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Lesson 2: Digital Electronics and Logic Gates (NOT, AND, OR)

Physics

Lesson 2: Digital Electronics and Logic Gates (NOT, AND, OR)

Overview

Overview

🌳 Concept tree

Lesson 2→Digital Electronics and Logic Gates (NOT, AND, OR)

├── Analog and digital signals

├── The binary number system

├── The advantage of digital systems→immunity to noise

├── Logic gates

├── Worked examples (Lesson 5)

├── Chapter summary

└── Common mistakes

Lesson 2: Digital Electronics and Logic Gates (NOT, AND, OR) · 1 / 9
Analog and digital signals

Analog and digital signals

  • All electronic systems deal with natural quantities (sound, light, temperature) by converting them to electrical signals; for example, the microphone converts sound to a voltage, the video camera converts an image to electric signals.
  • In TV, picture and sound are converted to electrical signals, then to electromagnetic waves at the transmitter, and back to electrical signals at the receiver.
  • Electronics in which the signal can take any value in a continuous range, imitating the natural quantity, is called analog electronics.
  • In digital electronics the signal has only two possible values representing two states, 0 and 1 (low and high voltage).
  • Any number, letter or symbol is encoded as a string of 0’s and 1’s (the binary system).
Lesson 2: Digital Electronics and Logic Gates (NOT, AND, OR) · 2 / 9
The binary number system

The binary number system

  • The decimal system uses ten digits and weights 100, 101, 102, … For example 17 = 1 × 101 + 7 × 100.
  • The binary system has two digits (0 and 1) and weights 20, 21, 22, 23 … For example:

3 = 1 × 21 + 1 × 20 = 11₂

5 = 1 × 22 + 0 × 21 + 1 × 20 = 101₂

13 = 8 + 4 + 0 + 1 = 1101₂

  • 10110₂ = 16 + 0 + 4 + 2 + 0 = 22.
  • With n binary digits (bits) we can represent 2n different values: 8 bits give 256 values.
  • An analog-to-digital converter (ADC) encodes the natural signal into binary code; at the receiver a digital-to-analog converter (DAC) decodes it back.
  • Pictures are divided into tiny elements called pixels and each is coded.
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The advantage of digital systems: immunity to noise

The advantage of digital systems: immunity to noise

  • In nature there are unwanted, random signals called electrical noise, caused by the random motion of electrons (charged particles whose random motion causes minute fluctuating currents).
  • Noise disturbs the information carried by an analog signal, and cannot easily be removed: in a weak radio station it is heard as a hiss, in a weak TV station (or with a poor antenna) it appears as "salt and pepper" spots.
  • In a digital system the information is not in the exact voltage but in whether the signal is the 0 state or the 1 state; a small noise added to either value does not change its state, so the information is recovered exactly.
  • This is the main advantage of digital electronics, and it is why mobile telephony, digital satellite TV, CDs and computers are digital.
  • The computer must convert everything (numbers, letters, images) to binary code.
  • It performs all calculations using Boolean (binary) algebra.
  • It stores information temporarily in RAM (random access memory) and permanently on the hard disk, in which small regions are magnetised in one direction for 0 and the opposite direction for 1.
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Logic gates

Logic gates

  • The circuits that perform logic operations on binary signals are called logic gates.
  • They are the building blocks of computers and communication systems and are made from transistors (as switches).
  • The basic gates are:
  • 1) NOT gate (inverter) one input, one output; the output is the opposite of the input.
A Y = NOT A
0 1
1 0
Switch analogya switch in parallel with the lamp: when the switch is closed (on) the lamp is off, and vice versa.
2) AND gatetwo or more inputs and one output; the output is 1 only if all inputs are 1 (the "coincidence" gate).
A B Y = A AND B
0 0 0
0 1 0
1 0 0
1 1 1
Switch analogytwo switches in series with a lamp: both must be closed for the lamp to light.
3) OR gatetwo or more inputs and one output; the output is 1 if at least one input is 1 (the "optionality" gate).
A B Y = A OR B
0 0 0
0 1 1
1 0 1
1 1 1
Switch analogytwo switches in parallel with a lamp: closing either one lights the lamp.
Combined gates.Placing a NOT gate after an AND gate gives NAND; after an OR gate it gives NOR:
A B AND NAND (= NOT AND) OR NOR (= NOT OR)
0 0 0 1 0 1
0 1 0 1 1 0
1 0 0 1 1 0
1 1 1 0 1 0
  • All the operations of a computer are built from such gates.
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Worked examples (Lesson 5)

Worked examples (Lesson 5)

Comparison aspectMain ideaKeywords
Example 5.1 — binary conversion.Convert 45 to binary: 45 = 32 + 8 + 4 + 1 = 101101₂. Convert 1001₂ to decimal: 8 + 0 + 0 + 1 = 9Convert101101₂1001₂decimal
Example 5.2 — a compound circuit.
  • The output of an OR gate with inputs A and B feeds an AND gate whose second input is C. For A = 1
  • B = 0
  • C = 1: OR gives 1
  • AND(1
  • 1) = 1. For A = 0
  • B = 0
  • C = 1: OR = 0 so output 0
outputgateinputsfeeds
Example 5.3 — truth table of "AND followed by NOT".
  • Rows (A
  • B): 00 → AND 0 → 1
  • 01 → 0 → 1
  • 10 → 0 → 1
  • 11 → 1 → 0
Rows
Example 5.4 — number of bits.To store 1000 different values you need 10 bits (210 = 1024)store1000differentvalues
Lesson 2: Digital Electronics and Logic Gates (NOT, AND, OR) · 6 / 9
Chapter summary

