of real numbers, which includes the natural numbers, the rational numbers, and the irrational numbers.

ℝ is the set of all 'possible real world quantities'.

Be familiar with the concept of ordinal numbers and their use to describe the numerical positions of objects.

When objects are placed in order, ordinal numbers are used to tell their position. For example, if we have a well-ordered set S = {'a', 'b', 'c', 'd'}, then 'a' is the 1st object, 'b' the 2nd, and so on.

Be familiar with the use of natural numbers for counting.

Be familiar with the use of real numbers for measurement.

Be familiar with the concept of a number base, in particular:

• decimal (base 10)
• binary (base 2)
• hexadecimal (base 16)

Students should be familiar with expressing a number's base using a subscript as follows:

• Base 10: Number₁₀, eg 67₁₀
• Base 2: Number₂, eg 10011011₂
• Base 16: Number₁₆, eg AE₁₆

Convert between decimal, binary and hexadecimal number bases.

Be familiar with, and able to use, hexadecimal as a shorthand for binary and to understand why it is used in this way.

Know that the bit is the fundamental unit of information.

A bit is either 0 or 1.

Know that a byte is a group of 8 bits.

Know that 2ⁿ different values can be represented with n bits.

For example, 3 bits can be configured in 2³ = 8 different ways: 000, 001, 010, 011, 100, 101, 110, 111.

Know the names, symbols and corresponding powers of 10 for the decimal prefixes:

• kilo, k - 10³
• mega, M - 10⁶
• giga, G - 10⁹
• tera, T - 10¹²

Know the names, symbols and corresponding powers of 2 for the binary prefixes:

• kibi, Ki - 2¹⁰
• mebi, Mi - 2²⁰
• gibi, Gi - 2³⁰
• tebi, Ti - 2⁴⁰

Know that quantities of bytes can be described using binary prefixes representing powers of 2 or using decimal prefixes representing powers of 10, eg one kibibyte is written as 1KiB = 2¹⁰ B and one kilobyte is written as 1 kB = 10³ B.

Historically the terms kilobyte, megabyte, etc have often been used when kibibyte, mebibyte, etc are meant.

Know the difference between unsigned binary and signed binary.

Students are expected to be able to convert between unsigned binary and decimal and vice versa.

Know that in unsigned binary the minimum and maximum values for a given number of bits, n, are 0 and 2ⁿ - 1 respectively.

Be able to add two unsigned binary integers.

Be able to multiply two unsigned binary integers.

Know that signed binary can be used to represent negative integers and that one possible coding scheme is two's complement.

This is the only representation of negative integers that will be examined. Students are expected to be able to convert between signed binary and decimal and vice versa.

Know how to represent negative and positive integers in two's complement.

Know how to perform subtraction using two's complement.

Know how to calculate the range of a given number of bits, n.

Know how numbers with a fractional part can be represented in fixed point form in binary in a given number of bits.

Be able to convert decimal to fixed point binary of a given number of bits.

Be able to convert fixed point binary to decimal of a given number of bits.

Differentiate between the character code representation of a decimal digit and its pure binary representation.

Describe ASCII and Unicode coding systems for coding character data.

Explain why Unicode was introduced.

Describe and explain the use of parity bits.

Describe and explain the use of majority voting.

Describe and explain the use of check digits.

Evaluate the use of parity bits, majority voting and check digits

Describe how bit patterns may represent other forms of data, including graphics and sound.

Understand the difference between analogue and digital:

• data
• signals

Describe the principles of operation of an analogue to digital converter (ADC).

Describe the principles of operation of a digital to analogue converter (DAC).

Explain how bitmaps are represented.

Explain resolution.

Resolution is expressed as number of dots per inch where a dot is a pixel.

Know that colour depth is the number of bits stored for each pixel.

Know that the size of an image in pixels is width of image in pixels × height of image in pixels.

The size of an image is also alternatively sometimes described as the resolution of an image.

Calculate storage requirements for bitmapped images and be aware that bitmap image files may also contain metadata.

Ignoring metadata, storage requirements = size in pixels x colour depth where size in pixels is width in pixels x height in pixels.

Be familiar with typical metadata.

eg width, height, colour depth.

Describe the digital representation of sound.

Understand sample resolution and its effect on the quality of audio recordings.

Understand sampling rate and its effect on the quality of audio recordings.

Know Nyquist's theorem.

Calculate sound sample sizes in bytes.

Describe the purpose of MIDI and the use of event messages in MIDI.

Describe the advantages of using MIDI files for representing music.

Know why images and sound files are often compressed and that other files, such as text files, can also be compressed.

Understand the difference between lossless and lossy compression and explain the advantages and disadvantages of each.

Explain the principles behind run length encoding (RLE) for lossless compression.

Explain the principles behind dictionary-based methods for lossless compression.

Understand what is meant by encryption and be able to define it.

Caesar and Vernam ciphers are at opposite extremes. One offers perfect security, the other doesn't. Between these two types are ciphers that are computationally secure – see below. Students will be assessed on the two types. Ciphers other than Caesar may be used to assess students' understanding of the principles involved. These will be explained and be similar in terms of computational complexity.

