Logic gates, truth tables and circuits

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Apuntes de la lección

What are Logic Gates?

A logic gate is an electronic component that performs a Boolean function — a logical operation on one or more binary inputs that gives a single binary output.
Inputs and outputs are binary: either 0 (low/off) or 1 (high/on).
Logic gates are the building blocks of all digital circuits, from simple devices to complete microprocessors (which can contain over 100 million gates).
Gates can be cascaded (connected in series) to build more complex circuits, just as Boolean functions can be composed.
Most modern gates are made from transistors (specifically MOSFETs), acting as electronic switches.

The Three Basic Gates: AND, OR, NOT

AND gate: Output is 1 only if all inputs are 1; otherwise output is 0.
OR gate: Output is 1 if at least one input is 1; output is 0 only when all inputs are 0.
NOT gate (inverter): Has one input; output is the opposite of the input (0 becomes 1, 1 becomes 0).
These three gates are fundamental — any other logic function can be built using combinations of them.
Each gate has a standard symbol used in circuit diagrams (distinctive shape set).

Truth Tables

A truth table lists all possible input combinations and the corresponding output for a logic gate or circuit.
For a gate with n inputs, there are 2ⁿ possible input combinations (e.g., 2 inputs → 4 rows).
AND truth table: 00→0, 01→0, 10→0, 11→1.
OR truth table: 00→0, 01→1, 10→1, 11→1.
NOT truth table: 0→1, 1→0.
Truth tables are used to describe and compare the behaviour of logic circuits.

Combining Gates into Circuits

Logic gates can be connected in series or parallel to form circuits that perform more complex functions.
The output of one gate becomes the input of another, allowing cascading.
Example: A circuit with an AND gate followed by a NOT gate produces a NAND function (output is 0 only when both inputs are 1).
Circuits can be described by Boolean expressions (e.g., Q = NOT (A AND B)).
To find the truth table of a circuit, work through each input combination step by step.

Other Important Gates (NAND, NOR, XOR, XNOR)

NAND = NOT AND: output is 0 only when all inputs are 1.
NOR = NOT OR: output is 1 only when all inputs are 0.
XOR (exclusive OR): output is 1 when inputs are different (01 or 10).
XNOR = NOT XOR: output is 1 when inputs are the same (00 or 11).
These gates are useful because they can be built more efficiently with transistors and are often used in real circuits.

Why Logic Gates Matter

Logic gates are used to build computer memory, registers, arithmetic logic units (ALUs), and multiplexers.
They enable computers to perform calculations and make decisions based on binary inputs.
All digital electronics, from calculators to smartphones, rely on logic gates.
Understanding logic gates is the first step to understanding how software controls hardware.

History and Development

The binary system was refined by Gottfried Leibniz (1705), influenced by the ancient I Ching.
Charles Babbage used mechanical logic gates in his Analytical Engine (1837).
Claude Shannon (1930s) showed that Boolean algebra could describe switching circuits, forming the basis of digital circuit design.
The first modern electronic AND gate was built by Walther Bothe in 1924.
Early computers used relays and vacuum tubes before transistors; today, CMOS technology is dominant.

Diapositivas

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Preguntas de práctica

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1.Which of the following is a logic gate?
Easy
- AAND
- BCPU
- CRAM
- DALU
2.What is the output of an AND gate when both inputs are 1?
Easy
- A0
- B1
- CUndefined
- DError
3.A NOT gate has one input and one output.
Easy
True or false?
4.Which gate gives an output of 1 only when both inputs are different?
Easy
- AAND
- BOR
- CXOR
- DNAND
5.Match each gate to its correct description.
Medium
- AND
- OR
- NOT
- Outputs 1 only if all inputs are 1
- Outputs 1 if at least one input is 1
- Outputs the opposite of the input
6.A NOR gate is the negation of an OR gate.
Easy
True or false?
7.Which of the following is NOT a basic logic gate?
Medium
- ANAND
- BAND
- COR
- DNOT
8.Arrange the following steps to create a truth table for a circuit with 2 inputs:
Medium
- List all possible input combinations
- Determine the output for each combination
- Write the inputs and outputs in a table
- Identify the logic gates in the circuit

