Basic Electronics Notes

This unit specifies the competencies required to apply basic electronics skills. It covers identifying electric circuits and electronic components, understanding semi-conductor theory, identifying and classifying memories, applying number systems and binary coding, and identifying emerging trends in electronics. It is a common unit of competency, so trainees across ICT Technician, Computer Science and Computer Programming Level 6 all sit it.

The six learning outcomes

What the written assessment looks like

Recent CDACC papers for this unit follow a consistent shape, and the exercises in these notes are written to match it.

• Time: 3 hours, separate answer booklet, no writing on the question paper
• Section A — 40 marks: answer all questions. Short items of 2 to 6 marks: definitions, differences, a small sketch, a one-step calculation
• Section B — 60 marks: answer any three of four or five scenario questions, each worth 20 marks and split into parts (a), (b), (c)
• Scenario style: a workshop, a smart home startup, a research lab or an agricultural sensor network, with calculations and a diagram embedded in the story

Definition of an electrical circuit

An electrical circuit is a complete, closed conducting path through which electric current flows from a source of electromotive force, through a load that does useful work, and back to the source. Break the path anywhere and current stops — that is the whole idea behind a switch, and behind a blown fuse.

Every working circuit has four essential parts:

Three conditions of a circuit

Basic electrical quantities and their units

Learn the quantity symbol, the unit, the unit symbol and the measuring instrument for each — assessors ask for all four.

Defining relationships

Multiples and sub-multiples

Ohm's law, power and resistivity

Ohm's law states that the current through a conductor is directly proportional to the potential difference across it, provided temperature and other physical conditions remain constant.

Resistivity of a conductor

Resistance depends on the material and on the shape of the conductor. This appears in papers as a straight calculation, usually about a transmission line or a cable run.

• Resistance is directly proportional to length — double the run, double the resistance
• Resistance is inversely proportional to cross-sectional area — a thicker cable has less resistance
• Watch the units: 1 mm² = 10⁻⁶ m², and 1 µΩm = 10⁻⁶ Ωm

A power distribution line uses an aluminium conductor 1.2 km long
with a cross-sectional area of 25 mm². The resistivity of aluminium
is 0.028 µΩm. Calculate the resistance of the conductor.

ρ = 0.028 µΩm = 0.028 × 10⁻⁶ Ωm = 2.8 × 10⁻⁸ Ωm
l = 1.2 km   = 1200 m
A = 25 mm²  = 25 × 10⁻⁶ m²

R = ρl / A
  = (2.8 × 10⁻⁸ × 1200) / (25 × 10⁻⁶)
  = (3.36 × 10⁻⁵) / (2.5 × 10⁻⁵)
  = 1.344 Ω

Types of electrical circuits: series, parallel and network laws

Circuits are classified two ways: by how components are connected (series, parallel or series-parallel) and by the kind of supply (d.c. or a.c.).

Advantages of parallel circuits

Papers regularly ask for three advantages. The reliable answers are:

1. Independent operation — each branch can be switched on or off without affecting the others
2. Full supply voltage to every load — each appliance receives the rated 240 V rather than a share of it
3. Fault tolerance — if one lamp burns out, the rest keep working
4. Loads can be added without re-rating the others, up to the capacity of the supply and protective device

Kirchhoff's laws

Almost every circuit calculation in this unit reduces to one of these two, plus Ohm's law. Two further theorems are named in papers:

• Superposition theorem — in a linear circuit with more than one source, the current in any branch equals the algebraic sum of the currents produced by each source acting alone, with all other sources replaced by their internal resistances.
• Thévenin's theorem — any linear two-terminal network can be replaced by a single voltage source V_TH in series with a single resistance R_TH, as seen from those two terminals.

Three resistors of 10 Ω, 20 Ω and 30 Ω are connected in
parallel across a 240 V d.c. supply. Find Rₜ, Iₜ and the power.

1/Rₜ = 1/10 + 1/20 + 1/30
      = 6/60 + 3/60 + 2/60  =  11/60
Rₜ   = 60/11              =  5.4545 Ω   ≈ 5.45 Ω

Iₜ   = V / Rₜ = 240 / 5.4545  =  44 A
Check by branches:
  I₁ = 240/10 = 24 A
  I₂ = 240/20 = 12 A
  I₃ = 240/30 =  8 A
  ΣI = 24+12+8 = 44 A  ✓ agrees with KCL

P   = V × Iₜ = 240 × 44   =  10 560 W  =  10.56 kW

A lighting circuit runs from a 240 V supply protected by a 13 A fuse.
Each bulb is rated 100 W. (a) How many bulbs can run at once?
(b) Energy used in 1 hour if all are on?

(a) Current per bulb  I = P/V = 100/240 = 0.4167 A
    Number of bulbs   n = 13 / 0.4167 = 31.2
    → 31 bulbs (you cannot have a fraction of a bulb;
      a 32nd would draw 13.33 A and blow the fuse)

(b) Total power P = 31 × 100 = 3100 W
    t = 1 hour = 3600 s
    W = P × t = 3100 × 3600 = 11 160 000 J = 11.16 MJ  (3.1 kWh)

Simple a.c. and d.c. circuits

In a direct current (d.c.) circuit, charge flows in one direction only and the voltage holds a steady value. Sources are cells, batteries, solar PV panels, d.c. generators and rectified power supplies. Every electronic device runs on d.c. internally — phones, laptops, routers and microcontrollers all sit at 5 V, 3.3 V or lower.

