This is a PLC Program to Implement Binary to BCD Converter.

Problem Description

Implementing Binary to BCD converter in PLC using Ladder Diagram programming language.

Problem Solution

- Writing truth table showing the relation between Binary as input and BCD as output.
- To obtain these equations, Karnaugh-Map method is again used.
- For each BCD output D4, D3, D2, D1 and D0, write Karnaugh-Map.
- From the K-Map, obtaining a simplified expression for each BCD output in terms of Binary inputs.
- Realize the code converter using the Logic Gates.
- And from the same simplified expressions, draw a Ladder Diagram to obtain BCD output in terms of Binary inputs.

**Truth Table relating Binary to BCD**

Decimal Binary input BCD output B3 B2 B1 B0 D4 D3 D2 D2 D0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 2 0 0 1 0 0 0 0 1 0 3 0 0 1 1 0 0 0 1 1 4 0 1 0 0 0 0 1 0 0 5 0 1 0 1 0 0 1 0 1 6 0 1 1 0 0 0 1 1 0 7 0 1 1 1 0 0 1 1 1 8 1 0 0 0 0 1 0 0 0 9 1 0 0 1 0 1 0 0 1 10 1 0 1 0 1 0 0 0 0 11 1 0 1 1 1 0 0 0 1 12 1 1 0 0 1 0 0 1 0 13 1 1 0 1 1 0 0 1 1 14 1 1 1 0 1 0 1 0 0 15 1 1 1 1 1 0 1 0 1

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

D4= m(10, 11, 12, 13, 14, 15) D3= m(8, 9) D2= m(4, 5, 6, 7, 14, 15) D1= m(2, 3, 6, 7, 12, 13) D0= m(1, 3, 5, 7, 9, 11, 13, 15)

**Realizing code conversion using Logic Gates**

PLC Program

Here is PLC program to Implement Binary to BCD Converter, 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) D4= O:2/0 (Output) D3= O:2/1 (Output) D2= O:2/2 (Output) D1= O:2/3 (Output) D0= O:2/4 (Output)

**Ladder Diagram to obtain BCD output**

Program Description

- D4 is MSB bit of BCD output.
- D3 is 2nd bit of BCD output and so are similarly D2, D1 and D0, 3rd, 4th and LSB of BCD output respectively.
- B3 to B0 are 4 Binary inputs which are converted into BCD numbers.
- RUNG000 is used for D4 bit and so on till RUNG004 which is used for LSB D0.
- As we apply any 4bit binary input, B3 to B0 are set to 1 such that D4 to D0 bits go high according to BCD patterns of the applied Binary input.

Runtime Test Cases

Hexa- Decimal Decimal Binary input BCD output B3 B2 B1 B0 D4 D3 D2 D2 D0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 2 2 0 0 1 0 0 0 0 1 0 3 3 0 0 1 1 0 0 0 1 1 4 4 0 1 0 0 0 0 1 0 0 5 5 0 1 0 1 0 0 1 0 1 6 6 0 1 1 0 0 0 1 1 0 7 7 0 1 1 1 0 0 1 1 1 8 8 1 0 0 0 0 1 0 0 0 9 9 1 0 0 1 0 1 0 0 1 A 10 1 0 1 0 1 0 0 0 0 B 11 1 0 1 1 1 0 0 0 1 C 12 1 1 0 0 1 0 0 1 0 D 13 1 1 0 1 1 0 0 1 1 E 14 1 1 1 0 1 0 1 0 0 F 15 1 1 1 1 1 0 1 0 1

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