Más preguntas

9.Which of the following are true about logic gates? (Select all that apply)
Medium
- AThey perform Boolean functions
- BThey can be made from transistors
- CThey always have two inputs
- DThey can be combined to build circuits
10.What is the output of the whole circuit when A=1 and B=1?
Medium
- A0
- B1
- CCannot be determined
- D2
11.A circuit consists of an AND gate followed by a NOT gate. What is this circuit's output when both inputs are 1?
Medium
- A0
- B1
- CUndefined
- DError
12.A truth table for a logic circuit with 4 inputs has 16 rows.
Easy
True or false?
13.Which of the following circuits is equivalent to a NAND gate?
Hard
- AAND followed by NOT
- BOR followed by NOT
- CNOT followed by AND
- DXOR followed by NOT
14.How many rows are in a truth table for a single NOT gate?
Medium
- A1
- B2
- C4
- D8
15.A logic gate can have more than one output.
Easy
True or false?
16.Which gate gives the opposite of an XOR gate?
Medium
- ANAND
- BNOR
- CXNOR
- DOR
17.Match each gate to its truth table output for inputs (0,0):
Medium
- AND
- OR
- NAND
- 0
- 1
18.A circuit has inputs A, B, and C. It consists of an AND gate for A and B, whose output goes into an OR gate with C. What is the output when A=1, B=0, C=1?
Hard
- A0
- B1
- C2
- DCannot be determined
19.The output of an OR gate is 0 only when both inputs are 0.
Easy
True or false?
20.Which of the following is the correct symbol for a NOT gate?
Medium
- AA triangle with a circle at the output
- BA D-shaped symbol
- CA rectangle with '≥1'
- DA rectangle with '&'
21.Which of the following is a compound logic gate?
Medium
- AAND
- BOR
- CNOT
- DNAND
22.A truth table shows the output of a logic circuit for all possible input combinations.
Easy
True or false?
23.Arrange the following gates in order of increasing number of inputs typically required (1 input, 2 inputs, 2 inputs, 2 inputs):
Medium
- NOT
- AND
- OR
- XOR
24.What is the output of a NOT gate when the input is 0?
Easy
- A0
- B1
- CUndefined
- DError
25.A circuit has three inputs A, B, C. It uses an OR gate for A and B, then an AND gate with C. What is the output when A=0, B=1, C=0?
Hard
- A0
- B1
- C2
- DCannot be determined
26.A NAND gate is the same as an AND gate followed by a NOT gate.
Easy
True or false?
27.How many inputs does a NOT gate have?
Easy
- A1
- B2
- C3
- DNone
28.Match each logic gate to its correct behaviour.
Easy
- AND gate
- OR gate
- NOT gate
- Output 1 only if all inputs are 1
- Output 1 if at least one input is 1
- Output is the opposite of the input
29.Arrange the steps in the correct order to complete a truth table for a circuit with two inputs A and B.
Medium
- List all possible combinations of A and B
- Calculate the output for each combination
- Draw a table with columns for A, B and the output
30.Which of the following statements about logic gates are correct? (Select all that apply)
Medium
- AA NAND gate is an AND gate followed by a NOT gate.
- BAn XOR gate outputs 1 when both inputs are the same.
- CA NOR gate is the opposite of an OR gate.
- DA NOT gate can have two inputs.
- ELogic gates can be combined to build more complex circuits.
31.The output of an XOR gate is 1 when both inputs are 1.
Easy
True or false?
32.Match each gate to its correct output for inputs (A=1, B=0).
Medium
- AND
- OR
- NAND
- XOR
- 0
- 1
33.A circuit has three inputs A, B, C. It consists of an AND gate for A and B, and the output of that gate goes into an OR gate with C. What is the output when A=1, B=0, C=1?
Medium
- A0
- B1
- C2
- DCannot be determined
34.Put the following logic gates in order of the number of inputs they typically have, from fewest to most.
Medium
- NOT gate
- AND gate
- NAND gate
- XOR gate
35.Which of the following are examples of compound logic gates? (Select all that apply)
Medium
- ANAND
- BNOR
- CAND-OR-invert (AOI)
- DXOR
- ENOT
36.A truth table for a circuit with 2 inputs has 4 rows.
Easy
True or false?
37.Which component is used to measure the current in the circuit?
Easy
- ACell
- BSwitch
- CLamp
- DAmmeter
38.If the switch is open, the lamp will not light.
Easy
True or false?
39.In a logic circuit, which of the following is the output of a NOR gate when both inputs are 0?
Medium
- A0
- B1
- CUndefined
- DDepends on the gate
40.Arrange the following Boolean expressions in order of the number of gates needed to implement them, from fewest to most.
Medium
- A AND B
- NOT A
- A OR (B AND C)
- (A AND B) OR (C AND D)
41.Complete the sentence.
Easy
The ____ gate outputs the opposite of its input.
42.How many rows are in a truth table for a circuit with 3 inputs?
Medium
43.What is the output of an OR gate when input A=0 and input B=1?
Easy
44.Name the gate that outputs 1 only when both inputs are 1.
Easy
45.What is the output of a NAND gate when both inputs are 1?
Medium
46.Write the Boolean expression for an AND gate with inputs A and B.
Medium
47.What is the Boolean expression for a NAND gate with inputs A and B?
Medium
48.A logic circuit has 4 inputs. How many rows will its truth table have?
Medium
49.Fill in the blanks to complete the truth table for an AND gate.
Easy
For an AND gate with inputs A and B, when A=0 and B=0, output = ____; when A=1 and B=1, output = ____.
50.What is the Boolean expression for the output of an OR gate with inputs A and B?
Medium
51.In this series circuit, if the cell provides 1.5 V and the lamp has a resistance of 3 Ω, the current flowing is ___ A.
Medium
In this series circuit, if the cell provides 1.5 V and the lamp has a resistance of 3 Ω, the current flowing is ____ A.
52.Complete the sentence: A NAND gate is the same as an ___ gate followed by a ___ gate.
Easy
A NAND gate is the same as an ____ gate followed by a ____ gate.
53.Explain how logic gates can be combined to create a circuit that performs a specific Boolean function.
Hard
54.How many rows are in a truth table for a circuit with 3 inputs?
Medium
- A9
- B10
- C8
- D7
55.A logic circuit has 4 inputs. How many rows will its truth table have?
Medium
- A16
- B17
- C18
- D15