In an alternating current (a.c.) circuit, the current periodically reverses direction and the voltage varies sinusoidally with time. Kenya's mains supply is 240 V at 50 Hz, meaning the waveform completes fifty full cycles every second. A.c. is used for generation and distribution because transformers can step it up for low-loss transmission and back down for safe use.

Peak, r.m.s. and average values

Assessment questions ask you to convert between these for a sinusoidal waveform. Memorise the three factors.

A sinusoidal voltage has a maximum value of 120 V.
Calculate its r.m.s. and average values.

Vᵣᵐᵣ = 0.707 × 120 = 84.84 V   (or 120/√2 = 84.85 V)
Vᴡᵛ  = 0.637 × 120 = 76.44 V   (or 2×120/π  = 76.39 V)

Note: the 240 V mains figure is an r.m.s. value.
Its peak is 240 × 1.414 = 339.4 V — which is why
insulation must be rated well above 240 V.

Analogue and digital circuits

A separate classification that papers ask you to differentiate.

Identification of electronic components

Components split into two families. Passive components cannot produce power gain — they resist, store or transform energy. Active components can control or amplify current, and need a supply to do it.

Resistors

A resistor opposes the flow of current and converts electrical energy into heat. Its value in ohms, its tolerance and its power rating are the three things you need before choosing one.

Characteristics

• Resistance value — from a fraction of an ohm to many megohms
• Tolerance — how far the actual value may stray from the marked one (±1 %, ±5 %, ±10 %)
• Power rating — watts it can dissipate without burning, typically 0.125 W to 5 W
• Temperature coefficient — how much the value drifts as it warms
• Resistors are non-polarised: they can be fitted either way round
• Preferred values follow the E-series (E12, E24), which is why you find 4.7 kΩ and 6.8 kΩ but not 5 kΩ

Types of resistor

Applications of resistors

Limiting current through an LED, dividing voltage to a safe level for a sensor input, setting the gain of an amplifier, pulling a logic input to a known state, biasing a transistor, and discharging a capacitor safely after power-off.

Reading the resistor colour code

Read from the band nearest an end, keeping the tolerance band — usually gold or silver, and spaced slightly apart — on the right.

A resistor carries the bands Red, Violet, Brown, Gold.
(a) Determine its value. (b) State the tolerance.
(c) Explain what that tolerance means in practical use.

(a) Red = 2, Violet = 7, Brown = ×10
    Value = 27 × 10 = 270 Ω
(b) Gold = ±5 %
(c) The true resistance may lie anywhere between
    270 − 5%  = 256.5 Ω  and
    270 + 5%  = 283.5 Ω
    The designer must ensure the circuit still works
    anywhere in that band. Where the exact value matters
    — a timing circuit or a precision divider — a
    ±1 % (brown) resistor is specified instead.

Capacitors

A capacitor stores energy in the electric field between two conducting plates separated by an insulating dielectric. Capacitance is measured in farads (F), though practical values are microfarads, nanofarads and picofarads.

Characteristics

• Blocks d.c., passes a.c. — once charged, no steady current flows through it
• Opposition to a.c. is capacitive reactance, X_C = 1/(2πfC), which falls as frequency rises
• Has a working voltage that must never be exceeded
• Capacitance rises with plate area and with the dielectric constant, and falls as plate separation increases
• Electrolytic and tantalum types are polarised — fitting them backwards can make them vent or burst
• Charges to 63 % of the supply in one time constant, and is taken as fully charged after five

Capacitors in series and parallel — the opposite of resistors

C1 = 4 F and C2 = 2 F are connected in series across 12 V.
Find (i) total capacitance, (ii) total charge,
(iii) the voltage across each capacitor.

(i)  1/Cₜ = 1/4 + 1/2 = 1/4 + 2/4 = 3/4
     Cₜ   = 4/3 = 1.333 F

(ii) Q = Cₜ × V = 1.333 × 12 = 16 C
     (In series the SAME charge flows through both.)

(iii) V₁ = Q/C₁ = 16/4 = 4 V
      V₂ = Q/C₂ = 16/2 = 8 V
      Check: 4 + 8 = 12 V  ✓

Note the pattern: the SMALLER capacitor takes the
LARGER share of the voltage.

Applications of capacitors

Smoothing the ripple after a rectifier, coupling an audio signal while blocking d.c. bias, decoupling supply noise beside an IC, setting the frequency of an oscillator or 555 timer, correcting power factor in industrial plant, and tuning a radio receiver.

Inductors, reactance and impedance

An inductor is a coil of wire that stores energy in a magnetic field when current flows. Inductance is measured in henries (H).

Characteristics

• Opposes any change in current — current through an inductor cannot jump instantly
• Passes d.c. easily but opposes a.c. more strongly as frequency rises — the opposite of a capacitor
• Lenz's law: the induced e.m.f. always acts in the direction that opposes the change producing it. That is the meaning of the minus sign in the formula
• Switching an inductor off produces a large back-e.m.f. spike, which is why relay and motor coils need a flyback diode

Impedance and resonance

In an a.c. circuit, total opposition is impedance Z, measured in ohms, combining resistance and reactance as a right-angled triangle rather than a simple sum.

Three resistors of 10 Ω, 20 Ω and 30 Ω in parallel are fed
from 240 V. A 50 µF capacitor is then added in series with
the parallel network, on a 50 Hz supply.

