This article is about Numbering System in PLC for understanding Digital System in Programmable logic controllers. Read Also Previous Articles if you did not read before.

- Lecture 1: What is Programmable Logic Controller in PLC?
- Lecture 2: PLC Hardware Components â€“ PC Information
- Lecture 3: PLC Internal Architecture and Diagram Explanation
- Lecture 4: What is PLC System? and Working Principle
- Lecture 5: How to Connect Input Devices to PLC? Input Devices Examples
- Lecture 6: How to Connect Output Devices to PLC? PLC Output Devices
- Lecture 7: PLC Applications Examples And Solutions

## Numbering System in PLC

The text explains the basic concepts of number systems and introduces the notion of binary digits as the fundamental units in digital systems. Here are the key points:

**Binary Digits:**

- Digital systems work with binary digits, represented by 0 and 1.
- These binary digits serve as off/on signals in digital systems.

**Decimal System:**

- The decimal system, also known as the denary system, is used for everyday calculations.
- It is based on 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
- In the decimal system, the position of a digit in a number determines its weight, with the weight increasing by a factor of 10 from right to left.

**Counting and Number Systems:**

- Counting can be done in any base (number system).
- The decimal system is convenient because most people have 10 fingers.
- Computers and PLC systems use the binary system (base 2) due to its convenience in their operations.
- PLC systems may use other number systems, such as the octal system (base 8) for addressing.

**Logic Systems:**

- Combinational logic systems take binary inputs and produce a binary output based on their current state.
- The relationship between inputs and the output in combinational logic systems can be represented using truth tables.
- Sequential logic systems consider the history of past inputs along with the present inputs to determine the output.
- Both combinational logic and sequential logic systems are introduced in the chapter.

Understanding number systems, especially binary, and logic systems is crucial in the context of digital systems and PLCs, as they form the basis for representing information and performing logical operations.

The denary or decimal system is the number system used for everyday calculations, and it is based on 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. In the decimal system, the position of a digit in a number determines its weight or place value.

For example, in the denary number 1234:

- The digit 1 is in the thousands place (10^3).
- The digit 2 is in the hundreds place (10^2).
- The digit 3 is in the tens place (10^1).
- The digit 4 is in the units place (10^0).

Each digit’s value is determined by multiplying the digit by its corresponding place value. The weights increase by a factor of 10 as we move from right to left.

It’s important to note that counting can be done using number systems other than the decimal system. Different cultures and historical contexts have used various number systems, such as binary (base 2), octal (base 8), and hexadecimal (base 16). In digital systems, the binary system (base 2) is particularly important as it aligns with the fundamental on/off nature of digital signals.

The denary system, or decimal system, is convenient for everyday counting because we have ten fingers, which naturally led to the use of ten digits: 0 to 9. However, in the realm of computers and PLC systems, counting is based on binary numbers because it aligns with the fundamental nature of digital signals, which can be represented by two states: on and off.

In binary, there are only two digits: 0 and 1. Computers and PLCs use binary numbers to represent and manipulate data internally. For example, binary digits, or bits, are used to represent the state of electronic switches or transistors in a computer’s memory or logic circuits. Binary numbers are also used for addressing memory locations and representing data in various formats.

Although the PLC itself works with binary numbers, other number systems are used when working with input and output addresses in PLC programming. One commonly used system is the octal system, which is based on the digits 0 to 7. Octal representation can be convenient when working with large binary numbers because each octal digit represents three binary digits.

In addition to number systems, the chapter also covers logic systems. Combinational logic systems take binary inputs and combine them to produce a binary output. The relationship between the inputs and the output can be described using truth tables, which show the output for all possible input combinations. Sequential logic systems, on the other hand, consider the history of past inputs in addition to the present inputs to determine the output. Both combinational and sequential logic systems play a crucial role in digital systems and are introduced in the chapter you mentioned.