# PLC Program to Convert Excess-3 to BCD

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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```

Sanfoundry Global Education & Learning Series – PLC Algorithms.