2. Logic circuits and hardware

• Problem statement: words, e.g. 'The alarm X sounds if the door is open (A = 1) AND either the window is open (B = 1) OR the motion sensor is on (C = 1).'
• Logic expression: X = A AND (B OR C). Use brackets to show which gate is worked out first.
• Logic circuit: gate symbols wired together — here an OR gate for B and C, feeding an AND gate with A.
• Truth table: every combination of inputs and the output for each.

Each gate in a circuit must have at most two inputs, and circuits have up to three inputs and one output. Build the circuit for the statement as written — do not simplify it.

With 3 inputs there are 2³ = 8 rows. List them in binary counting order (000 to 111) so none are missed. Add a working column for each gate, then the output.

X = A AND (B OR C)

From a circuit, label the output of each gate (P, Q…), work out each label as a column, then the final output.

From a circuit: start at the inputs and name each gate's output in words, working towards X. E.g. A and B go into NAND, C goes into NOT, both outputs into OR → X = (A NAND B) OR (NOT C).

From a statement: pick out the conditions and the joining words. 'Pump on if the tank is NOT full AND the timer is on, OR the override is pressed' → X = (NOT A AND B) OR C.

Keep the gate names (AND, OR, NOT, NAND, NOR, XOR) in capitals and bracket every gate that feeds another.

Use the rows where X = 1. For each such row, AND the inputs together, putting NOT in front of any input that is 0. Then OR the rows together.

(all other rows X = 0) gives

X = (NOT A AND B AND C) OR (A AND NOT B AND C)

Because each gate may have only two inputs, a three-input AND is drawn as two AND gates chained: (NOT A AND B) AND C. The same rows let you draw a circuit from a truth table.

A short loop prints the truth table of any expression, so you can check a hand-worked table:

from itertools import product

for a, b, c in product((0, 1), repeat=3):
    x = a and (b or c)
    print(a, b, c, int(bool(x)))

The central processing unit (CPU) processes data and instructions to make the computer work: it fetches instructions from memory, decodes them and executes them (calculations, comparisons, moving data, controlling other parts).

A microprocessor is a CPU built as a type of integrated circuit on a single chip. Most computers, phones and many devices use one.

In a von Neumann computer, the program instructions and the data are both stored in the same memory (RAM), and the CPU fetches them over the same buses, one at a time.

• RAM holds the program currently running and the data it is using.
• The CPU fetches each instruction from RAM, decodes it and executes it, reading or writing data in RAM when needed.

This is the stored program concept: to run a different program you just load different instructions into memory.

Fetch

1. The address in the PC is copied to the MAR (sent along the address bus).
2. The PC is incremented (1 is added) so it points to the next instruction.
3. The instruction at that address is sent along the data bus to the MDR (a read signal is sent on the control bus).
4. The instruction is copied from the MDR to the CIR.

Decode

1. The CU decodes the instruction in the CIR to work out what to do (the opcode) and on what (the operand).

Execute

1. The instruction is carried out — e.g. the ALU does a calculation and the result goes to the ACC, or data is read from or written to memory through the MAR and MDR.
2. The cycle repeats from the address now in the PC.

An instruction set is the list of all the machine code instructions a CPU can understand and execute (such as load, store, add, compare, jump). Each has its own binary opcode.

• Programs must be translated into the machine code of that instruction set before they can run.
• Different families of CPU have different instruction sets, so machine code for one will not run on another.

Primary storage is directly accessed by the CPU.

Similarities: both are primary storage; both are directly accessed by the CPU; both are on the motherboard/chips; both use random access.

Secondary storage is non-volatile storage for files, programs and the operating system that must be kept when the power is off. It is not directly accessed by the CPU — data is first loaded into RAM.

Primary vs secondary:

Both store data in binary, and both are needed for the computer to run programs.

• A hard disk has one or more platters coated in a magnetic material, spinning at high speed.
• Each surface is divided into tracks and sectors.
• A read/write head on a moving actuator arm moves across the platter to the right track.
• Writing: the head magnetises tiny areas of the surface in one of two directions to represent 1 or 0.
• Reading: the head detects the direction of magnetisation of each area as it passes underneath.

• Solid-state storage has no moving parts. It uses NAND flash memory made of transistors arranged in a grid of cells.
• Each cell uses a floating gate (and a control gate) to trap or release electrons.
• Writing: a voltage pushes electrons onto the floating gate (or removes them), setting the cell to 0 or 1; the charge stays without power, so it is non-volatile.
• Reading: a voltage is applied and the computer detects whether current flows, which tells it if the cell holds 0 or 1.
• Data is written in pages and erased in blocks; each cell can only be rewritten a limited number of times.

Virtual memory is an area of secondary storage (an HDD or SSD) that the operating system uses as if it were extra RAM.

1. When RAM is full, the OS takes data/program parts that are not currently needed and moves them out of RAM to the virtual memory area on the drive.
2. This frees RAM for the data that is needed now.
3. When the moved data is needed again, it is swapped back into RAM (and something else is moved out).

Why it is necessary: it stops the computer crashing or refusing to open programs when RAM is full, so more or larger programs can run than RAM alone could hold.

Drawback: the drive is much slower than RAM, so heavy swapping makes the computer slow (disk thrashing).