Standard function

Method

Majority expression

Gates

Levels

Inverters

Gate inputs

F = x 1 x 2 + x 1 x 2 x 3

AND/OR mapping

M ( M ( M ( x 1 , 0 , x 2 ) , 0 , x 3 ) , 1 , M ( x 1 , 0 , x 2 ) )

4

3

2

8

[15] [18] [20]

M ( M ( M ( x 1 , 0 , x 2 ) , 0 , x 3 ) , 1 , M ( x 1 , 0 , x 2 ) )

4

3

2

8

[16]

M ( M ( x 1 , 1 , x 2 ) , M ( x 1 , 0 , x 2 ) , M ( x 2 , 0 , x 3 ) )

4

2

2

9

[17]

M ( M ( x 1 , 0 , x 2 ) , M ( x 1 , 1 , x 2 ) , M ( x 1 , 1 , x 3 ) )

4

2

1

9

[19]

M ( M ( x 1 , 1 , x 2 ) , M ( x 1 , x 2 , x 3 ) , M ( x 1 , 0 , x 2 ) )

4

2

2

10

[21] [26]

M ( M ( x 1 , 0 , x 2 ) , M ( x 1 , 1 , x 2 ) , M ( x 1 , 1 , x 3 ) )

4

2

1

9

F = x 1 x 2 x 3 + x 2 x 3 + x 1 x 2 x 3

AND/OR mapping

M ( M ( M ( M ( x 1 , 0 , x 2 ) , 0 , x 3 ) , 0 , M ( M ( x 1 , 0 , x 2 ) , 0 , x 3 ) ) , 0 , M ( M ( x 1 , 0 , x 2 ) , 0 , x 3 ) )

8

4

4

16

[15] [16]

M ( M ( x 1 , 0 , x 3 ) , M ( x 1 , x 2 , x 3 ) , M ( x 1 , x 2 , x 3 ) )

4

2

4

11

[17]

M ( M ( M ( x 1 , x 2 , x 3 ) , 1 , x 1 ) , x 3 , M ( x 1 , x 2 , x 3 ) )

4

3

2

11

[18] [20]

M ( M ( x 1 , x 2 , x 3 ) , M ( x 1 , 0 , x 3 ) , M ( x 1 , x 2 , x 3 ) )

4

2

4

11

[19]

M ( M ( x 1 , x 2 , x 3 ) , M ( x 1 , x 2 , x 3 ) , M ( x 1 , 0 , x 2 ) )

4

2

3

11

[21] [26]

M ( M ( x 1 , 0 , x 3 ) , M ( x 1 , x 2 , x 3 ) , M ( x 1 , x 2 , x 3 ) )

4

2

2

11

F = x 1 + x 2 x 3

AND/OR mapping

M ( M ( x 2 , 0 , x 3 ) , 1 , x 1 )

2

2

0

4

[15] [16] [18] [19]

M ( M ( x 2 , 0 , x 3 ) , 1 , x 1 )

2

2

0

4

[17]

M ( M ( x 1 , 1 , x 3 ) , x 1 , x 2 )

2

2

0

5

[20] [21] [26]

M ( M ( x 2 , 0 , x 3 ) , 1 , x 1 )

2

2

0

4

F = x 1 x 2 + x 2 x 3

AND/OR mapping

M ( M ( x 1 , 0 , x 2 ) , 1 , M ( x 2 , 0 , x 3 ) )

3

2

1

6

[15] [16] [18] [19]

M ( M ( x 1 , 0 , x 2 ) , 1 , M ( x 2 , 0 , x 3 ) )

3

2

1

6

[17]

M ( M ( x 1 , 1 , x 2 ) , x 1 , M ( x 2 , 1 , x 3 ) )

3

2

1

7

[20] [21] [26]

M ( M ( x 1 , 0 , x 2 ) , 1 , M ( x 2 , 0 , x 3 ) )

3

2

1

6

F = x 1 x 2 x 3 + x 1 x 2 x 3

AND/OR mapping

M ( M ( M ( x 1 , 0 , x 2 ) , 0 , x 3 ) , 1 , M ( M ( x 1 , 0 , x 2 ) , 0 , x ) )

5

3

3

10

[15] [18] [20]

M ( M ( M ( x 1 , 0 , x 2 ) , 0 , x 3 ) , 1 , M ( M ( x 1 , 0 , x 2 ) , 0 , x ) )

5

3

3

10

[16] [19]

M ( M ( x 1 , 1 , x 2 ) , M ( x 2 , 0 , x 3 ) , M ( x 1 , 0 , x 3 ) )

4

2

3

9

[17]

M ( M ( x 1 , 1 , x 2 ) , M ( x 2 , 0 , x 3 ) , M ( x 1 , 0 , x 3 ) )

4

2

2

9

[21] [26]

M ( M ( x 1 , 1 , x 2 ) , M ( x 2 , 1 , x 3 ) , M ( x 1 , 1 , x 3 ) )

4

2

2

9