Chapter summary

Comparison aspectMain ideaKeywords
Metal
  • positive ions and a cloud of free electrons
  • Pure silicon: covalent bonds
  • at low T no free electrons
  • at higher T bonds break and free electrons + holes appear in equal numbers
positiveionscloudfree
•
  • Conductivity of a semiconductor depends on two carriers (electrons and holes) and increases with temperature
  • semiconductors are sensitive to light
  • heat
  • pressure etc
  • so they serve as sensors
Conductivitysemiconductordependscarriers
Doping
  • pentavalent donors give n-type (n = p + ND)
  • trivalent acceptors give p-type (p = n + NA)
  • np = nᵢ2
pentavalentdonorsgivetype
p-n junction (diode)
  • depletion region
  • internal field
  • forward bias conducts
  • reverse bias blocks
  • used for rectification and
  • reverse-biased
  • as a variable capacitor (varactor
  • electronic tuning)
depletionregioninternalfield
Transistor (n-p-n or p-n-p)
  • IE = IB + IC
  • α = IC/IE ≈ 1
  • β = IC/IB ≫ 1
  • β = α/(1−α). Used as amplifier and switch/inverter: VCC = VCE + IC RC
Usedamplifierswitchinverter
•
  • Digital electronics encodes information in binary
  • immune to noise. Logic gates NOT
  • AND
  • OR (and combinations) are made of transistors
Digitalelectronicsencodesinformation
Lesson 2: Digital Electronics and Logic Gates (NOT, AND, OR) · 7 / 9
Common mistakes

Common mistakes

  • A donor atom becomes a positive ion in n-type material; an acceptor becomes a negative ion in p-type material. The crystal as a whole is neutral.
  • The "n" and "p" in the junction refer to carriers’ sign in the regions, not to the charge of the whole region.
  • Forward bias = p to positive terminal.
  • α is slightly less than 1, β is large; never swap them.
  • In digital circuits, a high input to the transistor switch gives a low output.
  • .egp-ex{margin:18px 0;border:1px solid rgba(79,63,224,.2);border-radius:16px;overflow:hidden;background:#fff}.egp-ex-h{padding:10px 16px;font-weight:800;background:linear-gradient(90deg,#4f3fe0,#22c1c3);color:#fff}.egp-ex-tabs{display:flex;flex-wrap:wrap;gap:6px;padding:10px 12px;background:#f7f6ff}.egp-ex-b{border:1px solid rgba(79,63,224,.3);background:#fff;border-radius:20px;padding:5px 14px;font-weight:700;cursor:pointer}.egp-ex-b.on{background:#4f3fe0;color:#fff}.egp-ex-p{padding:12px 16px}
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Part 9

Part 9

  • 📖

🔍 In-Depth Explanations, Deductions & Multi-Book Insights:

Physics (Thanaweya Amma 2026/2027)

  • Lesson 2 – Digital Electronics and Logic Gates (NOT, AND, OR)
  • Analog electronics processes continuous voltage variations vulnerable to noise.
  • Digital electronics processes discrete binary logic (0 and 1) offering superior noise immunity.
  • Logic gates (NOT, AND, OR) form the computational building blocks of microprocessors.

🌳 Conceptual Hierarchy Tree

Digital Systems and Logic Gates

├── 1. Analog vs. Digital Signals
│ ├── AnalogContinuous waveform susceptible to atmospheric noise distortion
│ └── DigitalBinary pulses (High 1 / Low 0) easily cleaned by filtering noise
└── 2. Fundamental Logic Gates
├── NOT Gate (Inverter1 input, 1 output): Output = A̅ (Flips 0 to 1, and 1 to 0)
├── AND Gate (Conjunction2+ inputs, 1 output): Output = A · B (1 only if ALL inputs are 1)
└── OR Gate (Disjunction2+ inputs, 1 output): Output = A + B (1 if ANY input is 1)
📋 Master Teacher's Blackboard Secrets
RULE 1NOT Gate has only ONE input and ONE output: Output is always the inverse of input.
RULE 2AND Gate output is 1 ONLY when ALL inputs are 1 (equivalent to series switches).
RULE 3OR Gate output is 0 ONLY when ALL inputs are 0 (equivalent to parallel switches).
📊 MatrixLogic Gates Truth Tables Combined Matrix
Input A Input B NOT Gate (A̅) AND Gate (A · B) OR Gate (A + B)
0 0 1 0 0
0 1 1 0 1
1 0 0 0 1
1 1 0 1 1
Lesson 2: Digital Electronics and Logic Gates (NOT, AND, OR) · 9 / 9