Logic Gates and Digital Logic
What is a Logic Gate?; The AND Gate; The OR Gate; The NOT Gate; The NAND and NOR Gates; The XOR and XNOR Gates; Boolean Algebra; De Morgan's Laws; The Half Adder; The Full Adder; Applications of Logic Gates; Practical Exercises; Digital Logic and Binary Signals; Gate Functions and Truth Tables at a Glance; Combining Gates to Build Simple Circuits; Real-World Applications of Logic Circuits
On this page19 sections
- 01Learning Objectives
- 02What is a Logic Gate?
- 03The AND Gate
- 04The OR Gate
- 05The NOT Gate
- 06The NAND and NOR Gates
- 07The XOR and XNOR Gates
- 08Boolean Algebra
- 09De Morgan's Laws
- 10The Half Adder
- 11The Full Adder
- 12Applications of Logic Gates
- 13Practical Exercises
- 14Digital Logic and Binary Signals
- 15Gate Functions and Truth Tables at a Glance
- 16Combining Gates to Build Simple Circuits
- 17Real-World Applications of Logic Circuits
- 18Practical Work
- 19Scenario-Based Questions
Learning Objectives
- Explain what a logic gate is and how it uses bits.
- Draw truth tables for the AND, OR and NOT gates.
- Describe the NAND, NOR, XOR and XNOR gates.
- Explain the use of Boolean algebra and adders.
What is a Logic Gate?
A logic gate is a tiny circuit that takes one or more binary inputs, each a 0 or a 1, and produces a single binary output according to a fixed logical rule. Gates are built from transistors and are the building blocks of every digital device; the ALU, memory and control circuits are all combinations of gates. To describe a gate, engineers use a truth table, a list of every input combination with its output. A two-input gate has 4 rows, a three-input gate 8.
The AND Gate
An AND gate has two or more inputs and its output is 1 only when all inputs are 1; if any input is 0, the output is 0. Its symbol is a flat-sided capital D with inputs on the left and the output on the right. The expression is Output = A AND B, also written as A. B or AB. A strong room that opens only when the correct code is entered AND a guard presses the button is a real-world AND because both must hold. Switches wired in series light a bulb only when both are on.
The OR Gate
An OR gate outputs 1 when at least one input is 1, and 0 only when all inputs are 0. Its symbol is the AND shape with a curved inlet, and the expression is Output = A OR B, written as A + B. An emergency light that comes on when switch A OR switch B is pressed is a real-world OR because one condition is enough. Switches wired in parallel light a bulb when either is closed.
The NOT Gate
A NOT gate has a single input and inverts it; input 0 gives output 1, and input 1 gives output 0. Its symbol is a triangle followed by a small bubble. The expression is Output = NOT A, written with a bar above the A. A fire alarm that stays silent while an override switch is ON sounds only when the override is NOT on.
The NAND and NOR Gates
NAND stands for NOT AND, which is an AND gate followed by an inverter, so its output is 0 only when all inputs are 1 and 1 in every other case; the expression is NOT (A AND B). NOR stands for NOT OR, which is an OR gate followed by an inverter whose output is 1 only when all inputs are 0; the expression is NOT (A OR B). NAND is called a universal gate because every other gate can be built from NAND gates alone; an AND gate is a NAND plus a NOT, and a NOT gate joins a NAND's inputs together.
The XOR and XNOR Gates
XOR stands for exclusive OR. Its output is 1 when the inputs differ and 0 when they are the same, so 0,1 and 1,0 give 1, while 0,0 and 1,1 give 0. Its symbol is the OR shape with an extra curved inlet, and the expression is A XOR B. XOR is essential in electronics; it builds the adders in the ALU, creates parity bits and appears in encryption. XNOR is the opposite; its output is 1 when the inputs are the same and 0 when they differ, meaning NOT (A XOR B); XNOR circuits compare two values for equality.
The table below compares all seven gates.