Apuntes de repaso

## Logic Gates, Truth Tables and Circuits ### What is a logic gate? A logic gate is a device that performs a Boolean function: a logical operation on one or more binary inputs that produces a single binary output. Gates are built from electronic switches (diodes or transistors, usually MOSFETs). They can be cascaded to build complex circuits like multiplexers, registers, ALUs, and microprocessors. ### The seven basic logic gates There are seven basic logic gates: NOT, OR, NOR, AND, NAND, XOR, XNOR. At KS3, you need to know AND, OR, and NOT. #### AND gate - Output is 1 only if **all** inputs are 1. - Truth table (2 inputs A, B): | A | B | Q | |---|---|---| | 0 | 0 | 0 | | 0 | 1 | 0 | | 1 | 0 | 0 | | 1 | 1 | 1 | - Symbol: D-shaped with flat back. #### OR gate - Output is 1 if **at least one** input is 1. - Truth table: | A | B | Q | |---|---|---| | 0 | 0 | 0 | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 1 | - Symbol: curved back, pointed front. #### NOT gate (inverter) - Output is the opposite of the input. - Truth table: | A | Q | |---|---| | 0 | 1 | | 1 | 0 | - Symbol: triangle with a small circle at the output. ### Combining gates into circuits Gates can be combined to create more complex logic. For example, an AND gate followed by a NOT gate makes a NAND gate. When drawing circuits, label inputs and outputs clearly, and work out the truth table step by step. ### Why logic gates matter Logic gates are the building blocks of all digital electronics. They allow computers to make decisions based on binary inputs, forming the basis of all computation. ### Key points to remember - Binary: 0 = off/false, 1 = on/true. - Truth tables list all possible input combinations and the resulting output. - For 2 inputs, there are 4 combinations (00, 01, 10, 11). - For 3 inputs, there are 8 combinations. - Always work from inputs to outputs when analysing a circuit.