Parallel resistance (from LO1):  R = 60/11 = 5.4545 Ω
Current before the capacitor:    I = 240/5.4545 = 44 A

X₊ = 1 / (2πfC)
   = 1 / (2 × 3.1416 × 50 × 50 × 10⁻⁶)
   = 1 / (0.015708)
   = 63.66 Ω

Z  = √(R² + X₊²)
   = √(5.4545² + 63.66²)
   = √(29.75 + 4052.6)
   = √4082.35  =  63.89 Ω

New current I = V/Z = 240 / 63.89 = 3.76 A

The capacitor dominates: current drops from 44 A to under 4 A.
An industrial use of combining R and C is a snubber network
across contactor contacts, which suppresses arcing and
voltage transients when the contacts open.

Diodes, integrated circuits and safe handling

A diode is a two-terminal semiconductor that conducts in one direction only. The terminals are the anode (positive) and the cathode (marked with a band). The physics is in LO3; here it is the component itself that matters.

Identification of integrated circuit characteristics

An integrated circuit (IC) is a complete circuit — transistors, resistors, diodes and their interconnections — fabricated on a single chip of semiconductor, usually silicon, and sealed in a package with external pins.

Reasons for using ICs in electronic design

1. Very small size and light weight compared with the discrete circuit they replace
2. Low cost per function, because thousands of chips are produced on a single wafer
3. High reliability — far fewer soldered joints and interconnections to fail
4. Low power consumption and higher operating speed, since signals travel shorter distances
5. Easier design and maintenance — one chip replaces a board of parts and is simply swapped if faulty
6. Consistent performance, because all components on the chip are made together and age together

Limitations

• Not repairable — a faulty IC is replaced, never fixed internally
• Sensitive to electrostatic discharge and to exceeding the supply voltage
• Limited power handling, so high-power stages still use discrete devices
• Inductors and large-value capacitors cannot be practically fabricated on chip

Classification by scale of integration

ICs are also classified by function: analogue or linear ICs (operational amplifiers, voltage regulators such as the 7805, audio amplifiers), digital ICs (logic gates, counters, memories, microprocessors), and mixed-signal ICs containing both, such as analogue-to-digital converters.

Definition of semiconductor and related terms

A semiconductor is a material whose electrical conductivity lies between that of a conductor and an insulator, and which can be controlled by adding impurities, by temperature, by light or by an applied voltage. That controllability is the entire reason modern electronics exists.

Atom

The smallest particle of an element that still has the properties of that element.

Nucleus

The dense centre of an atom, containing protons (positive) and neutrons (neutral).

Electron

A negatively charged particle orbiting the nucleus in shells.

Neutron

A neutral nuclear particle that adds mass, binds protons together against repulsion, and gives rise to isotopes.

Valence shell

The outermost electron shell; it determines chemical and electrical behaviour.

Valence electron

An electron in the valence shell. Semiconductors have four of them.

Free electron

An electron with enough energy to escape its atom and drift through the material.

Hole

The vacancy left by a departed electron; behaves as a mobile positive charge carrier.

Covalent bond

A bond formed when neighbouring atoms share valence electrons.

Doping

Deliberately adding a small amount of impurity to change conductivity.

Intrinsic

A pure, undoped semiconductor. Electrons and holes exist in equal numbers.

Extrinsic

A doped semiconductor — either P-type or N-type.

Majority carrier

The carrier present in larger numbers: electrons in N-type, holes in P-type.

Minority carrier

The carrier present in smaller numbers: holes in N-type, electrons in P-type.

Biasing

Applying an external d.c. voltage to set a device's operating condition.

Depletion region

The carrier-free zone either side of a P-N junction.

Barrier potential

The voltage across the depletion region: about 0.7 V for silicon, 0.3 V for germanium.

Intrinsic versus extrinsic semiconductors

Advantages of semiconductor devices over valves and other devices

1. Very small size and light weight, allowing miniaturised equipment
2. Low power consumption, with no heater or filament required
3. No warm-up time — they operate the instant power is applied
4. Long operating life and high mechanical ruggedness, with no fragile glass envelope
5. Low operating voltage, so they are safer and cheaper to supply
6. Cheap to mass produce and easily integrated into ICs
7. Silent operation with no vibration

Disadvantages: sensitive to heat and to electrostatic discharge; limited power handling compared with valves; performance drifts with temperature; permanently damaged by voltage or current overload; and they cannot be repaired once failed.

Description of the structure of matter

All matter is made of atoms. An atom has a nucleus of protons and neutrons, surrounded by electrons in shells labelled K, L, M, N outward from the centre. Each shell holds at most 2n² electrons, where n is the shell number: 2, 8, 18, 32.

An atom is electrically neutral because the number of protons equals the number of electrons. Only the valence electrons in the outermost shell take part in conduction — inner-shell electrons are bound too tightly to matter.

Electrons in conductors and semiconductors

Types of semiconductor materials

Silicon

• Atomic number 14, four valence electrons, energy gap about 1.1 eV
• Extremely abundant — sand is silicon dioxide, so raw material cost is low
• Tolerates higher temperature, up to about 150 °C, before leakage becomes a problem
• Low reverse leakage current
• Forms a stable oxide, SiO₂, which makes reliable ICs possible
• Forward voltage drop about 0.7 V

Germanium

• Atomic number 32, four valence electrons, energy gap about 0.7 eV
• Lower forward drop of about 0.3 V, which suits very small signal detection
• Higher leakage current and a low temperature limit of roughly 70 °C
• Scarcer and more expensive than silicon, so now largely replaced by it

Compound semiconductors also matter: gallium arsenide (GaAs) for high-frequency and microwave devices, gallium nitride (GaN) for efficient power conversion and blue LEDs, and silicon carbide (SiC) for high-voltage, high-temperature power electronics.

