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A-Level CS Flashcards: Fundamentals

Computer Science — Fundamentals Flashcards

20 interactive flashcards for A-Level Computer Science. Press Space to flip, rate 1-4.

What These Flashcards Cover

These flashcards test the foundational concepts that underpin all of computer science: how numbers are represented, how logic gates work, how processors execute instructions, and how operating systems manage resources.

Key areas:

  • Number Systems: Binary (base 2), denary (base 10), hexadecimal (base 16). Conversion between bases. Binary arithmetic: addition, subtraction (two’s complement). Overflow occurs when a result exceeds the representable range.
  • Binary Representation: Unsigned binary: magnitude only. Signed binary (two’s complement): the MSB indicates sign. To negate: invert all bits and add 1. Range for nn bits: −2n−1-2^{n-1} to 2n−1−12^{n-1} - 1.
  • Floating Point Representation: Mantissa and exponent. Normalised form: 0.1xxxxx×2e0.1xxxxx \times 2^{e}. IEEE 754 single precision: 1 sign bit, 8 exponent bits (biased by 127), 23 mantissa bits. Precision limitations lead to rounding errors.
  • Boolean Algebra: AND (∧\land), OR (∨\lor), NOT (¬\lnot), XOR (⊕\oplus). Laws: commutative, associative, distributive, De Morgan’s (¬(A∧B)=¬A∨¬B\lnot(A \land B) = \lnot A \lor \lnot B). Karnaugh maps for simplification.
  • Logic Gates: AND, OR, NOT, NAND, NOR, XOR. NAND and NOR are universal gates (can construct any circuit). Half adder: adds two bits. Full adder: adds two bits plus a carry.
  • Processor Architecture: Von Neumann architecture: CPU, memory, I/O connected by a bus. Fetch-decode-execute cycle: fetch instruction from memory, decode it, execute it, store result. Registers: accumulator, program counter, memory address register, memory data register.
  • Operating Systems: Manages hardware and software resources. Functions: memory management (paging, virtual memory), process management (scheduling, multitasking), file management, security, and user interface.
  • Assembly Language: Low-level language with a 1-to-1 mapping to machine code. Instructions: LOAD, STORE, ADD, SUB, JMP, JZ (jump if zero), JNZ. Assembler translates assembly to machine code.

Intuition

Think of binary as a simpler version of denary — the same principles apply, just with fewer digits. Denary has digits 0-9 and each position is a power of 10. Binary has digits 0-1 and each position is a power of 2. Converting between them is like translating between languages.

The CPU is like a chef following a recipe. The program counter tells the chef which recipe step to do next. The fetch-decode-execute cycle is: read the step (fetch), understand what it means (decode), and do it (execute). The registers are like the chef’s countertop — small, fast workspace.

Common Pitfalls

  1. Confusing mantissa and exponent in floating point. The mantissa is the significand (the “significant digits”). The exponent scales the number. Swapping them or miscounting bits gives wildly wrong values.
  2. Forgetting the bias in floating point exponents. The stored exponent is biased by 127 (single precision). A stored exponent of 130 means actual exponent of 3, not 130.
  3. Two’s complement confusion. To negate a binary number, invert all bits and add 1. A common error is inverting and forgetting to add 1, or adding 1 and forgetting to invert.
  4. Misapplying De Morgan’s laws. ¬(A∧B)=¬A∨¬B\lnot(A \land B) = \lnot A \lor \lnot B and ¬(A∨B)=¬A∧¬B\lnot(A \lor B) = \lnot A \land \lnot B. The operator flips (AND becomes OR and vice versa). A common error is not flipping the operator.

Cross-References