Boolean Algebra
Boolean algebra is the mathematics of 0 and 1. AND behaves like multiplication (0 x 1 = 0, 1 x 1 = 1), OR behaves like addition except that 1 + 1 = 1, and NOT is the complement. The order of operations is NOT first, then AND, then OR, unless brackets change it; in Output = A AND (B OR NOT C), the NOT C is done first, then the bracket, then the AND.
De Morgan's Laws
De Morgan's laws convert one logical form into another. The first law says NOT (A AND B) = (NOT A) OR (NOT B); the opposite of both being true is that at least one is false. The second law says NOT (A OR B) = (NOT A) AND (NOT B); the opposite of at least one being true is that both are false. The second law is exactly how a NOR gate behaves; the first lets a designer rebuild an AND circuit from OR and NOT gates. Prove either law by comparing both sides in a truth table.
The Half Adder
Combinational logic is a circuit whose output depends only on the present inputs, with no memory. A classic example is the half adder, which adds two bits, producing 0 + 0 = 0, 1 + 0 = 1, and 1 + 1 = 10, meaning 0 with a carry of 1. Its sum comes from an XOR gate and its carry from an AND gate, both fed by the same two inputs; the sum is A XOR B and the carry is A AND B. When both inputs are 1, XOR gives 0 and AND gives 1, which is exactly the 10.
The Full Adder
A half adder cannot handle a carry from a previous column, so real arithmetic uses a full adder with three inputs, namely A, B and a carry-in (Cin). Its sum is A XOR B XOR Cin, and its carry-out is (A AND B) OR (Cin AND (A XOR B)). The table below shows the eight combinations. To add multi-digit numbers, engineers chain one full adder per column, passing each carry-out to the next carry-in, exactly how the ALU adds.
Applications of Logic Gates
Logic gates appear throughout a computer. The ALU uses them for arithmetic, where XOR and AND gates build the adders, while other combinations carry out comparisons. Control circuits in the CPU, memory and keyboard decode signals and synchronise operations. Real-world systems work the same way; an ATM dispenses cash only when the card is valid AND the PIN is correct AND the balance is enough, and a home alarm sounds when the door OR the window sensor is triggered AND the system is armed. For any scenario, write the Boolean expression, build the truth table, and break the rule into AND, OR and NOT steps.
Practical Exercises
Test yourself with these problems before the Week 10 assessment.
State the output of AND, OR and NOT for inputs A = 1, B = 0.
Write the Boolean expression for output 1 only when A is 1 and B is 0.
Write the truth table for a NAND gate.
Draw the symbol for an XOR gate and describe its output rule.
Add 1 + 1 with a half adder and state the sum and carry.
Prove that NOT (A AND B) equals (NOT A) OR (NOT B).
Explain how a full adder is built from the same gates as a half adder.
Suggest a real gadget that uses an AND logic rule and justify your answer.
Digital Logic and Binary Signals
Digital logic is the branch of electronics that processes binary information, signals that are either 0 or 1, low or high. Every modern computer is built from circuits that follow these simple two-valued rules, and the building blocks of those circuits are called logic gates.
Inside the computer, a binary 1 is represented by a small voltage being present and a binary 0 by its absence. As signals travel along the wires of the CPU, gates read the incoming voltages, carry out a logical rule, and produce a single output voltage. Combining thousands of these simple decisions produces the arithmetic, comparison and control operations of a processor.
Because the rules are so few, they can be written precisely and tested. A logic gate is defined by its truth table, a table that lists every possible combination of inputs and the output each one produces. This week's periods build from the three basic gates, AND, OR and NOT, to the derived gates NAND, NOR and XOR, and then to full combinational circuits, exactly the path engineers follow when they design a chip.
Digital circuits work with two states, 0 and 1.
Logic gates read binary inputs and produce one binary output.
Combining gates builds the arithmetic and decision circuits of the CPU.
Truth tables record the behaviour of each gate for every input combination.
This overview connects Week 8's binary number systems with the ALU work from Week 1, showing how the 0s and 1s of data are actually manipulated inside the processor.