P-type and N-type materials

Pure silicon barely conducts at room temperature because each atom's four valence electrons are locked into covalent bonds with four neighbours. Doping adds a controlled impurity — roughly one atom in ten million — and transforms conductivity.

P-N junction diode operation

Join P-type to N-type and you form a P-N junction. At the boundary, free electrons from the N side diffuse across and recombine with holes on the P side. This leaves exposed ions and creates a thin depletion region containing no free carriers, with a potential barrier across it — about 0.7 V for silicon and 0.3 V for germanium.

Forward biasing

The positive terminal of the supply is connected to the P side and the negative to the N side.

• The applied voltage opposes the barrier potential, so the depletion region narrows
• Once the supply exceeds the barrier (0.7 V Si, 0.3 V Ge), majority carriers cross freely
• A large forward current flows and the diode acts almost like a closed switch
• Forward resistance is low, typically a few ohms
• A series resistor is essential, or the current will destroy the diode

Reverse biasing

The positive terminal is connected to the N side and the negative to the P side.

• The applied voltage reinforces the barrier, so the depletion region widens — and the wider it is, the more the junction behaves like a capacitor, which is what a varactor exploits
• Majority carriers are pulled away from the junction and cannot cross
• Only a small reverse leakage current flows, carried by minority carriers
• Reverse resistance is very high, so the diode acts like an open switch

Breakdown: avalanche and Zener

If reverse voltage keeps rising, the junction eventually breaks down and conducts heavily. Two distinct mechanisms produce this, and papers ask about both.

• Avalanche breakdown occurs in lightly doped junctions at higher voltages, typically above about 6 V. The wide depletion region and strong electric field accelerate the few minority carriers to high velocity. They collide with atoms in the lattice and knock out further electron-hole pairs by impact ionisation. Those new carriers are accelerated in turn and collide again, so the carrier population multiplies like an avalanche and reverse current rises sharply.
• Zener breakdown occurs in heavily doped junctions at lower voltages, below about 5 V. The depletion region is so narrow that the field rips electrons directly out of covalent bonds without any collision.

Practical applications of reverse breakdown: Zener diodes used as voltage regulators and reference sources; avalanche photodiodes used in optical receivers because the multiplication amplifies weak light signals; and transient voltage suppression diodes that clamp surges to protect circuits.

Breakdown is only safe when the current is limited by a series resistor. Beyond the rated peak inverse voltage (PIV), an ordinary rectifier diode suffers permanent thermal damage.

Operation of transistors

A bipolar junction transistor (BJT) is a three-layer, two-junction semiconductor device with terminals named emitter (E), base (B) and collector (C). It can amplify a small signal or switch a large current.

Three construction facts explain everything the device does:

• The emitter is heavily doped — its job is to inject carriers
• The base is very thin and lightly doped — most carriers pass straight through it
• The collector is moderately doped and physically largest — it collects carriers and dissipates the heat

How an NPN transistor works

For normal amplifying operation the emitter-base junction is forward biased and the collector-base junction is reverse biased.

1. The forward-biased emitter-base junction lets the heavily doped emitter inject a large flood of electrons into the base
2. The base is thin and lightly doped, so only about 1–5 % of those electrons recombine with holes there and leave as base current I_B
3. The remaining 95–99 % are swept across into the reverse-biased collector by its positive potential, forming the collector current I_C
4. A small change in I_B therefore produces a large change in I_C — that is current amplification

A PNP transistor works identically but with every polarity reversed and holes as the carriers. Its emitter is held positive with respect to the collector, and it is turned on by making the base more negative than the emitter. Holes injected from the emitter cross the thin N base and are collected by the negative collector.

A transistor has Iᵝ = 200 µA, β = 120, Vᶜᶜ = 12 V, Rᶜ = 600 Ω.
Find (i) Iᶜ, (ii) the voltage across Rᶜ, (iii) VᶜᲩ.

(i)   Iᶜ = β × Iᵝ
         = 120 × 200 × 10⁻⁶
         = 0.024 A = 24 mA

(ii)  Vᵣᶜ = Iᶜ × Rᶜ
         = 0.024 × 600
         = 14.4 V

(iii) VᶜᲩ = Vᶜᶜ − IᶜRᶜ
         = 12 − 14.4
         = −2.4 V

A negative VᶜᲩ is impossible, so the transistor is
SATURATED. It cannot supply 24 mA into that load from
a 12 V rail. The actual collector current is limited to
Iᶜ(sat) = Vᶜᶜ/Rᶜ = 12/600 = 20 mA, and VᶜᲩ falls to
about 0.2 V. This is exactly what you want from a
transistor used as a SWITCH.

Also find IᲩ:  IᲩ = Iᵝ + Iᶜ = 0.0002 + 0.020 = 20.2 mA

Regions of operation

The transistor as a switch

Driven only between cut-off and saturation, a transistor behaves like a relay with no moving parts. With no base current it is off and the load is dead. With enough base current to saturate it, the collector-emitter path drops only about 0.2 V, so almost the full supply appears across the load and power wasted in the transistor is small. This is how a microcontroller output, which can supply only a few milliamps, controls a motor, a relay coil or a wireless transmitter drawing hundreds of milliamps.

To guarantee saturation, designers supply a base current several times larger than I_C/β — an overdrive factor of 2 to 10 — because β varies between individual devices and falls with temperature.

