plc karnaugh - 7.11

13. Consider the following boolean equation.

X= ( A + BA) A + ( CD + CD + CD)

a)Can this Boolean equation be converted directly ladder logic. Explain your answer, and if necessary, make any changes required so that it may be converted to ladder logic.

b)Write out ladder logic, based on the result in step a).

c)Simplify the equation using Boolean algebra and write out new ladder logic.

d)Write a Karnaugh map for the Boolean equation, and show how it can be used to obtain a simplified Boolean equation.

7.4PRACTICE PROBLEM SOLUTIONS

1.

				AB	AB	A B	AB
	CD			1	1	1	1
				1	1	0	1
	CD
				0	0	0	1
	C D
				0	0	0	1
	CD

2.

			CD
		00	01	11	10
00		0	0	0	0
AB 01		0	0	1	1	X = BC
11		0	0	1	1
10		0	0	0	0
	B		C

X

plc karnaugh - 7.12

3.

	CD	CD	CD	CD
AB	1	0	0	1
AB	0	0	0	0
AB	0	0	0	0
AB	0	1	1	0

-For all, B is true

B( AD + AD)

4.

FOR X						FOR Y
			CD						CD
		00	01	11	10			00	01	11	10
00		0	0	0	0	00		0	1	0	0
AB 01		0	0	0	0	AB 01		0	0	1	1
11		1	1	0	0	11		0	0	1	1
10		1	1	0	0	10		0	1	0	0

X = A

Y =

D + B C

C

B

C

A

C

X

B

C

D

Y

B

C

plc karnaugh - 7.13

5.

								FG
		00					01		11			10
DE	00	0					0		0			0	Y = G( E + D)
	01	0					1		1			0
	11	0					1		1			0
	10	0					1		1			0
		G							E					Y
									D

6.

						ABC	ABC	ABC	ABC	ABC	ABC	ABC	ABC
						1	1	0	1	0	0	0	0
	DE
						1	1	0	0	0	0	0	0
	DE
DE						1	1	0	0	0	0	0	0
						1	1	0	1	0	0	0	0
DE

ABCE

AB

output = AB + ABCE

A

B

output

A

B

C

E

7.

		A		B
							X
		D		B

plc karnaugh - 7.14

8.

						ABC	ABC	ABC	ABC	ABC	ABC	ABC	ABC
						0	0	0	0	0	1	0	0
	DE
						0	0	0	0	0	1	0	0
	DE
DE						0	1	1	1	0	1	1	0
						0	1	0	1	0	1	0	0
DE

X = ABC + D( ABC + ABC + EC)

A B C

D A B

A B

E C

X

C

C

plc karnaugh - 7.15

9.

AB

AB

A B

AB

CD

1

0

0

1

Z=B*(C+D)+A

D

1

0

0

1

B

C

CD

0

0

0

0

C D

1

1

0

1

CD

A

B

C

D

Z

A

B

C

D

A

B

C

D

A

B

C

D

A

B

C

D

A

B

C

D

A

B

C

D

plc karnaugh - 7.16

10.

A	B	C	D	X
0	0	0	0	0
0	0	0	1	0
0	0	1	0	0
0	0	1	1	0
0	1	0	0	0
0	1	0	1	0
0	1	1	0	1
0	1	1	1	1
1	0	0	0	0
1	0	0	1	0
1	0	1	0	1
1	0	1	1	0
1	1	0	0	0
1	1	0	1	0
1	1	1	0	1
1	1	1	1	0

						CD	CD			CD					CD
	AB					0	1			0					0
						0	1			0					0
	AB
						0	0			0					0
	AB
						1	1			0					0
	AB

11.

A	B	C	out					C + A B
0	0	0	0
0	0	1	1
0	1	0	0				AB
0	1	1	1					AB				A B					AB
1	0	0	0		C		1	1				1				1
1	0	1	1
1	1	0	1				1	0				0				0
					C
1	1	1	1