Gate Functions and Truth Tables at a Glance
The six gates can be grouped by how they behave. AND outputs 1 only when all inputs are 1. OR outputs 1 when at least one input is 1. NOT inverts a single input. NAND is the opposite of AND, outputting 0 only when all inputs are 1. NOR is the opposite of OR, outputting 1 only when all inputs are 0. XOR outputs 1 only when the two inputs differ.
A truth table is a complete check of a gate or a circuit. For two inputs A and B there are four combinations, 00, 01, 10 and 11, so a two-input truth table has four rows. The AND column reads 0, 0, 0, 1. The OR column reads 0, 1, 1, 1. NAND is the exact opposite of AND, 1, 1, 1, 0, while NOR is the opposite of OR, 1, 0, 0, 0. XOR reads 0, 1, 1, 0 because it is 1 only when the inputs differ.
To construct any truth table, a student lists every combination of inputs, then applies the gate rule row by row. This disciplined row by row method is exactly how combinational circuits are analysed in Period 3, and it is worth practising until it becomes automatic.
AND, output 1 only when every input is 1.
OR, output 1 when at least one input is 1.
NOT, single input inverted, 0 becomes 1 and 1 becomes 0.
NAND, output 0 only when every input is 1.
NOR, output 1 only when every input is 0.
XOR, output 1 when the inputs differ.
Combining Gates to Build Simple Circuits
Few real systems use a single gate. Engineers combine gates so that the output depends on several conditions at once, and a circuit built from connected gates is called a combinational logic circuit, because its output is a pure function of its present inputs.
A simple combined circuit can be designed step by step. Consider a system that rings a bell when a button is pressed at the same time as a key is turned. The button and the key feed an AND gate, and the result joins a second AND gate with a master switch, so the bell rings only when the master switch, the button and the key are all active. Each added gate makes the decision more selective.
Analysing such a circuit means writing the Boolean expression, building the truth table row by row, and checking it against the intended behaviour. Building the truth table for a three-input circuit produces eight rows, and the output column should match, row by row, the real-life rule the circuit is meant to enforce.
Real-World Applications of Logic Circuits
Logic circuits power the decisions of everyday machines. In a school, a door lock opens only if a correct code is entered AND a valid card is presented, an AND rule. An overhead fan in a laboratory turns on if the room is hot OR the air quality check fails, an OR rule. The alarm system from Period 3, Alarm equals D OR W AND A, is a real combination of OR and AND logic.
Inside the computer, the adder circuits of the ALU are built from XOR and AND gates, while comparison circuits decide whether one number is equal to another using XNOR logic. Even the most powerful processor is, at heart, billions of these simple gates wired together into one enormous logic circuit.
Combinational circuits combine gates so that output depends on several conditions.
Boolean expressions and truth tables let engineers verify a circuit before building it.
Alarm systems, door locks and the adder of the CPU are all built from combined gates.
This is the foundation for Week 10, where learners turn logic design into working programmes and simulations of digital circuits.
