Standard function

Method

Majority expression

Gates

Levels

Inverters

Gate inputs

$F=x_1{x}_2+{x^{\prime }}_1{x^{\prime }}_2{x}_3$

AND/OR mapping

$M\left(M\left(M\left({x^{\prime }}_1,0,{x^{\prime }}_2\right),0,x_3\right),1,M\left(x_1,0,x_2\right)\right)$

4

3

2

8

[15] [18] [20]

$M\left(M\left(M\left({x^{\prime }}_1,0,{x^{\prime }}_2\right),0,x_3\right),1,M\left(x_1,0,x_2\right)\right)$

4

3

2

8

[16]

$M\left(M\left({x^{\prime }}_1,1,x_2\right),M\left(x_1,0,x_2\right),M\left({x^{\prime }}_2,0,x_3\right)\right)$

4

2

2

9

[17]

$M\left(M\left(x_1,0,x_2\right),M{\left(x_1,1,x_2\right)}^{\prime },M\left(x_1,1,x_3\right)\right)$

4

2

1

9

[19]

$M\left(M\left({x^{\prime }}_1,1,x_2\right),M\left(x_1,{x^{\prime }}_2,x_3\right),M\left(x_1,0,x_2\right)\right)$

4

2

2

10

[21] [26]

$M\left(M\left(x_1,0,x_2\right),M{\left(x_1,1,x_2\right)}^{\prime },M\left(x_1,1,x_3\right)\right)$

4

2

1

9

$F=x_1{x}_2{x}_3+x_2{x^{\prime }}_3+x_1{x^{\prime }}_2{x^{\prime }}_3$

AND/OR mapping

$\begin{array}{l}M(M\left(M\left(M\left(x_1,0,x_2\right),0,x_3\right),0,M\left(M\left({x^{\prime }}_1,0,x_2\right),0,{x^{\prime }}_3\right)\right),\\ 0,M\left(M\left(x_1,0,{x^{\prime }}_2\right),0,{x^{\prime }}_3\right))\end{array}$

8

4

4

16

[15] [16]

$M\left(M\left(x_1,0,x_3\right),M\left(x_1,x_2,{x^{\prime }}_3\right),M\left({x^{\prime }}_1,{x^{\prime }}_2,{x^{\prime }}_3\right)\right)$

4

2

4

11

[17]

$M\left(M{\left(M\left(x_1,x_2,x_3\right),1,x_1\right)}^{\prime },x_3,M\left(x_1,x_2,{x^{\prime }}_3\right)\right)$

4

3

2

11

[18] [20]

$M\left(M\left(x_1,x_2,{x^{\prime }}_3\right),M\left({x^{\prime }}_1,0,{x^{\prime }}_3\right),M\left(x_1,{x^{\prime }}_2,x_3\right)\right)$

4

2

4

11

[19]

$M\left(M\left(x_1,x_2,{x^{\prime }}_3\right),M\left(x_1,{x^{\prime }}_2,x_3\right),M\left({x^{\prime }}_1,0,x_2\right)\right)$

4

2

3

11

[21] [26]

$M\left(M\left(x_1,0,x_3\right),M{\left(x_1,x_2,x_3\right)}^{\prime },M\left(x_1,x_2,{x^{\prime }}_3\right)\right)$

4

2

2

11

$F=x_1+x_2{x}_3$

AND/OR mapping

$M\left(M\left(x_2,0,x_3\right),1,x_1\right)$

2

2

0

4

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

$M\left(M\left(x_2,0,x_3\right),1,x_1\right)$

2

2

0

4

[17]

$M\left(M\left(x_1,1,x_3\right),x_1,x_2\right)$

2

2

0

5

[20] [21] [26]

$M\left(M\left(x_2,0,x_3\right),1,x_1\right)$

2

2

0

4

$F=x_1{x}_2+{x^{\prime }}_2{x}_3$

AND/OR mapping

$M\left(M\left(x_1,0,x_2\right),1,M\left({x^{\prime }}_2,0,x_3\right)\right)$

3

2

1

6

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

$M\left(M\left(x_1,0,x_2\right),1,M\left({x^{\prime }}_2,0,x_3\right)\right)$

3

2

1

6

[17]

$M\left(M{\left(x_1,1,x_2\right)}^{\prime },x_1,M\left(x_2,1,x_3\right)\right)$

3

2

1

7

[20] [21] [26]

$M\left(M\left(x_1,0,x_2\right),1,M\left({x^{\prime }}_2,0,x_3\right)\right)$

3

2

1

6

$F=x_1{x}_2{x}_3+{x^{\prime }}_1{x^{\prime }}_2{x^{\prime }}_3$

AND/OR mapping

$M\left(M\left(M\left(x_1,0,x_2\right),0,x_3\right),1,M\left(M\left({x^{\prime }}_1,0,{x^{\prime }}_2\right),0,x^{\prime }\right)\right)$

5

3

3

10

[15] [18] [20]

$M\left(M\left(M\left(x_1,0,x_2\right),0,x_3\right),1,M\left(M\left({x^{\prime }}_1,0,{x^{\prime }}_2\right),0,x^{\prime }\right)\right)$

5

3

3

10

[16] [19]

$M\left(M\left({x^{\prime }}_1,1,x_2\right),M\left({x^{\prime }}_2,0,{x^{\prime }}_3\right),M\left(x_1,0,x_3\right)\right)$

4

2

3

9

[17]

$M\left(M{\left(x_1,1,x_2\right)}^{\prime },M\left(x_2,0,x_3\right),M\left({x^{\prime }}_1,0,{x^{\prime }}_3\right)\right)$

4

2

2

9

[21] [26]

$M\left(M\left(x_1,1,x_2\right),M{\left(x_2,1,x_3\right)}^{\prime },M\left({x^{\prime }}_1,1,x_3\right)\right)$

4

2

2

9