A Level Computer Science CAIE

This subject is broken down into 77 topics in 17 modules:

  1. Information Representation 5 topics
  2. Processor Fundamentals 4 topics
  3. Security, Privacy and Data Integrity 2 topics
  4. Ethics and Ownership 2 topics
  5. Database and Data Modelling 3 topics
  6. Algorithm Design and Problem-solving 4 topics
  7. Programming 6 topics
  8. Data Representation 6 topics
  9. Communication and Internet Technologies 6 topics
  10. Hardware 9 topics
  11. System Software 7 topics
  12. Security 4 topics
  13. Monitoring and Control Systems 2 topics
  14. Computational Thinking and Problem-solving 4 topics
  15. Algorithm Design Methods 3 topics
  16. Further Programming 4 topics
  17. Software Development 6 topics
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  • 17
    modules
  • 77
    topics
  • 28,986
    words of revision content
  • 3+
    hours of audio lessons

This page was last modified on 28 September 2024.

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Computer Science

Information Representation

Number Representation

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Number Representation

Number Representation

Binary Representation

  • Binary is a base-2 number system most commonly used in digital systems, as it can easily be represented by two states: On (1) or Off (0)
  • A binary digit, or bit, is the smallest unit of data in computing and can represent two discrete states
  • Eight bits together form one byte, the basic addressable element in many computer architectures
  • Binary numbers are often needed to be padded with leading zeros to make up a certain bit-length
  • Binary can be converted back and forth with other number systems like decimal, octal, and hexadecimal

Decimal Representation

  • Decimal is a base-10 number system used universally in mathematics and arithmetic
  • Ten distinct symbols (0-9) are used to represent numbers in the decimal system
  • Despite its widespread use, decimal is less computer-friendly and is often converted to binary or other forms for easier processing

Octal Representation

  • Octal is a base-8 number system, not as widely used as binary or decimal, but sometimes seen in computing
  • Eight distinct symbols (0-7) are used to represent numbers in the octal system
  • Each octal digit corresponds to three binary digits, which can simplify certain binary operations

Hexadecimal Representation

  • Hexadecimal is a base-16 number system, commonly used in computing to reduce the number of digits needed to represent binary numbers
  • Sixteen distinct symbols (0-9, A-F) are used to represent numbers in the hexadecimal system
  • Each hexadecimal digit corresponds to four binary digits, making this system particularly useful in information representation

Two's Complement

  • Two's complement is a method of representing negative binary numbers in a normalized way
  • In two's complement notation, the leftmost bit indicates the sign (0 for positive, 1 for negative)
  • To obtain a negative number in two's complement, one inverts the binary representation of the positive number and adds 1 to the least significant bit

Floating Point Representation

  • The IEEE 754 Floating Point Representation allows for the representation of very large or very small numbers by separating a number into its sign, exponent and mantissa
  • Any number can be represented in scientific notation, which forms the basis of floating point representation
  • Floating point representation allows efficient scaling of numbers, but can suffer from rounding errors

Character Representation

  • Text and special characters are often represented as binary using standardized codes such as ASCII and Unicode
  • The ASCII code standard assigns unique binary numbers to 128 characters, including basic Latin alphabet characters, digits, symbols, and control codes
  • Unicode extends this to a wider range of characters, including those from non-Latin scripts, and is used worldwide for its compatibility and flexibility.

Course material for Computer Science, module Information Representation, topic Number Representation

Computer Science

Hardware

Logic Gates and Circuit Design

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Logic Gates and Circuit Design

Logic Gates

  • Logic gates are the basic building blocks of any digital system.
  • These gates are used to create a circuit that performs a specific task.
  • The seven basic logic gates are: NOT, AND, OR, XOR (exclusive OR), NAND (Not AND), NOR (Not OR) and XNOR (exclusive NOR)
  • A logic gate can be thought of as a simple device that will return a number of outputs, given a number of 'binary' inputs.
  • The NOT gate also known as an inverter is a gate that outputs '1' when its input is '0' and vice-versa.
  • The output of AND gate is '1' only when all its inputs are '1'.
  • The output of OR gate is '1' if any of its inputs are '1'.
  • The output of XOR gate is '1' if an odd number of inputs are '1'.
  • NAND is an AND gate followed by a NOT gate. Its output is '1' when any of its inputs are '0'.
  • NOR is an OR gate followed by a NOT gate. Its output is '0' when any of its inputs are '1'.
  • XNOR is a gate that outputs '0' when an odd number of its inputs are '1'.

Circuit Design

  • Circuit design involves the construction of a physical system to execute a specific function.
  • An understanding of Boolean algebra is integral for circuit design. It is a mathematical approach to logic where variables are either true or false, represented by '1' and '0' respectively.
  • Truth tables are used to understand and analyse logic circuits. They show possible input-output combinations for any given logic circuit.
  • Circuit design also requires the use of certain design tools, typically schematic capture tools and some kind of simulation tool.
  • Circuit optimisation is another key element of circuit design. An optimised circuit uses the least number of gates, the least amount of wiring and the smallest area.
  • The output of a circuit can be affected by the propagation delay, the length of time starting when the input to a circuit changes and until the circuit’s output has settled to its new value.
  • Flip-flops are a type of logic circuit, referred to as bistable multi-vibrator. It is a circuit that has two stable states and can be used to store state information.

De Morgans Theorem

  • De Morgan's Theorem provides an established means of simplifying complex gate circuits.
  • It states that the complement of a conjunction of variables is equal to the disjunction of their complements and vice versa.
  • It provides a methodology to convert NAND gates into AND-OR logic and NOR gates into OR-AND logic.
  • A’ + B’ = (A.B)’ and A’.B’ = (A + B)’ are the two basic expressions that represent De Morgan's theorem.

Course material for Computer Science, module Hardware, topic Logic Gates and Circuit Design

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