| A | B | A AND B |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
| A | B | A OR B |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
| A | NOT A |
|---|---|
| 0 | 1 |
| 1 | 0 |
| A | B | NAND (A AND B) | NOR (A OR B) |
|---|---|---|---|
| 0 | 0 | 1 | 1 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 0 |
| A | B | A XOR B | XNOR (A XOR B) |
|---|---|---|---|
| 0 | 0 | 0 | 1 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 1 |
| Gate | Rule | Symbol feature | Boolean expression | Memory phrase |
|---|---|---|---|---|
| AND | 1 only if all inputs are 1 | Flat D shape | A. B | All must be true |
| OR | 1 if at least one input is 1 | Curved inlet on the left | A + B | Any can be true |
| NOT | Inverts the single input | Triangle plus bubble | A with a bar | Flip it |
| NAND | 0 only if all inputs are 1 | AND shape plus bubble | NOT (A AND B) | Not all |
| NOR | 1 only if all inputs are 0 | OR shape plus bubble | NOT (A OR B) | None at all |
| XOR | 1 if inputs differ | Extra curved line on the left | A XOR B | Different |
| XNOR | 1 if inputs are the same | XOR shape plus bubble | NOT (A XOR B) | Same |
| A | B | Sum (XOR) | Carry (AND) |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 1 |
| A | B | Cin | Sum | Cout |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 | 0 |
| 0 | 1 | 0 | 1 | 0 |
| 0 | 1 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 | 0 |
| 1 | 0 | 1 | 0 | 1 |
| 1 | 1 | 0 | 0 | 1 |
| 1 | 1 | 1 | 1 | 1 |
| Term | Meaning |
|---|---|
| Logic gate | A tiny circuit that outputs 0 or 1 according to a fixed logical rule |
| Truth table | A list of every input combination with its output |
| AND gate | Outputs 1 only when all inputs are 1 |
| OR gate | Outputs 1 when at least one input is 1 |
| NOT gate | Inverts its single input |
| NAND gate | AND followed by NOT, outputs 0 only when all inputs are 1 |
| NOR gate | OR followed by NOT, outputs 1 only when all inputs are 0 |
| XOR gate | Outputs 1 when the inputs differ |
| XNOR gate | Outputs 1 when the inputs are the same |
| Boolean algebra | The mathematics of 0 and 1 used to describe logic circuits |
| De Morgan's laws | Rules that convert NOT (A AND B) and NOT (A OR B) into simpler forms |
| Half adder | A circuit that adds two bits, producing a sum and a carry |
| Full adder | A circuit that adds two bits plus a carry-in |
| ALU | Arithmetic Logic Unit, the part of the CPU that performs calculations |
| Combinational logic | A circuit whose output depends only on present inputs, with no memory |
| Transistor | The electronic switch from which gates are built |
Practical Work
- Draw the truth tables for AND, OR and NOT.
- Write the truth table for the NAND gate.
- Explain how a half adder adds two bits.
- Simplify a simple Boolean expression.
Scenario-Based Questions
- A student builds a circuit with two switches wired so a lamp turns on only when both switches are closed. Identify the logic gate that models this circuit and draw its truth table.
- An engineer needs a gate that outputs 0 only when both inputs are 1. Identify the gate, write its Boolean expression and explain why NAND gates are called universal gates.
- A student adds binary 1 + 1 using a half adder. State the sum and carry produced and explain why a full adder is needed when adding multi-bit numbers.
- Using De Morgan's first law, prove that NOT (A AND B) equals (NOT A) OR (NOT B) by constructing a truth table for both expressions and comparing the output columns.
- A security system activates an alarm when at least one of three sensors detects motion. Identify the type of logic gate used at each stage, write the Boolean expression for the output and explain why OR rather than AND is appropriate.
- A computer technician explains that the ALU inside the CPU is built from logic gates. Name two specific operations the ALU performs and identify which gates are used to implement each operation.
- A student is asked to design a circuit whose output is 1 only when inputs A and B are different. Identify the gate, write the Boolean expression and draw the truth table to verify the design.
LEARNING OBJECTIVES: BY THE END OF THE LESSON STUDENTS SHOULD BE ABLE TO:
| Cognitive | i. Explain what a logic gate is and how it uses bits. ii. Draw truth tables for the AND, OR and NOT gates. iii. Describe the NAND, NOR, XOR and XNOR gates. iv. Explain the use of Boolean algebra and adders. |
| Affective | i. Appreciate the value of Logic Gates and Digital Logic in school, at home and in the community. ii. Show willingness to use digital tools carefully, safely and responsibly. |
| Psychomotor | i. Draw the truth tables for AND, OR and NOT. ii. Write the truth table for the NAND gate. iii. Explain how a half adder adds two bits. iv. Simplify a simple Boolean expression. |
Rationale: A logic gate is a tiny circuit that takes one or more binary inputs, each a 0 or a 1, and produces a single binary output according to a fixed logical rule. Understanding what is a Logic Gate?, the AND Gate, the OR Gate, the NOT Gate helps learners use digital technology confidently, safely and responsibly.
