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CLO1 - M5 - Mc Cluskey Method

Boole Algebra and Logic Series

Introduction:

129

Completion of K-Map matter often becomes difficult because we have to determine that the combination of cell graphically (mapping)Mc Cluskey With this method we can more easily determine the simplest option of the many possibilities that exist, because although it is still visually, the method of Mc Cluskey use the table to determine the combination of selection combined

Introduction (continued)

130

Examples of problems:How do I determine the simplest combination options of merging the cell as shown in K-Map this?

00 01 11 10

00

01

11

10

A B

C DT

101198

14151312

6754

2310

1X1X

0X1X

X10X

XX01

Mc Cluskey Method (continued)

131

00 01 11 10

00

01

11

10

A B

C DT

101198

14151312

6754

2310

11X1

X001

0011

0111

Example1 How many combined 4 cells that could be made?Is there a cell '1' which have only one possibility of joint selection?How many possible choices can be made from a cell composite "1" that have not been selected?Minimal options which includes most cell "1" that have not been selected?

Mc Cluskey Method (continued)

132

Example 1 00 01 11 10

00

01

11

10

A B

C DT

101198

14151312

6754

2310

11X1

X001

0011

0111

Mc Cluskey Method (continued)

0 1 3 4 5 8 10 11 12

B C V V V

B D V V V

A C V V V V

A D V V V

A B V V V

C D V V V V

133

Example 1

T =

Mc Cluskey Method (continued)

134

00 01 11 10

00

01

11

10

A B

C DT

101198

14151312

6754

2310

1XXX

10X1

X011

01X0

Example 2How many combined 4 cells that could be made?Is there a cell '1' which have only one possibility of joint selection?How many possible choices can be made from a cell composite "1" that have not been selected?Which option is the most widely cell contains "1" that have not been selected?

Mc Cluskey Method (continued)

135

Example 200 01 11 10

00

01

11

10

A B

C DT

101198

14151312

6754

2310

1XXX

10X1

X011

01X0

Mc Cluskey Method (continued)

3 4 5 10 12 14

B D V

B D V V V

B C V V V

A D V V V

A C V

A B V

C D V

136

Example 2

T =

Mc Cluskey Method (continued)

137

00 01 11 10

00

01

11

10

A B

C DT

101198

14151312

6754

2310

1111

0XX1

110X

XX01

Example 3 How many combined 4 cells that could be made?Is there a cell '1' which have only one possibility of joint selection?How many possible choices can be made from a cell composite "1" that have not been selected?Which option is the most widely cell contains "1" that have not been selected?

Mc Cluskey Method (continued)

138

Example 300 01 11 10

00

01

11

10

A B

C DT

101198

14151312

6754

2310

1111

0XX1

110X

XX01

Mc Cluskey Method (lanjutan)

0 6 7 8 9 10 11 12

B D V V V

B C V V

A D V V

A C V V

A C V V V

A D V V

A B V V V V

C D V V V

C D V V

139

Example 3

T =

Mc Cluskey Method (lanjutan)

CONCLUSION:With the method of Mc Cluskey possible to obtain a combined selection of several possible combinations equally simple.The next election can be based on:The simplicity of the equation (the number of inputs, the number of inverse form, SOP-POS)Circuit simplicity (ease of component selection with respect to the number of gates in each IC chip)Exercise:How many possible answers to

T = m (0, 1, 6, 8, 9, 10, 11, 14, 15) + d (4, 5, 7)?

140

141