Definition of memory

Memory is the part of an electronic system that stores data, instructions and results, either temporarily during processing or permanently for later use. Every memory is an array of cells, each holding one bit — a single 0 or 1 — with a unique address so the processor can find it.

Key memory characteristics

• Volatility — does the content survive a power cut?
• Access time — how long from request to data, in nanoseconds or milliseconds
• Capacity — how much it holds
• Cost per bit — fast memory is always expensive memory
• Access method — random, direct or sequential
• Read/write ability — read-write, read-mostly, or read-only

Classification of memories

RAM — Random Access Memory

RAM is the computer's working memory. Any location can be reached in the same time regardless of its address, which is what "random access" means. It is volatile: switch off and the contents are lost. RAM holds the operating system, the programs currently running and the data being worked on.

Main memory versus cache memory

Cache is organised in levels: L1 is smallest and fastest and sits inside each core, L2 is larger, and L3 is shared across cores. Hit rates above 90 % are normal, which is why cache has such a large effect on real performance.

ROM — Read Only Memory

ROM holds data permanently and is non-volatile. It stores firmware — the instructions a device needs the instant it powers on.

Functions of ROM

1. Stores the bootstrap loader / BIOS or UEFI that starts the computer and locates the operating system
2. Holds the power-on self-test (POST) routines that check hardware at start-up
3. Stores permanent firmware for embedded devices such as routers, washing machines and microwave controllers
4. Holds fixed data tables such as character generators, look-up tables and calibration constants
5. Provides basic input/output routines that let the processor communicate with attached hardware before the operating system loads

DAM — Direct Access Memory

Direct access memory is storage in which the read head moves straight to the region holding the data and then searches a short distance sequentially. It sits between pure random access (RAM) and pure sequential access (tape). Hard disk drives, optical discs and floppy disks all use direct access: the head steps to the right track, then waits for the right sector to rotate underneath it.

Types of memories

Semiconductor memories

These store data as charge or as the state of transistors on a silicon chip. They have no moving parts, which makes them fast, silent, shock-resistant and power-efficient.

• Registers — a handful of the fastest stores, inside the CPU itself
• SRAM — CPU cache at levels L1, L2 and L3
• DRAM — main memory modules
• ROM, PROM, EPROM, EEPROM — firmware and configuration
• Flash (NAND and NOR) — SSDs, microSD cards, USB flash drives, phone storage

Magnetic memories

These store data as the direction of magnetisation of tiny regions on a coated surface. A read/write head magnetises a spot one way for 1 and the other way for 0.

• Hard disk drive (HDD) — rigid spinning platters, high capacity, low cost per gigabyte, direct access
• Magnetic tape — sequential access, very cheap per terabyte, still used for archival backup
• Floppy disk — obsolete, but a classic example of removable magnetic direct-access storage
• Magnetic stripe cards — bank and access control cards

Optical and solid-state secondary memory

• CD-ROM, DVD, Blu-ray — data stored as pits and lands read by a laser; direct access; cheap to distribute, slow to write
• Solid-state drive (SSD) — NAND flash; no moving parts, very fast, shock-proof, more expensive per gigabyte and with a finite write endurance
• USB flash drive and memory card — small, removable NAND flash for transfer and expansion
• Cloud storage — remote disk arrays reached over a network; unlimited scaling but dependent on connectivity

Structure of a magnetic disk

A hard disk contains one or more rigid platters coated with magnetic material, spinning on a common spindle. Read/write heads on an actuator arm float microscopically above each surface.

Disk performance calculations

An HDD has: capacity 1 TB, rotational speed 7200 rpm,
transfer rate 150 MB/s.

(i)  Time to transfer 600 MB
     t = 600 / 150 = 4 seconds

(ii) Revolutions per second
     n = 7200 / 60 = 120 rev/s

(iii) Average rotational latency
     One revolution takes 1/120 = 0.00833 s = 8.33 ms
     Average latency = half a revolution
                     = 8.33 / 2 = 4.17 ms

The memory hierarchy

Systems combine several memory technologies. Moving down the hierarchy, capacity and cost-effectiveness rise while speed falls.

Definition of number system and binary code

A number system is a method of representing quantities using a defined set of symbols (digits) and a base or radix — the number of distinct digits available. The value of a digit depends on its position, which is why these are called positional systems.

A binary code is a scheme for representing numbers, letters or other information as patterns of 0s and 1s so that digital circuits can process them.

Advantages of binary coding

1. Only two states are needed — a transistor either conducts or it does not, so circuits are simple and cheap
2. High noise immunity — a signal has to be corrupted a long way before a 0 is mistaken for a 1
3. Reliable storage — two magnetic directions, two charge states or two light levels are easy to distinguish
4. Suits Boolean logic directly, so arithmetic, comparison and decision-making use the same gates
5. Error detection and correction are straightforward using parity and Hamming codes
6. Easy compression, encryption and transmission, since everything is a uniform stream of bits

Base conversion

Any base to decimal — multiply by place value and add

1101₂  = 1×2³ + 1×2² + 0×2¹ + 1×2⁰
       = 8 + 4 + 0 + 1                 = 13₁₀

257₈   = 2×8² + 5×8¹ + 7×8⁰
       = 128 + 40 + 7                  = 175₁₀

2AF₁₆ = 2×16² + 10×16¹ + 15×16⁰
       = 512 + 160 + 15                = 687₁₀

Decimal to any base — repeated division, read remainders upward

45 ÷ 2 = 22 r 1   ↑        45 ÷ 8 = 5 r 5   ↑
22 ÷ 2 = 11 r 0   ↑         5 ÷ 8 = 0 r 5   ↑
11 ÷ 2 =  5 r 1   ↑        45₁₀ = 55₈
 5 ÷ 2 =  2 r 1   ↑
 2 ÷ 2 =  1 r 0   ↑        45 ÷ 16 = 2 r 13 (D)  ↑
 1 ÷ 2 =  0 r 1   ↑         2 ÷ 16 = 0 r 2       ↑
45₁₀ = 101101₂              45₁₀ = 2D₁₆

