10.1 Standard logic gate symbols

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Chapter 10 · Boolean logic

10.1 Standard logic gate symbols

Logic gates are the building blocks of digital electronic circuits. In this topic you need to recognise the six standard gate symbols and understand how truth tables organise every possible combination of binary inputs.

Logic gatesBinary inputsBinary outputTruth tables2ⁿ combinations

10.1.1 Logic gate symbols

Electronic circuits in computers, solid-state drives and control devices are made from large numbers of logic gates. A logic gate accepts one or more binary inputs and produces a binary output. Binary means that each input or output can have only one of two states: 0 or 1.

Several gates can be connected together to form a logic circuit. A logic circuit is designed to perform a particular function. The output produced by a gate or a whole circuit can be checked systematically using a truth table.

The six standard gates

The six gates introduced in the textbook are:

Figure 10.1 from the textbook showing the standard symbols for NOT, AND, OR, NAND, NOR and XOR gates
GateNumber of inputs in this courseOutput
NOT11 binary output
AND21 binary output
OR21 binary output
NAND21 binary output
NOR21 binary output
XOR21 binary output
Important: Topic 10.1 is about recognising the standard symbols and setting up truth-table inputs. The exact function and output rule for each of the six gates is covered in Topic 10.2.
Check the standard gate symbols and inputs.

Truth tables

A truth table is used to trace the output of a logic gate or a logic circuit. It lists every possible combination of binary inputs and then shows the output produced for each combination.

The NOT gate has only one input. The other five standard gates shown in Figure 10.1 have two inputs. A complete truth table must include every possible input combination, so the number of rows grows as the number of inputs increases.

Input-combination rule: the pattern shown in the source is 2n possible combinations for n binary inputs. Therefore, 2 inputs give 4 combinations, 3 inputs give 8, and 4 inputs give 16.

All possible input combinations

2 inputs · 2² = 4
AB
00
01
10
11
3 inputs · 2³ = 8
ABC
000
001
010
011
100
101
110
111
4 inputs · 2⁴ = 16
ABCD
0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
1010
1011
1100
1101
1110
1111

The order above follows binary counting. For example, a three-input truth table begins at 000 and ends at 111. A four-input table begins at 0000 and ends at 1111. When outputs are added later, each input row gets the corresponding output value for the gate or circuit being tested.

Exam tip: before working out any outputs, first make sure your truth table contains every input combination. Missing or repeating a row can make the rest of the table incorrect.
Check truth-table input combinations.

Topic 10.1 revision checklist

Explain that logic gates take binary inputs and produce a binary output.
Explain that several logic gates can be combined to form a logic circuit.
Recognise the symbols for NOT, AND, OR, NAND, NOR and XOR.
State that NOT has one input and the other five standard gates have two inputs.
Explain the purpose of a truth table.
List all four input combinations for two binary inputs.
List all eight input combinations for three binary inputs.
List all sixteen input combinations for four binary inputs.
Use the pattern 2ⁿ to determine how many input combinations are required.
Ready for a mixed Topic 10.1 check?
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