Pre-requisite Knowledge: In Week 5, learners studied Number Systems and Data Representation, including understanding Number Systems, binary Number System, converting Decimal to Binary. The knowledge from that week is used again in this lesson.
Learning Material/Teaching Aid: Whiteboard, markers, computer or laptop where available, printed notes and charts on Logic Gates and Digital Logic, practical task sheets, learners' notebooks and pens.
Reference Materials: Digital Technology for Senior Secondary Schools (SS 2); NERDC Digital Technology Curriculum; Digital Technology SS 2 First Term Notes (Week 6); First Term examination and Continuous Assessment question papers.
LESSON DEVELOPMENT
| Stage/Step (Time) | Teacher's Activities | Student's Activities | Learning Points |
|---|---|---|---|
| Introduction 5 MINUTES | Welcomes learners, revises Week 5 (Number Systems and Data Representation) with two quick oral questions, and asks what they already know about Logic Gates and Digital Logic. Elicits responses and writes the topic on the board. | Recall the previous lesson and share what they already know about Logic Gates and Digital Logic. | Connecting prior knowledge to Logic Gates and Digital Logic. |
| Step 1 6 MINUTES | Covers What is a Logic Gate?: A logic gate is a tiny circuit that takes one or more binary inputs, each a 0 or a 1, and produces a single binary output according to a fixed logical rule. Covers The AND Gate: An AND gate has two or more inputs and its output is 1 only when all inputs are 1; if any input is 0, the output is 0. Covers The OR Gate: An OR gate outputs 1 when at least one input is 1, and 0 only when all inputs are 0. Also covers The NOT Gate. | Listen, take notes and answer oral questions on "What is a Logic Gate?" and related points. | Understanding: What is a Logic Gate?; The AND Gate; The OR Gate; and related ideas. |
| Step 2 6 MINUTES | Covers The NAND and NOR Gates: NAND stands for NOT AND, which is an AND gate followed by an inverter, so its output is 0 only when all inputs are 1 and 1 in every other case; the expression is NOT (A AND B). Covers The XOR and XNOR Gates: XOR stands for exclusive OR. Covers Boolean Algebra: Boolean algebra is the mathematics of 0 and 1. Also covers De Morgan's Laws. | Copy the key points, give examples from school and everyday life, and ask questions on "The NAND and NOR Gates" and related points. | Understanding: The NAND and NOR Gates; The XOR and XNOR Gates; Boolean Algebra; and related ideas. |
| Step 3 6 MINUTES | Covers The Half Adder: Combinational logic is a circuit whose output depends only on the present inputs, with no memory. Covers The Full Adder: A half adder cannot handle a carry from a previous column, so real arithmetic uses a full adder with three inputs, namely A, B and a carry-in (Cin). Covers Applications of Logic Gates: Logic gates appear throughout a computer. Also covers Practical Exercises. | Discuss in pairs, then report one point on "The Half Adder" and related points to the class. | Understanding: The Half Adder; The Full Adder; Applications of Logic Gates; and related ideas. |
| Step 4 6 MINUTES | Covers Digital Logic and Binary Signals: Digital logic is the branch of electronics that processes binary information, signals that are either 0 or 1, low or high. Covers Gate Functions and Truth Tables at a Glance: The six gates can be grouped by how they behave. Covers Combining Gates to Build Simple Circuits: Few real systems use a single gate. Also covers Real-World Applications of Logic Circuits. | Respond to questions, complete the examples on the board and note down "Digital Logic and Binary Signals" and related points. | Understanding: Digital Logic and Binary Signals; Gate Functions and Truth Tables at a Glance; Combining Gates to Build Simple Circuits; and related ideas. |
| Practical Work 6 MINUTES | Guides learners through the practical work: (i) Draw the truth tables for AND, OR and NOT. (ii) Write the truth table for the NAND gate. (iii) Explain how a half adder adds two bits. Moves round the class to check progress and correct unsafe or careless use. | Carry out the practical tasks individually or in pairs and record what they did in their notebooks. | Applying the lesson through hands-on practice. |
| Evaluation 3 MINUTES | Asks learners to: i. Explain what a logic gate is and how it uses bits. ii. Draw truth tables for the AND, OR and NOT gates. iii. Describe the NAND, NOR, XOR and XNOR gates. iv. Explain the use of Boolean algebra and adders. | Respond verbally and in writing to the evaluation questions. | Assessment and consolidation of the lesson content. |
| Conclusion 2 MINUTES | Recaps the main points: what is a Logic Gate, the AND Gate, the OR Gate, the NOT Gate, the NAND and NOR Gates. Links them to the assignment and previews Week 7: Computer Networks. | Listen, ask questions and copy the assignment. | Reinforcement of key concepts and a preview of the next lesson. |
Assignment: i. A student builds a circuit with two switches wired so a lamp turns on only when both switches are closed. Identify the logic gate that models this circuit and draw its truth table. ii. An engineer needs a gate that outputs 0 only when both inputs are 1. Identify the gate, write its Boolean expression and explain why NAND gates are called universal gates.
