This is a PLC program to implement Excess-3 to BCD converter.

Problem Description

Implementing Excess-3 to BCD conversion in PLC using Ladder Diagram programming language

Problem Solution

- BCD can be derived from Excess-3 code by reversing the process used in conversion of BCD to Excess-3 code which is to subtract 0011 or 0011 0011 from given BCD number.
- For example, Decimal number 12 is represented as 0100 0101 in Excess-3 code. If we subtract 3 (0011 0011) from given Excess-3 code, then the corresponding BCD is 0001 0010.
- Write the truth table relating Excess-3 and BCD.
- Write Karnaugh-Map for each output and obtain simplified expression.
- Implement Excess-3 code to BCD converter using Logic Gates.
- Implement Logic Gates’ circuit in PLC using Ladder Diagram programming language.

**Truth Table relating BCD and Excess-3 codes**

Decimal Excess-3 inputs BCD outputs E3 E2 E1 E0 B3 B2 B1 B0 0 0 0 0 0 x x x x 1 0 0 0 1 x x x x 2 0 0 1 0 x x x x 3 0 0 1 1 0 0 0 0 4 0 1 0 0 0 0 0 1 5 0 1 0 1 0 0 1 0 6 0 1 1 0 0 0 1 1 7 0 1 1 1 0 1 0 0 8 1 0 0 0 0 1 0 1 9 1 0 1 1 0 1 1 0 10 1 0 1 0 0 1 1 1 11 1 0 0 1 1 0 0 0 12 1 1 0 0 1 0 0 1 13 1 1 0 1 x x x x 14 1 1 1 0 x x x x 15 1 1 1 1 x x x x

**Boolean expression for each Excess-3 code bits**

B3= m( 11, 12) + d (0, 1, 2, 13, 14, 15) B2= m(7, 8, 9, 10) + d (0, 1, 2 13, 14, 15) B1= m(5, 6, 9, 10) + d (0, 1, 2 13, 14, 15) B0= m(4, 6, 8, 10, 12) + d (0, 1, 2 13, 14, 15)

**Karnaugh-Map for each output**

**Realizing code conversion using Logic Gates**

PLC Program

Here is PLC program to implement Excess-3 to BCD converter, along with program explanation and run time test cases.

List of Inputs and Outputs E3= I:1/0 (Input) E3= I:1/1 (Input) E1= I:1/2 (Input) E0= I:1/3 (Input) B3= O:2/0 (Output) B2= O:2/1 (Output) B1= O:2/2 (Output) B0= O:2/3 (Output)

**Ladder Diagram to obtain Excess-3 code output**

Program Description

- By simply reversing the process of BCD to Excess-3 Code conversion, BCD can be derived from given Excess-3 code.
- RUNG000 to RUNG003 are for BCD bits B3 to B0 respectively.
- Simplified expression is converted into Logic Circuit and the circuit is implemented in Ladder Diagram as shown in fig above.
- RUNG000 is for B3 in which two AND gates and output of these gates are ORed together to form bit B3. I:1/0, I:1/2, I:1/3 are connected in series as an AND gate and I:1/0, I:1/1 are connected similarly in series.
- Output of these AND gates (E3E2E1 and E3E2) are connected in parallel to each other contributing as OR function.
- Similarly all other inputs in Rungs are connected.

Runtime Test Cases

Decimal Excess-3 inputs BCD outputs E3 E2 E1 E0 B3 B2 B1 B0 3 0 0 1 1 0 0 0 0 4 0 1 0 0 0 0 0 1 5 0 1 0 1 0 0 1 0 6 0 1 1 0 0 0 1 1 7 0 1 1 1 0 1 0 0 8 1 0 0 0 0 1 0 1 9 1 0 1 1 0 1 1 0 10 1 0 1 0 0 1 1 1 11 1 0 0 1 1 0 0 0 12 1 1 0 0 1 0 0 1

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