Truth-Tables, Boolean Equations

What Is a Truth Table?

A Truth Table lists all possible input combinations for a logic circuit and the corresponding output for each combination. It's used to visualise and analyze logic gates and expressions.

Example: 2-input AND Gate

A	B	Output (A AND B)
0	0	0
0	1	0
1	0	0
1	1	1

Boolean Equations

Boolean Equations represent logic operations mathematically, using symbols like:

+ → OR

· → AND

¬ or ' → NOT

Common Logic Functions

Operation	Symbol	Equation Example	Output Rule
AND	·	A · B	Output is 1 only if both are 1
OR	+	A + B	Output is 1 if either is 1
NOT	¬ or '	¬A or A'	Output is 1 if A is 0
XOR	⊕	A ⊕ B	Output is 1 if inputs differ

Example: Boolean Equation to Truth Table

Let’s take a logic expression: Y = A · B + ¬C

A	B	C	¬C	A·B	Y (A·B + ¬C)
0	0	0	1	0	1
0	0	1	0	0	0
0	1	0	1	0	1
0	1	1	0	0	0
1	0	0	1	0	1
1	0	1	0	0	0
1	1	0	1	1	1
1	1	1	0	1	1

 

Scan cycle of PLC

Understanding PLC Program Execution and Scan Time

In an automated system, a Programmable Logic Controller (PLC) continuously executes its logic program in a repetitive cycle, known as the scan cycle, as long as the system remains powered.

How a PLC Executes a Program

1. Input Status Update The PLC reads signals from physical input devices (sensors, switches) and stores them in a dedicated memory area called the I/O Image Table. This acts as a snapshot of all input states.

2. Logic Evaluation The PLC executes the program from the first rung to the last, using the I/O Image Table rather than real-time input values. This ensures consistent logic evaluation during the scan.

3. Output Update Once all logic instructions are processed, the PLC updates the output states—activating actuators, relays, etc.—based on the computed results.

 What Is Scan Time?

Scan time is the total time taken to complete one full input-process-output cycle.

• For modern PLCs and small programs, scan time may be just a few milliseconds.

• Older PLCs or complex programs may take 50–100 ms or more, potentially causing sluggish responses in fast-changing processes.

If scan time is excessive, the system may fail to detect quick events, leading to inaccurate control or missed inputs.

 Role of Special-Purpose I/O Modules

To overcome scan time limitations, certain tasks are handled by dedicated I/O modules:

• High-Speed Counters: Capture fast pulses from devices like shaft encoders.

• Precision Timers: Measure short durations more accurately than standard scan-based logic.

• Isolated I/O Units: Operate independently from the scan cycle to ensure reliable real-time performance.

These modules collect data at hardware speed, unaffected by PLC scan delays. The PLC simply reads their accumulated values for decision-making.

Learn about Siemens Logo PLC and its Programming

Getting Started with LOGO! – Siemens Universal Logic Module

🧩 What Is LOGO?

LOGO! is a compact, modular logic controller developed by Siemens, designed to simplify small automation projects. It combines key elements of control, display, power, and communication into one easy-to-use unit, making it a popular choice for both industrial and residential automation solutions.

🛠️ Key Integrated Features of LOGO!

LOGO! is engineered with built-in components that reduce the need for additional hardware:

• Logic Controller: Executes automation programs through intuitive ladder logic or function block diagrams.

• Integrated Display Panel: Features a backlit screen for on-site monitoring and basic user interaction.

• Power Supply Unit: Powers the internal logic and connected components.

• Expansion Interface: Allows connection to I/O expansion modules for scaling up applications.

• Micro SD Card Slot: Stores program data, configuration files, and can be used for firmware updates.

• Text Display Expansion (TDE) Interface: Connects to an optional external text display unit for enhanced visualization.

• Standard Logic Functions: Includes ready-to-use blocks like:

  • ON-delay / OFF-delay timers

  • Pulse generators

  • Softkey operations

• Digital and Analog Flags: Used for internal status signaling and memory functions.

• Configurable Inputs and Outputs: Based on model type, these can include digital I/O, analog inputs (e.g., 0–10V), or relay outputs.

🌐 Enhanced Features in LOGO! 8

The latest LOGO! 8 version builds on previous generations with modern enhancements:

• Ethernet Communication Interface: Enables integration with other LOGO! modules, PCs, or SCADA systems using protocols like Modbus TCP.

• Functional Earth (FE) Terminal: Improves electrical safety and shielding performance by connecting to protective ground.

• Ethernet Status LED: Indicates data transmission activity and network connection health.

💡 Application Areas for LOGO!

LOGO! is versatile across multiple domains, offering simple yet powerful automation solutions:

🏠 Residential & Installation Engineering:

• Staircase lighting control

• Outdoor lighting automation

• Sun blinds and roller shutter management

• Shop window display timing

• Energy-saving scheduling for electrical loads

🧰 Industrial & Machinery Solutions:

• Compact switch cabinet automation

• Simple motor or gate control systems

• Air-conditioning and HVAC applications

• Rainwater harvesting pump control

• Monitoring systems for small mechanical setups

Learn More 

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