Decimal fractions — repeated multiplication, read downward

0.625 × 2 = 1.25   → 1   ↓
0.250 × 2 = 0.50   → 0   ↓
0.500 × 2 = 1.00   → 1   ↓   stop when the fraction reaches 0
0.625₁₀ = 0.101₂

Combined: 45.625₁₀ = 101101.101₂

Grouping shortcuts — binary to octal and hexadecimal

Because 8 = 2³ and 16 = 2⁴, you never need to go through decimal. Group the binary digits from the binary point outward: threes for octal, fours for hexadecimal, padding with leading zeros.

11010110₂
Octal :  011 | 010 | 110   →  3  2  6   =  326₈
Hex   :  1101 | 0110       →  D  6      =  D6₁₆
Check :  128+64+16+4+2     =  214₁₀

Hex to binary — one nibble per digit:
3F → 0011 1111
2A → 0010 1010
5C → 0101 1100
7D → 0111 1101

Hexadecimal arithmetic

Method 1 — column addition in hex:
      3 F
    + 2 A
    -----
  F + A = 15 + 10 = 25 = 16 + 9  → write 9, carry 1
  3 + 2 + 1(carry) = 6           → write 6
  Result = 69₁₆

Method 2 — via decimal (use this to check):
  3F₁₆ = 3×16 + 15 = 63
  2A₁₆ = 2×16 + 10 = 42
  63 + 42 = 105
  105 ÷ 16 = 6 r 9  →  69₁₆  ✓

In binary: 6 → 0110, 9 → 1001
  69₁₆ = 0110 1001₂

Binary arithmetic

Addition

  carries  1111
           1 0 1 1      (11)
        +  1 1 0 1      (13)
        -----------
         1 1 0 0 0      (24)  ✓ 11 + 13 = 24

Subtraction by direct borrowing

           1 1 0 1      (13)
        −  1 0 1 0      (10)
        -----------
           0 0 1 1      (3)   ✓

Subtraction using 1's complement

Form the 1's complement of the subtrahend by inverting every bit, add it to the minuend, then apply the end-around carry: if a carry comes out of the most significant bit, add it back to the least significant bit and the answer is positive. If there is no carry, the answer is negative and you must take the 1's complement of the result.

10100111  invert →  01011000     (1's complement)

    1101 1001      (217)
  + 0101 1000      (1's comp of 167)
  -------------
  1 0011 0001      carry out of MSB = 1
          → end-around carry: add the 1 back
    0011 0001
  +         1
  -------------
    0011 0010      = 50₁₀

Check: 217 − 167 = 50  ✓

Subtraction using 2's complement

Computers do not really subtract — they add the 2's complement of the second number. Form it by inverting every bit and adding 1. Any final carry out is simply discarded.

10          = 0000 1010
invert      = 1111 0101        (1's complement)
add 1       = 1111 0110        (2's complement of 10)

  0000 1101      (13)
+ 1111 0110      (−10)
-----------
1 0000 0011      discard the carry → 0000 0011 = 3  ✓

Multiplication

       1 0 1 1        (11)
   ×     1 0 1        (5)
   ---------------
       1 0 1 1        × 1
     0 0 0 0          × 0, shifted one place
   1 0 1 1            × 1, shifted two places
   ---------------
   1 1 0 1 1 1        (55)   ✓ 11 × 5 = 55

Division

        1 1 0        ← quotient = 6
      _______
 1 0 ) 1 1 0 0
       1 0
       ---
        1 0
        1 0
        ---
         0 0
           0
         ---
           0          remainder = 0   ✓ 12 ÷ 2 = 6

Binary codes

A binary code assigns a fixed bit pattern to each symbol. Codes exist because raw binary is not always convenient — digital clocks, calculators and meters need to drive decimal displays directly.

8421 BCD — Binary Coded Decimal

In 8421 BCD each decimal digit is replaced by its own 4-bit binary equivalent. The name comes from the place values of the four bits: 8, 4, 2, 1. It is a weighted code.

   5  6  9                2  5  9
   |  |  |                |  |  |
0101 0110 1001        0010 0101 1001

Compare 259 in the two forms:
  Pure binary : 259 = 1 0000 0011   (9 bits)
  8421 BCD    : 259 = 0010 0101 1001 (12 bits)

• Only the patterns 0000 to 1001 are valid; 1010 to 1111 are illegal in BCD
• Conversion between BCD and decimal is trivial, which suits displays and keypads
• It wastes storage — six of the sixteen possible patterns are never used, roughly 20 % less efficient than pure binary
• Arithmetic circuits are more complex than for pure binary

2421 BCD

2421 BCD is another weighted code, but the bit weights are 2, 4, 2, 1 rather than 8, 4, 2, 1. It is self-complementing: the 9's complement of any digit is found simply by inverting all four bits.

Advantages of 2421 BCD: it is self-complementing, so subtraction by 9's complement needs only an inverter rather than a subtractor; and because it is weighted, the decimal value can still be recovered by simple addition of the bit weights, unlike a purely unweighted code.

