
С2. МОИ. Презентации / Булевы функции 6 (v. 1.1)
.pdf
Метод каскадов
x1
x1
f0 (x2 , x3, x4 )
(00000110)
f1(x2 , x3, x4 )
(01101110)
21

x1 |
x2 |
x3 |
x4 |
f |
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 |
1 |
|
|
|
|
|
0 |
1 |
1 |
0 |
1 |
|
|
|
|
|
0 |
1 |
1 |
1 |
0 |
|
|
|
|
|
1 |
0 |
0 |
0 |
0 |
|
|
|
|
|
1 |
0 |
0 |
1 |
1 |
|
|
|
|
|
1 |
0 |
1 |
0 |
1 |
|
|
|
|
|
1 |
0 |
1 |
1 |
0 |
|
|
|
|
|
1 |
1 |
0 |
0 |
1 |
|
|
|
|
|
1 |
1 |
0 |
1 |
1 |
|
|
|
|
|
|
|
|
|
|
1 |
1 |
1 |
0 |
1 |
|
|
|
|
|
1 |
1 |
1 |
1 |
0 |
Метод каскадов
f0 (x2 , x3, x4 )
x2 f0 (0, x3, x4) x2 f0 (1, x3, x4)
22

x1 |
x2 |
x3 |
x4 |
f |
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 |
1 |
|
|
|
|
|
0 |
1 |
1 |
0 |
1 |
|
|
|
|
|
0 |
1 |
1 |
1 |
0 |
|
|
|
|
|
1 |
0 |
0 |
0 |
0 |
|
|
|
|
|
1 |
0 |
0 |
1 |
1 |
|
|
|
|
|
1 |
0 |
1 |
0 |
1 |
|
|
|
|
|
1 |
0 |
1 |
1 |
0 |
|
|
|
|
|
1 |
1 |
0 |
0 |
1 |
|
|
|
|
|
1 |
1 |
0 |
1 |
1 |
|
|
|
|
|
|
|
|
|
|
1 |
1 |
1 |
0 |
1 |
|
|
|
|
|
1 |
1 |
1 |
1 |
0 |
Метод каскадов
f0 (x2 , x3, x4 )
x2 f0 (0, x3, x4) x2 f0 (1, x3, x4)
x2 f00 (x3, x4 ) x2 f01(x3, x4 )
23

x1 |
x2 |
x3 |
x4 |
f |
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 |
1 |
|
|
|
|
|
0 |
1 |
1 |
0 |
1 |
|
|
|
|
|
0 |
1 |
1 |
1 |
0 |
|
|
|
|
|
1 |
0 |
0 |
0 |
0 |
|
|
|
|
|
1 |
0 |
0 |
1 |
1 |
|
|
|
|
|
1 |
0 |
1 |
0 |
1 |
|
|
|
|
|
1 |
0 |
1 |
1 |
0 |
|
|
|
|
|
1 |
1 |
0 |
0 |
1 |
|
|
|
|
|
1 |
1 |
0 |
1 |
1 |
|
|
|
|
|
|
|
|
|
|
1 |
1 |
1 |
0 |
1 |
|
|
|
|
|
1 |
1 |
1 |
1 |
0 |
Метод каскадов
f0 (x2 , |
) |
x2 f0 |
, x4) x2 f0 (1, x3, x4) |
x2 f00 (x3, x4 ) x2 f01(x3, x4 )
24

x1 |
x2 |
x3 |
x4 |
f |
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 |
1 |
|
|
|
|
|
0 |
1 |
1 |
0 |
1 |
|
|
|
|
|
0 |
1 |
1 |
1 |
0 |
|
|
|
|
|
1 |
0 |
0 |
0 |
0 |
|
|
|
|
|
1 |
0 |
0 |
1 |
1 |
|
|
|
|
|
1 |
0 |
1 |
0 |
1 |
|
|
|
|
|
1 |
0 |
1 |
1 |
0 |
|
|
|
|
|
1 |
1 |
0 |
0 |
1 |
|
|
|
|
|
1 |
1 |
0 |
1 |
1 |
|
|
|
|
|
|
|
|
|
|
1 |
1 |
1 |
0 |
1 |
|
|
|
|
|
1 |
1 |
1 |
1 |
0 |
Метод каскадов
f0 (x2 , x3, x4 )
x2 f0 (0, x3, x4) x2 f0 (1, x3, x4)
x2 f00 (x3, x4 ) x2 f01(x3, x4 )
25

