PLC Program to Perform Various Boolean Functions with Don’t Care Condition

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.

plc-program-implement-various-boolean-functions-dont-care-condition-01

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
plc-program-implement-various-boolean-functions-dont-care-condition-02

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

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He lives in Bangalore, and focuses on development of Linux Kernel, SAN Technologies, Advanced C, Data Structures & Alogrithms. Stay connected with him at LinkedIn.

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