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Boolean logic

Logic values, operations, and truth tables

This track explains TRUE/FALSE conditions, why AND needs two active inputs, how OR differs from XOR, and how to move an expression into an FBD diagram.

What you learn

TRUE and FALSE describe condition state: button pressed, sensor active, permissive available.

AND, OR, NOT, and XOR combine simple conditions into expressions.

In FBD each operation becomes a block and connections show signal flow.

A truth table checks every input combination before running the diagram.

Track topics

TRUE / FALSEANDORNOTXORtruth tableslogic expressionspractical tasks

Related lessons

Logic lessons

Next: PLC and FBD
01

Логические значения TRUE и FALSE

Что означают TRUE и FALSE в PLC-программах и как они связаны с реальными сигналами.

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02

Логическая операция AND

AND включает выход только при одновременном выполнении всех разрешающих условий.

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03

Логическая операция OR

OR объединяет несколько команд или условий, когда достаточно хотя бы одного активного сигнала.

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04

Логическая операция NOT

NOT инвертирует сигнал и помогает описывать запреты, аварии и активные низкие сигналы.

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05

Таблицы истинности

Как проверять поведение логических схем по всем сочетаниям входных сигналов.

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06

De Morgan's Laws in Logic Diagrams

Transform NOT, AND, and OR expressions, verify equivalence with a truth table, and apply De Morgan's laws in FBD.

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07

Binary Half Adder

Learn how XOR and AND add two one-bit binary numbers and produce the SUM and CARRY signals.

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Practice

Basic logic examples

Open an example, toggle inputs, and compare the output with the truth table.

Lamp from one button

A direct input-to-output connection shows the basic meaning of TRUE/FALSE.

Open example

Lamp from two buttons with AND

The lamp turns on only when both buttons are active.

Open example

Lamp from two conditions with OR

One active condition is enough to turn on the output.

Open example

A AND NOT B

Permissive A works only while blocking condition B is not active.

Open example

XOR as different states

The output is TRUE when two inputs are in different states.

Open example