Be familiar with the term cipher.

Be familiar with the term plaintext.

Be familiar with the term ciphertext.

Be familiar with Caesar cipher and be able to apply it to encrypt a plaintext message and decrypt a ciphertext.

Be able to explain why Caesar cipher is easily cracked.

Be familiar with Vernam cipher or one-time pad and be able to apply it to encrypt a plaintext message and decrypt a ciphertext.

Since the key k is chosen uniformly at random, the ciphertext c is also distributed uniformly. The key k must be used once only. The key k is known as a one-time pad.

Explain why Vernam cipher is considered as a cypher with perfect security.

Compare Vernam cipher with ciphers that depend on computational security.

Vernam cipher is the only one to have been mathematically proved to be completely secure. The worth of all other ciphers ever devised is based on computational security. In theory, every cryptographic algorithm except for Vernam cipher can be broken, given enough ciphertext and time.

Define the term hardware.

Define the term software.

Understand the relationship between hardware and software.

Explain what is meant by system software.

Explain what is meant by application software.

Understand the need for, and attributes of, different types of software.

Know that system software includes operating systems (OSs), utility programs, libraries and translators (compiler, assembler, interpreter).

Understand the need for, and functions of operating systems (OSs).

Understand the need for, and functions of utility programs.

Understand the need for, and functions of libraries.

Understand the need for, and functions of translators (compiler, assembler, interpreter).

Understand that a role of the operating system is to hide the complexities of the hardware.

Know that the OS handles resource management, managing hardware to allocate processors, memories and I/O devices among competing processes.

Show awareness of the development of types of programming languages and their classification into low- and high-level languages.

Know that low-level languages are considered to be:

• machine-code
• assembly language

Know that high-level languages include imperative high-level language.

Describe machine-code language and assembly language.

Understand the advantages and disadvantages of machine-code and assembly language programming compared with high-level language programming.

Explain the term 'imperative high-level language' and its relationship to low-level languages.

Understand the role of assemblers.

Understand the role of compilers.

Understand the role of interpreters.

Explain the differences between compilation and interpretation. Describe situations in which each would be appropriate.

Explain why an intermediate language such as bytecode is produced as the final output by some compilers and how it is subsequently used.

Understand the difference between source and object (executable) code.

Construct truth tables for the NOT logic gate.

Students should know and be able to use ANSI/IEEE standard 91-1984 Distinctive shape logic gate symbols for these logic gates.

Construct truth tables for the AND logic gate.

Construct truth tables for the OR logic gate.

Construct truth tables for the XOR logic gate.

Construct truth tables for the NAND logic gate.

Construct truth tables for the NOR logic gate.

Be familiar with drawing and interpreting logic gate circuit diagrams involving one or more of the above gates.

Complete a truth table for a given logic gate circuit.

Write a Boolean expression for a given logic gate circuit.

Draw an equivalent logic gate circuit for a given Boolean expression.

Be familiar with the use of Boolean identities and De Morgan's laws to manipulate and simplify Boolean expressions.

Have an understanding and knowledge of the basic internal components of a computer system.

Although exam questions about specific machines will not be asked, it might be useful to base this section on the machines used at the centre.

Understand the role of the processor.

Understand the role of main memory.

Understand the role of the address bus.

Understand the role of the data bus.

Understand the role of the control bus.

Understand the role of I/O controllers.

Be able to explain the difference between von Neumann and Harvard architectures and describe where each is typically used.

Embedded systems such as digital signal processing (DSP) systems use Harvard architecture processors extensively. Von Neumann architecture is used extensively in general purpose computing systems.

Understand the concept of addressable memory.

Be able to describe the stored program concept: machine code instructions stored in main memory are fetched and executed serially by a processor that performs arithmetic and logical operations.

Explain the role and operation of the arithmetic logic unit.

Explain the role and operation of the control unit.

Explain the role and operation of the clock.

Explain the role and operation of general-purpose registers.

Explain the role and operation of the program counter.

Explain the role and operation of the current instruction register.

Explain the role and operation of the memory address register.

Explain the role and operation of the memory buffer register.

Explain the role and operation of the status register.

Explain how the Fetch-Execute cycle is used to execute machine code programs, including the stages in the cycle (fetch, decode, execute) and details of registers used.

Understand the term 'processor instruction set' and know that an instruction set is processor specific.

Know that instructions consist of an opcode and one or more operands (value, memory address or register).

A simple model will be used in which the addressing mode will be incorporated into the bits allocated to the opcode so the latter defines both the basic machine operation and the addressing mode. Students will not be expected to define opcode, only interpret opcodes in the given context of a question.

For example, 4 bits have been allocated to the opcode (3 bits for basic machine operation, eg ADD, and 1 bit for the addressing mode). 4 bits have been allocated to the operand, making the instruction, opcode + operand, 8 bits in length. In this example, 16 different opcodes are possible (2⁴ = 16).