Logic gate: A device that performs a Boolean function, a logical operation performed on one or more binary inputs that produces a single binary output.
Boolean function: A logical operation performed on one or more binary inputs that produces a single binary output.
Binary: A number system with only two digits: 0 and 1, representing off/on or false/true.
Truth table: A table showing all possible input combinations and the corresponding output for a logic gate or circuit.
AND gate: A logic gate whose output is 1 only if all inputs are 1.
OR gate: A logic gate whose output is 1 if at least one input is 1.
NOT gate: A logic gate whose output is the opposite of its input; also called an inverter.
NAND gate: A logic gate that is the negation of the AND statement; output is 0 only if all inputs are 1.
NOR gate: A logic gate that is the negation of the OR statement; output is 1 only if all inputs are 0.
XOR gate: A logic gate that outputs 1 if the inputs are different (exclusive OR).
XNOR gate: A logic gate that is the negation of the exclusive OR statement; outputs 1 if the inputs are the same.
Circuit: A combination of logic gates connected together to perform a more complex function.
MOSFET: Metal–oxide–semiconductor field-effect transistor, the primary electronic component used to build logic gates today.

Tarjetas

What is a logic gate?

A logic gate is a device that performs a Boolean function, a logical operation on one or more binary inputs that produces a single binary output.

What are the seven basic logic gates?

NOT, OR, NOR, AND, NAND, XOR, and XNOR.

What does the AND gate output?

The AND gate outputs 1 only if all its inputs are 1; otherwise it outputs 0.

What does the OR gate output?

The OR gate outputs 1 if at least one of its inputs is 1; it outputs 0 only if all inputs are 0.

What does the NOT gate do?

The NOT gate inverts its input: it outputs 1 if the input is 0, and 0 if the input is 1.

What is the output of a NAND gate?

A NAND gate is the negation of AND: it outputs 0 only when all inputs are 1; otherwise it outputs 1.

What is the output of a NOR gate?

A NOR gate is the negation of OR: it outputs 1 only when all inputs are 0; otherwise it outputs 0.

What is the output of an XOR gate?

An XOR (exclusive OR) gate outputs 1 if the number of 1 inputs is odd; for two inputs, it outputs 1 when exactly one input is 1.

What is the output of an XNOR gate?

An XNOR gate is the negation of XOR: it outputs 1 when the number of 1 inputs is even; for two inputs, it outputs 1 when both inputs are the same.

What is a truth table?

A truth table lists all possible combinations of inputs and shows the corresponding output for a logic gate or circuit.

Draw the truth table for a 2-input AND gate.

A B | Q 0 0 | 0 0 1 | 0 1 0 | 0 1 1 | 1

Draw the truth table for a 2-input OR gate.

A B | Q 0 0 | 0 0 1 | 1 1 0 | 1 1 1 | 1

Draw the truth table for a NOT gate.

A | Q 0 | 1 1 | 0

How can logic gates be combined?

Logic gates can be cascaded (connected in series or parallel) to form circuits that implement more complex Boolean functions.

What are some devices built from logic circuits?

Logic circuits include multiplexers, registers, arithmetic logic units (ALUs), computer memory, and complete microprocessors.

What is the fundamental concept behind all electronic digital computers?

Using electrical switches to implement logic, based on switching circuit theory, which showed that two-valued Boolean algebra can describe switching circuits.

What are the two common sets of symbols for logic gates?

The 'distinctive shape' set (traditional schematics) and the 'rectangular shape' set (ANSI/IEEE and IEC standards).

What is the standard that defines logic gate symbols?

ANSI/IEEE Std 91-1984 and its supplement 91a-1991, plus IEC 60617-12.

What is a compound logic gate? Give an example.

A compound logic gate combines multiple basic gates into one circuit, e.g., AND-OR-invert (AOI) and OR-AND-invert (OAI).

Why are compound logic gates often used?

Because their construction using MOSFETs is simpler and more efficient than the sum of individual gates.

What is the primary way of building logic gates today?

Using MOSFETs (metal–oxide–semiconductor field-effect transistors) as electronic switches.

Who refined the binary number system and when?

Gottfried Wilhelm Leibniz, published in 1705.

Who described logical operations using electrical switching circuits in 1886?

Charles Sanders Peirce.

Who invented the first modern electronic AND gate in 1924?

Walther Bothe, inventor of the coincidence circuit.

What is the output of a 2-input XOR gate when both inputs are 1?

0, because XOR outputs 1 only when the inputs are different.

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