This is a PLC program to implement various boolean functions.

Problem Description

Implement following Boolean Functions in PLC Ladder Diagram programming language,

F(w,x,y)=∑(1,3,5,7) F(a,b,c,d)=∑(0,1,2,3,5,7,9,11)

Problem Solution

- Here in these 2 equations, inputs for equation (1) are w, x, and y while for equation (2) are a, b, c, and d.
- To solve this problem, we must first minimize the expression by using Karnaugh-Map method.

**Output of these equations obtained by solving K-Map is as given below.**

F(w,x,y) = y F(a,b,c,d)= ¯ab+¯ad+ ¯b d

PLC Program

Here is PLC program to implement various boolean functions, along with program explanation and run time test cases.

W = I:1/0 (Input) X = I:1/1 (Input) Y = I:1/2 (Input) F(w,x,y) = O:2/0 (Output)

Program Description

- As you can see the output of equation (1) is F(w,x,y)=y which shows that O:2/0 will go high when Y or I:1/2 is set to 1 and this is obtained by simplifying the equation by Karnaugh Map method.
- Output remains high until input Y is set irrespective of inputs W and X, that is I:1/0 and I:1/1 respectively.

**List of Inputs and Outputs for Equation (2)**

A = I:1/0 (Input) B = I:1/1 (Input) C = I:1/2 (Input) D = I:1/3 (Input) F(A,B,C,D)= O:2/0 (Output)

Program Description

- Output F(a,b,c,d)/O:2/0 here will go high in 3 conditions. As we can see from the ladder diagram and in the Boolean function which was solved using Karnaugh Map.
- There are 3 pairs of inputs connected in parallel to each other which represent OR function and connecting each of them pair of two inputs in AND function.
- Output goes high in following three conditions.
- Whenever A (I:1/0) and B (I:1/1) are Low irrespective of other input states.
- Whenever A (I:1/0) is Low AND D (I:1/3) is High irrespective of other input states.
- And whenever B (I:1/1) is Low and D (I:1/3) is High irrespective of other input states.

Runtime Test Cases

Equation(1) Inputs Output W x y O:2/0 0 0 0 LOW 0 0 1 HIGH 0 1 0 LOW 0 1 1 HIGH 1 0 0 LOW 1 0 1 HIGH 1 1 0 LOW 1 1 1 HIGH

Equation(2) Inputs Output A B C D O:2/0 0 0 0 0 HIGH 0 0 0 1 HIGH 0 0 1 0 HIGH 0 0 1 1 HIGH 0 1 0 0 LOW 0 1 0 1 HIGH 0 1 1 0 LOW 0 1 1 1 HIGH 1 0 0 0 LOW 1 0 0 1 HIGH 1 0 1 0 LOW 1 0 1 1 HIGH 1 1 0 0 LOW 1 1 0 1 LOW 1 1 1 0 LOW 1 1 1 1 LOW

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