Grade 11 Computer Studies · Strand 1.0 Foundation of Computer Studies · Sub-strand 1.3 Logic Gates
These are free study notes for Grade 11 learners. They follow the official KICD curriculum design for Grade 11 Computer Studies (the same topics, in the same order, that your teacher uses) and are taken from our full Grade 11 Computer Studies notes. Build every truth table the same way: list all input combinations in binary order first (00, 01, 10, 11), then work out one column at a time.
A security light comes on only when it is dark and someone moves. A washing machine starts only when the door is shut and water is in. Devices make these decisions with logic gates, tiny circuits that are the building blocks of every processor. In this topic we learn the six logic gates, their symbols and truth tables, how to predict outputs, how to derive boolean expressions from truth tables, and how gates are used in real life.
Logic gates
Logic gate
An electronic circuit that takes one or more binary inputs and gives one binary output according to a fixed rule.
Truth table
A table that shows the output of a gate or circuit for every possible combination of inputs.
Boolean expression
A way of writing a logic rule using letters and operators, such as Y = A.B.
In logic, 1 stands for true (on, high voltage) and 0 for false (off, low voltage). Gates are made from transistors, and a modern processor holds billions of them.
The six gates
| Gate | Rule | Real-life example |
|---|---|---|
| AND | Output is 1 only when ALL inputs are 1 | A bank safe needs two keys turned; two switches in series |
| OR | Output is 1 when AT LEAST ONE input is 1 | A bell at the front or back door; two switches in parallel |
| NOT | Output is the opposite of the input | A fridge light is on when the door is not closed |
| NAND | NOT AND: output is 0 only when all inputs are 1 | Basis of much computer memory |
| NOR | NOT OR: output is 1 only when all inputs are 0 | An alarm-free state: no sensor is on |
| XOR | Output is 1 when the inputs are different | A staircase light with two switches |
Memory aids
A bubble on a symbol always means "invert". In boolean work, the plus sign means OR and not adding: 1 OR 1 gives 1. NAND and NOR are called universal gates, as any other gate can be built from them alone.
Truth tables for combinations of gates
The number of rows is 2 for one input, 4 for two inputs and 8 for three inputs. Count in binary from 000 to 111 so that no combination is missed. Add a column for each middle step.
| A | B | C | A.B | C' | Y = A.B + C' |
|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 1 | 1 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 1 | 1 |
| 0 | 1 | 1 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 1 | 1 |
| 1 | 0 | 1 | 0 | 0 | 0 |
| 1 | 1 | 0 | 1 | 1 | 1 |
| 1 | 1 | 1 | 1 | 0 | 1 |
Predicting outputs
Work from the inputs towards the output, one gate at a time. To name an unknown gate, compare its outputs for inputs 00, 01, 10, 11: AND 0001; OR 0111; NAND 1110; NOR 1000; XOR 0110.
Deriving boolean expressions from truth tables
Sum of products method
- Find the rows where the output is 1.
- For each of those rows, write an AND term: use the letter if the input is 1, and NOT the letter if it is 0.
- Join the terms with OR.
- Check the expression against the table.
A table with outputs 0, 1, 1, 0
Y is 1 in rows A is 0, B is 1 (term A'.B) and A is 1, B is 0 (term A.B').
So Y = A'.B + A.B', which is the XOR gate.
Logic gates in real life
- Washing machines: start only if the door is closed AND water is in.
- Cars: a seat-belt warning sounds if the engine is on AND the belt is NOT fastened.
- Calculators and processors: XOR and AND gates add binary digits.
- Traffic lights, lifts, phones and school bells follow logic rules.
Modelling gates with a circuit
- Use dry cells only, never mains electricity.
- For AND, connect two switches in series with a bulb; for OR, connect them in parallel.
- Test all four rows and record the truth table.
- Open the switches afterwards so that the wires do not heat up.
Key points to remember
- A logic gate gives a binary output from binary inputs by a fixed rule.
- AND needs all inputs 1; OR needs at least one; NOT inverts; NAND and NOR are inverted AND and OR; XOR needs different inputs.
- A truth table has 2, 4 or 8 rows for 1, 2 or 3 inputs.
- To derive an expression, take the rows with output 1, write AND terms, and join them with OR.
- Logic gates are in washing machines, cars, calculators and all digital devices.
Practice questions
Define a logic gate. (1 mark)
Show the answer
An electronic circuit that gives one binary output from binary inputs according to a fixed rule.
Draw the truth table of a NOR gate, in the form "inputs give output". (2 marks)
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0, 0 gives 1; 0, 1 gives 0; 1, 0 gives 0; 1, 1 gives 0.
State the difference between OR and XOR. (2 marks)
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For inputs 1 and 1, OR gives 1 while XOR gives 0; XOR is 1 only when the inputs differ.
For Y = (A + B).C, find Y when A is 0, B is 1 and C is 1. (2 marks)
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A + B is 1, and 1 AND 1 gives 1.
How many rows does the truth table of a four-input circuit have? (1 mark)
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2 × 2 × 2 × 2 = 16.
A gate has outputs 1, 1, 1, 0 for inputs 00, 01, 10, 11. Name it and write its expression. (2 marks)
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NAND; Y = (A.B)'
Y is 1 only in rows 0, 0 and 1, 1. Derive the boolean expression. (2 marks)
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Y = A'.B' + A.B
Give two real-life applications of logic gates. (2 marks)
Show the answer
For example: a seat-belt warning (AND with NOT) and a staircase light (XOR).
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