Excess-3 code

Excess-3 is formed by adding 3 (0011₂) to each BCD digit. It is an unweighted, self-complementing code.

Decimal 5:  BCD 0101 + 0011 = 1000   Excess-3
Decimal 2:  BCD 0010 + 0011 = 0101   Excess-3

Self-complementing check:
Excess-3 of 4 = 0111.  Invert → 1000 = Excess-3 of 5.
And 4 + 5 = 9. ✓

Gray code

Gray code is an unweighted code in which only one bit changes between consecutive values. This eliminates the momentary wrong readings that occur when several bits change at once in a mechanical encoder, so it is used in shaft encoders, position sensors and Karnaugh maps.

Binary :  1   0   1   1
          |  / |  / |  /
MSB kept: 1
1 XOR 0 = 1
0 XOR 1 = 1
1 XOR 1 = 0
Gray   :  1 1 1 0

ASCII and parity

ASCII (American Standard Code for Information Interchange) is a 7-bit code representing 128 characters: letters, digits, punctuation and control codes. 'A' is 65 (100 0001₂), 'a' is 97, and '0' is 48. Unicode is its modern multi-byte successor, covering every writing system.

Parity adds one extra bit so that the total number of 1s is even (even parity) or odd (odd parity). It detects any single-bit error but cannot correct it. Hamming code adds several parity bits and can both detect and correct a single-bit error.

BCD arithmetic

BCD arithmetic follows binary rules but with a correction step, because the four-bit groups must never stray outside 0000–1001.

BCD addition — the add-six rule

Add the groups as plain binary. Then, for any group whose result exceeds 9 or which generates a carry out, add 0110 (6) to that group and propagate any resulting carry to the next group.

   0010 0101      (25)
 + 0011 0010      (32)
 -------------
   0101 0111      (57)   both groups ≤ 9, already valid BCD

   0010 1000      (28)
 + 0011 0101      (35)
 -------------
   0101 1101      units group = 1101 = 13, illegal
 +      0110      add 6 to that group
 -------------
   0110 0011      (63)   ✓ 28 + 35 = 63

575 = 0101 0111 0101
895 = 1000 1001 0101

Units :  0101 + 0101 = 1010  → illegal, add 0110
         1010 + 0110 = 1 0000  → write 0000, carry 1
Tens  :  0111 + 1001 + 1 = 1 0001 → carry out, so add 0110
         0001 + 0110 = 0111  → write 0111, carry 1
Hundreds: 0101 + 1000 + 1 = 1110 → illegal, add 0110
         1110 + 0110 = 1 0100 → write 0100, carry 1
Thousands: the final carry = 0001

Result = 0001 0100 0111 0000  =  1470₁₀
Check: 575 + 895 = 1470  ✓

BCD subtraction

Subtract as binary. Wherever a group required a borrow, subtract 0110 (6) from that group to correct it. BCD hardware normally uses 9's or 10's complement addition instead.

   0101 0010      (52)
 − 0010 0111      (27)
 -------------
   0010 1011      units group borrowed and is illegal (1011)
 −      0110      subtract 6 from that group
 -------------
   0010 0101      (25)   ✓ 52 − 27 = 25

BCD multiplication and division

These are rarely performed directly in BCD hardware. The standard method, and the one to state in an assessment, is:

1. Convert each BCD operand to its decimal or pure binary value
2. Perform the multiplication or division
3. Convert the result back into BCD, digit by digit

0010 0011 (23) × 0011 (3)
  23 × 3 = 69
  6 → 0110,  9 → 1001
  Result = 0110 1001

0100 1000 (48) ÷ 0110 (6)
  48 ÷ 6 = 8
  Result = 1000

Description of emerging trends

An emerging trend is a new technology, technique or practice that is gaining ground and beginning to change how work is done in a field. In electronics the direction of travel is consistent: smaller, faster, cheaper, more connected and more intelligent.

How IoT smart sensors work

An IoT-enabled smart sensor in a household device follows the same five stages every time, and describing them in order is what earns the marks:

1. Sensing. A transducer converts a physical quantity — temperature, humidity, soil moisture, current, motion — into an electrical signal, usually a small analogue voltage.
2. Signal conditioning and conversion. The signal is amplified and filtered, then an analogue-to-digital converter turns it into a digital value the processor can use.
3. Local processing. An embedded microcontroller reads the value, timestamps it, compares it against thresholds and may act immediately, for example switching a relay.
4. Communication. A wireless module — Wi-Fi, Bluetooth, Zigbee, LoRa or a cellular modem — transmits the reading to a gateway and on to a cloud server.
5. Cloud analysis and feedback. The server stores and analyses the data, shows it on a dashboard or phone app, raises alerts, and can send commands back to actuators in the device, closing the control loop.

Quantum computing and electronics

Classical electronics stores information in bits that are strictly 0 or 1. A quantum computer uses qubits, which can exist in a superposition of both states at once and can be entangled with one another, so n qubits explore 2ⁿ combinations simultaneously. For certain problems — factoring large numbers, searching unsorted data, simulating molecules and optimising large systems — this offers speed-ups no classical machine can match.

For the electronics trade the consequences are: new demand for cryogenic and microwave control hardware; the need for post-quantum cryptography, because current public-key encryption would be breakable; hybrid systems where a classical processor offloads specific problems to a quantum co-processor; and faster materials and chip design through quantum simulation. Practical machines remain expensive, error-prone and limited to specialised tasks, so classical electronics is not being replaced.

