This is a PLC Program to Implement BCD to Gray Code Conversion.

Problem Description

Implementing BCD TO Gray Code conversion in PLC using Ladder Diagram programming language.

Problem Solution

- In Gray Code only one bit changes at a time.
- Writing truth table showing the relation between Binary as input and Gray code as output.
- Since input is BCD, only 10 combinations can be made using 4 bits. (0 to 9).
- For each Gray code output D3, D2, D1 and D0, write Karnaugh-Map.
- From the K-Map, obtaining a simplified expression for each Gray Code output in terms of BCD inputs.
- Realize the code converter using the Logic Gates.
- By following actual process to convert BCD into Gray Code, Truth Table can be written as given below.

**Truth Table relating BCD to Gray Code**

Decimal BCD input Gray Code output B3 B2 B1 B0 D3 D2 D2 D0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 2 0 0 1 0 0 0 1 1 3 0 0 1 1 0 0 1 0 4 0 1 0 0 0 1 1 0 5 0 1 0 1 0 1 1 1 6 0 1 1 0 0 1 0 1 7 0 1 1 1 0 1 0 0 8 1 0 0 0 1 1 0 0 9 1 0 0 1 1 1 0 1

**Boolean expression for each BCD bits can be written as**

D3= m(8, 9) D2= m(4, 5, 6, 7, 8, 9) D1= m(2, 3, 4, 5) D0= m(1, 2, 5, 6, 9)

**Realizing code conversion using Logic Gates**

PLC Program

Here is PLC program to Implement BCD to Gray Code Conversion, along with program explanation and run time test cases.

List of Inputs and Outputs B3= I:1/0 (Input) B2= I:1/1 (Input) B1= I:1/2 (Input) B0= I:1/3 (Input) D3= O:2/0 (Output) D2= O:2/1 (Output) D1= O:2/2 (Output) D0= O:2/3 (Output)

**Ladder Diagram to obtain Gray Code output**

Program Description

- Simply by observing the logic circuit, ladder diagram is made.
- RUNG000 for output bit D3 (O:2/0) is as described earlier that the MSB of Gray Code and Binary are same, so passed the same B3 (I:1/0) bit directly.
- Since inputs are BCD, D2 (O:2/1) is obtained by just ORing inputs B2 (I:1/1) and B3 (I:1/0).
- By simplifying Boolean expressions, we can see that each inputs are EX-ORed with each other in different Rungs.

Runtime Test Cases

Decimal BCD input Gray Code output B3 B2 B1 B0 D3 D2 D2 D0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 2 0 0 1 0 0 0 1 1 3 0 0 1 1 0 0 1 0 4 0 1 0 0 0 1 1 0 5 0 1 0 1 0 1 1 1 6 0 1 1 0 0 1 0 1 7 0 1 1 1 0 1 0 0 8 1 0 0 0 1 1 0 0 9 1 0 0 1 1 1 0 1

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