This is a PLC Program to Implement Various Boolean Functions With Don’t Care Condition.

Problem Description

Implement given Boolean Function having don’t care conditions.

F(A,B,C,D)=∑m(0,1,5,9,13,14,15) + d(3,4,7,10,11)

Problem Solution

- Here in this equation inputs are A, B, C, and D and output is F (A, B, C, D) and d(3,4,7,10,11) denotes don’t care condition. To solve this problem, we must first minimize the equation by using Karnaugh-Map method which is given below.
- If don’t care condition exists, it means that output will not get affected by its state. Even if the state is true or false, output remains unchanged.

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PLC Program

Here is PLC program to Implement Various Boolean Functions With Don’t Care Condition, along with program explanation and run time test cases.

**List of Inputs and Outputs**

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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)

**Ladder diagram for the give expression**

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 D, that is when I:1/3 is high irrespective of other input states.
- Whenever A (I:1/0) and C (I:1/1) both are high irrespective of other input states.
- Whenever A (I:1/0) and C (I:1/1) both are low irrespective of other input states.

Runtime Test Cases

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

**Sanfoundry Global Education & Learning Series – PLC Algorithms.**

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