# PLC Program to Implement 2-bit Magnitude Comparator

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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)```
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)```
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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