Understand and apply immediate addressing.

Immediate addressing: the operand is the datum.

Understand and apply direct addressing.

Direct addressing: the operand is the address of the datum. Address to be interpreted as meaning either main memory or register.

Understand and apply the basic machine-code operations of:

• load
• add
• subtract
• store
• branching (conditional and unconditional)
• compare
• logical bitwise operators (AND, OR, NOT, XOR)
• logical
• shift right
• shift left
• halt

Use the basic machine-code operations above when machine-code instructions are expressed in mnemonic form—assembly language, using immediate and direct addressing.

Explain the effect on processor performance of multiple cores.

Explain the effect on processor performance of cache memory.

Explain the effect on processor performance of clock speed.

Explain the effect on processor performance of word length.

Explain the effect on processor performance of address bus width.

Explain the effect on processor performance of data bus width.

Know the main characteristics, purpose and suitability of barcode readers and understand their principles of operation.

Know the main characteristics, purpose and suitability of digital cameras and understand their principles of operation.

Know the main characteristics, purpose and suitability of laser printers and understand their principles of operation.

Know the main characteristics, purpose and suitability of RFID and understand their principles of operation.

Explain the need for secondary storage within a computer system.

Know the main characteristics, purposes, suitability and understand the principles of operation of the hard disk.

Know the main characteristics, purposes, suitability and understand the principles of operation of the optical disk.

Know the main characteristics, purposes, suitability and understand the principles of operation of the solid-state disk (SSD).

SSD = NAND flash memory + a controller that manages pages, and blocks and complexities of writing. Based on floating gate transistors that trap and store charge. A block, made up of many pages, cannot overwrite pages; a page has to be erased before it can be written to but technology requires the whole block to be erased. Lower latency and faster transfer speeds than a magnetic disk drive.

Compare the capacity and speed of access of various media and make a judgement about their suitability for different applications.

Show awareness of current individual (moral), social (ethical), legal and cultural opportunities and risks of computing.

Understand that:

• developments in computer science and digital technologies have dramatically altered the shape of communications and information flows in societies, enabling massive transformations in the capacity to:
• monitor behaviour
• amass and analyse personal information
• distribute, publish, communicate and disseminate personal information
• computer scientists and software engineers therefore have power, as well as the responsibilities that go with it, in the algorithms that they devise and the code that they deploy.
• software and their algorithms embed moral and cultural values.
• the issue of scale, for software the whole world over, creates potential for individual computer scientists and software engineers to produce great good, but with it comes the ability to cause great harm.

Be able to discuss the challenges facing legislators in the digital age.

Teachers may wish to employ two very powerful techniques, hypotheticals and case studies, to engage students in the issues.

Hypotheticals allow students to isolate quickly important ethical principles in an artificially simplified context. For example, a teacher might ask students to explain and defend how, as a Google project manager, they would evaluate a proposal to bring Google's Street View technology to a remote African village. What questions should be asked? Who should be consulted? What benefits, risks and safeguards considered? What are the trade-offs?

Case studies allow students to confront the tricky interplay between the sometimes competing ethical values and principles relevant in real world settings. For example, the Google Street View case might be used to tease out the ethical conflicts between individual and cultural expectations, the principle of informed consent, Street View's value as a service, its potential impact on human perceptions and behaviours, and its commercial value to Google and its shareholders.

There are many resources available on the Internet to support teaching of this topic.

Define serial transmission methods.

Define parallel transmission methods.

Discuss the advantages of serial over parallel transmission.

Define and compare synchronous and asynchronous data transmission.

Describe the purpose of start and stop bits in asynchronous data transmission.

Define baud rate.

Define bit rate.

Define bandwidth.

Define latency.

Define protocol.

Differentiate between baud rate and bit rate.

Bit rate can be higher than baud rate if more than one bit is encoded in each signal change.

Understand the relationship between bit rate and bandwidth.

Bit rate is directly proportionate to bandwidth.

Understand and explain the operation of a physical star topology.

Understand and explain the operation of a logical bus network topology.

A network physically wired in star topology can behave logically as a bus network by using a bus protocol and appropriate physical switching.

Differentiate between the physical star topology and the logical bus network topology.

Explain peer-to-peer networking and describe situations where it might be used.

In a peer-to-peer network, each computer has equal status.

Explain client-server networking and describe situations where it might be used.

Explain the purpose of WiFi.

A wireless local area network that is based on international standards.

Used to enable devices to connect to a network wirelessly.

Be familiar with the components required for wireless networking.

• Wireless network adapter
• Wireless access point

Be familiar with the purpose of Service Set Identifier (SSID).

Be familiar with how wireless networks are secured using WPA (Wifi Protected Access)/WPA2.

Be familiar with how wireless networks are secured by disabling SSID (Service Set Identifier) broadcasting.

Be familiar with how wireless networks are secured using a MAC (Media Access Control) address allow list.

Explain the wireless protocol Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) with and without Request to Send/Clear to Send (RTS/CTS).