x1 |
x2 |
x3 |
x4 |
f |
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 |
1 |
|
|
|
|
|
0 |
1 |
1 |
0 |
1 |
|
|
|
|
|
0 |
1 |
1 |
1 |
0 |
|
|
|
|
|
1 |
0 |
0 |
0 |
0 |
|
|
|
|
|
1 |
0 |
0 |
1 |
1 |
|
|
|
|
|
1 |
0 |
1 |
0 |
1 |
|
|
|
|
|
1 |
0 |
1 |
1 |
0 |
|
|
|
|
|
1 |
1 |
0 |
0 |
1 |
|
|
|
|
|
1 |
1 |
0 |
1 |
1 |
|
|
|
|
|
|
|
|
|
|
1 |
1 |
1 |
0 |
1 |
|
|
|
|
|
1 |
1 |
1 |
1 |
0 |
Метод каскадов
f0 (x2 , x3, x4 )
x2 f0 (0, x3, x4) x2 f0 (1, x3, x4)
x2 f00 (x3, x4 ) x2 f01(x3, x4 )
f1(x2 , x3, x4 )
x2 f1(0, x3, x4) x2 f1(1, x3, x4)
26

x1 |
x2 |
x3 |
x4 |
f |
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 |
1 |
|
|
|
|
|
0 |
1 |
1 |
0 |
1 |
|
|
|
|
|
0 |
1 |
1 |
1 |
0 |
|
|
|
|
|
1 |
0 |
0 |
0 |
0 |
|
|
|
|
|
1 |
0 |
0 |
1 |
1 |
|
|
|
|
|
1 |
0 |
1 |
0 |
1 |
|
|
|
|
|
1 |
0 |
1 |
1 |
0 |
|
|
|
|
|
1 |
1 |
0 |
0 |
1 |
|
|
|
|
|
1 |
1 |
0 |
1 |
1 |
|
|
|
|
|
|
|
|
|
|
1 |
1 |
1 |
0 |
1 |
|
|
|
|
|
1 |
1 |
1 |
1 |
0 |
Метод каскадов
f0 (x2 , x3, x4 )
x2 f0 (0, x3, x4) x2 f0 (1, x3, x4)
x2 f00 (x3, x4 ) x2 f01(x3, x4 )
f1(x2 , x3, x4 )
x2 f1(0, x3, x4) x2 f1(1, x3, x4)
x2 f10 (x3, x4 ) x2 f11(x3, x4 )
27

x1 |
x2 |
x3 |
x4 |
f |
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 |
1 |
0 |
1 |
1 |
0 |
1 |
0 |
1 |
1 |
1 |
0 |
1 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
1 |
1 |
1 |
0 |
1 |
0 |
1 |
1 |
0 |
1 |
1 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
1 |
0 |
1 |
1 |
1 |
1 |
1 |
0 |
1 |
1 |
1 |
1 |
1 |
0 |
Метод каскадов
f0 (x2 , x3, x4 )
x2 f0 (0, x3, x4) x2 f0 (1, x3, x4)
, x ) x2 f01(x3, x4 )
x2 f1 4) x2 f1(1, x3, x4)
x2 f10 (x3, x4 ) x2 f11(x3, x4 )
28

x1 |
x2 |
x3 |
x4 |
f |
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 |
1 |
|
|
|
|
|
0 |
1 |
1 |
0 |
1 |
|
|
|
|
|
0 |
1 |
1 |
1 |
0 |
|
|
|
|
|
1 |
0 |
0 |
0 |
|
|
|
|
|
|
1 |
0 |
0 |
1 |
|
|
|
|
|
|
1 |
0 |
1 |
0 |
|
|
|
|
|
|
1 |
0 |
1 |
1 |
|
|
|
|
|
|
1 |
1 |
0 |
0 |
1 |
|
|
|
|
|
1 |
1 |
0 |
1 |
1 |
|
|
|
|
|
|
|
|
|
|
1 |
1 |
1 |
0 |
1 |
|
|
|
|
|
1 |
1 |
1 |
1 |
0 |
Метод каскадов
f0 (x2 , x3, x4 )
x2 f0 (0, x3, x4) x2 f0 (1, x3, x4)
x2 f00 (x3, x4 ) x2 f01(x3, x4 )
1(1, x3, x4)
x2 f10 (x3, x4 ) x2 f11(x3, x4 )
29

Метод каскадов
x2
x1 x2
x1 x2
x2
f00 (x3, x4 )
(0000)
f01(x3, x4 )
(0110)
f10 (x3, x4 )
(0110)
f11(x3, x4 )
(1110)
30