This is a PLC Program to Implement 2-bit Magnitude Comparator.
Problem Description
Implementing 2-bit comparator in PLC using Ladder Diagram programming language.
Problem Solution
- For a 2-bit comparator, each input word is 2 bit long.
- Writing truth table showing the comparison of input words.
- For each output AB, write Karnaugh-Map.
- From the K-Map, obtaining a simplified expression for each output in terms of 2-bit inputs.
- Realize the code converter using the Logic Gates.
By comparing both word inputs, Truth Table can be written as given below.
Decimals Inputs Outputs A1 A0 B1 B0 A<B A=B A>B 0 0 0 0 0 0 1 0 1 0 0 0 1 1 0 0 2 0 0 1 1 1 0 0 3 0 0 1 0 1 0 0 4 0 1 1 0 0 0 1 5 0 1 1 1 0 1 0 6 0 1 0 1 1 0 0 7 0 1 0 0 1 0 0 8 1 1 0 0 0 0 1 9 1 1 0 1 0 0 1 10 1 1 1 1 0 1 0 11 1 1 1 0 1 0 0 12 1 0 1 0 0 0 1 13 1 0 1 1 0 0 1 14 1 0 0 1 0 0 1 15 1 0 0 0 0 1 0
Boolean expression for each output bit can be written as
A<B = m(1, 2, 3, 6, 7, 11) A=B = m(0, 5, 10, 15) A>B = m(4, 8, 9, 12, 13, 14)
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Realizing code conversion using Logic Gates
PLC Program
Here is PLC program to Implement 2-bit Magnitude Comparator, along with program explanation and run time test cases.
List of Inputs and Outputs A1 = I:1/0 (Input) A0 = I:1/1 (Input) B1 = I:1/2 (Input) B0 = I:1/3 (Input) A<B = O:2/0 (Output) A=B = O:2/1 (Output) A>B = O:2/2 (Output)
Ladder Diagram to obtain Binary output
Program Description
- RUNG000 is used to detect if A is less than B. first compares A1 and B1 bits. If A1 is less than B1 then O:2/0 is set otherwise it similarly compares A0 and B0.
- RUNG001 is used to detect the condition when A=B are equal. ANDing of two EX-NOR gates ae obtained by simplifying expression using De-Morgan’s Theorem.
- O:2/1 is set only when A1A0=B1B0.
- RUNG002 works similarly as RUNG000, it first compares A1 and B1, if A1 is greater than B1 then output O:2/2 is set to 1 and if not, it compares A0 and B0.
Runtime Test Cases
Decimals Inputs Outputs A1 A0 B1 B0 A<B A=B A>B 0 0 0 0 0 0 1 0 1 0 0 0 1 1 0 0 2 0 0 1 1 1 0 0 3 0 0 1 0 1 0 0 4 0 1 1 0 0 0 1 5 0 1 1 1 0 1 0 6 0 1 0 1 1 0 0 7 0 1 0 0 1 0 0 8 1 1 0 0 0 0 1 9 1 1 0 1 0 0 1 10 1 1 1 1 0 1 0 11 1 1 1 0 1 0 0 12 1 0 1 0 0 0 1 13 1 0 1 1 0 0 1 14 1 0 0 1 0 0 1 15 1 0 0 0 0 1 0
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