On this page9 sections
- 01Lesson objectives
- 02Key vocabulary
- 03Common misconceptions
- 04Teacher activities
- 05Student activities
- 06Practical / learning evidence
- 07Resources and preparation
- 08Assessment for learning
- 09Inclusion and homework
Lesson objectives
By the end of the week, learners should be able to:
- Define AND, OR and NOT gates and state the operation of each.
- Complete truth tables for each gate and each compound expression.
- Simplify a Boolean expression using De Morgan's laws.
- Draw simple gate circuits on paper.
- State why combinational circuits produce predictable outputs.
Key vocabulary
- Logic gate: a circuit performing a fundamental boolean operation.
- AND gate: produces one output only when all inputs are true.
- OR gate: produces output when any input is true.
- NOT gate: inverts its single input.
- Truth table: a table listing outputs for every input combination.
- Boolean expression: a formula using AND OR NOT operators.
- De Morgan's laws: rules simplifying complex boolean expressions.
- Combinational circuit: a circuit whose output depends only on current inputs.
- Predictable output: a value determined purely by the inputs present.
Common misconceptions
- "A truth table lists one column for inputs." Truth tables list outputs as the final column.
- "De Morgan's laws apply to normal arithmetic." They apply only to boolean logic.
- "Combinational circuits have memory." Combinational circuits depend only on current inputs.
Teacher activities
- Starter: ask what happens to an AND gate when one input is false.
- Define AND, OR and NOT one by one and build truth tables.
- Demonstrate De Morgan's laws by simplifying a compound expression.
- Draw a simple AND circuit showing two inputs meeting at an output.
- Contrast combinational circuits with sequential circuits briefly.
- Close with the truth-table task and exit question.
Student activities
- Answer the starter and explain why AND gives zero when any input is false.
- Name the three basic gates and give the truth condition for each.
- Complete truth tables for AND, OR and NOT.
- Simplify a compound expression using De Morgan's laws step by step.
- Draw a simple AND circuit and label the inputs and output.
- Contrast combinational circuits with sequential circuits in one sentence.
Practical / learning evidence
Three complete truth tables, one De Morgan simplification with steps, one circuit drawing and a combinational versus sequential comparison. Submit all four for marking.
Resources and preparation
Printed truth tables, blank circuit templates and sample expressions. Offline route: paper versions, no device needed. Display any logic gates carefully and avoid touching circuit boards.
Assessment for learning
Inspect each truth table for every row filled correctly. Check the De Morgan simplification for valid steps. Mark the circuit for correct gates and connections. Flag any learner who claims a combinational circuit has memory.
Inclusion and homework
Provide the truth tables prefilled for the first row and allow oral completion of the rest. Reduce the circuit drawing to one simple gate. Extend confident learners with NAND and NOR combinations and a fourth truth-table exercise. Homework: simplify a second De Morgan expression and compare the two simplified results.