Solar PV and energy calculations

A solar panel delivers 24 V at 3 A. The system consumes
288 Wh per day.

(i)  Output power
     P = V × I = 24 × 3 = 72 W

(ii) Hours of operation required
     t = energy demand / panel power
       = 288 / 72
       = 4 hours of full sunshine per day

In practice you would oversize the panel, because
irradiance varies, panels lose efficiency when hot,
and the battery and charge controller are not 100 %
efficient. A common rule is to add 25–30 % margin,
which here means about a 90–95 W panel.

Challenges of emerging trends

Nanotechnology: two advantages and two challenges

Coping with emerging trends

Coping is not about resisting change; it is about staying employable and safe while it happens.

Every formula in this unit

Circuits and power

Alternating current

Components

Semiconductors

Memory and disks

Number systems

Energy and solar

Competence checklist

Tick each statement you could do unaided in an assessment. Your ticks are saved in this browser.

0 of 28 ticked

• Define a circuit and name its four essential parts
• State every electrical quantity, its unit and its measuring instrument
• Apply Ohm's law and all three power formulas
• Calculate conductor resistance from R = ρl/A with correct unit conversion
• Solve series, parallel and series-parallel networks and verify with Kirchhoff's laws
• Draw a labelled schematic with cell, resistor, ammeter, voltmeter and switch
• Differentiate a.c. from d.c. and analogue from digital
• Convert between peak, r.m.s. and average values and find the form factor
• Identify resistors, capacitors, inductors, diodes, transistors and ICs by symbol
• Read a four-band resistor colour code and state the tolerance range
• Describe the operation and types of a varistor
• Calculate capacitors in series and parallel, including charge sharing
• Calculate X_C, X_L, impedance Z and resonant frequency
• State the characteristics and applications of each inductor core type
• Give four reasons for using ICs and three ESD safety precautions
• Use a multimeter correctly for resistance, voltage and current
• Sketch and label a silicon atom and explain doping
• Distinguish intrinsic from extrinsic, and N-type from P-type
• Explain forward and reverse bias and the effect on the depletion layer
• Explain avalanche and Zener breakdown and give applications
• Explain NPN and PNP operation and calculate I_C, I_E and V_CE
• Classify memory into RAM, ROM and DAM and state the functions of ROM
• Compare SRAM with DRAM, and main memory with cache
• Draw a magnetic disk showing tracks, sectors, blocks and cylinders
• Perform disk transfer time and rotational latency calculations
• Convert freely between decimal, binary, octal and hexadecimal
• Subtract using 1's complement with end-around carry, and 2's complement
• Encode in 8421 BCD, 2421 BCD, Excess-3 and Gray, and do BCD arithmetic

Glossary

Ampere

Unit of current; one coulomb per second.

Avalanche breakdown

Reverse breakdown by impact ionisation multiplying carriers, typically above 6 V.

BCD

Binary Coded Decimal; each decimal digit replaced by its own four-bit code.

Biasing

Applying d.c. voltage to set a device's operating condition.

Cache

Small fast SRAM near the CPU holding recently used data.

Capacitance

Ability to store charge, measured in farads.

Cylinder

The same track position across every platter of a disk stack.

DAM

Direct access memory; jump near the target then scan, as on a hard disk.

Depletion region

Carrier-free zone either side of a P-N junction.

Doping

Adding a controlled impurity to change a semiconductor's conductivity.

DRAM

Dynamic RAM; one transistor and one capacitor per bit, needs refreshing.

E.m.f.

Energy supplied per coulomb by a source, in volts.

Excess-3

Unweighted self-complementing code formed by adding 0011 to BCD.

Extrinsic

A doped semiconductor, either N-type or P-type.

Form factor

Ratio of r.m.s. to average value; 1.11 for a sine wave.

Gray code

Code in which only one bit changes between consecutive values.

Hole

Vacancy left by a missing electron, acting as a positive carrier.

Impedance

Total a.c. opposition combining resistance and reactance, in ohms.

Integrated circuit

A complete circuit fabricated on a single chip of silicon.

Intrinsic

A pure, undoped semiconductor.

Kirchhoff's laws

Current into a junction equals current out; loop e.m.f.s equal loop p.d.s.

Lenz's law

An induced e.m.f. always opposes the change producing it.

Majority carrier

Electrons in N-type, holes in P-type.

Nanoelectronics

Electronics with critical dimensions below about 100 nanometres.

Parity

An extra bit making the count of 1s even or odd, for error detection.

PIV

Peak inverse voltage; the maximum reverse voltage a diode can withstand.

Reactance

Opposition to a.c. from capacitance or inductance, in ohms.

Resistivity

A material property, in ohm metres, relating R to length and area.

R.m.s.

The equivalent d.c. value of an a.c. waveform; 0.707 of the peak.

ROM

Read-only, non-volatile memory holding firmware and boot code.

Saturation

Transistor fully on; both junctions forward biased, V_CE about 0.2 V.

Sector

A radial wedge of a disk platter; with a track it defines a block.

Semiconductor

Material with conductivity between a conductor and an insulator.

SRAM

Static RAM; flip-flop cells, fast, no refresh, used for cache.

Time constant

τ = RC; 63 % of full charge in one, effectively full in five.

Tolerance

Permitted deviation of a component from its marked value.

Varistor

Voltage-dependent resistor whose resistance collapses above a threshold.

Volt

Unit of potential difference; one joule per coulomb.

Zener breakdown

Reverse breakdown by direct field emission in heavily doped junctions, below about 5 V.