умножение сделать на бумаге потом перерисовать.
Мн(4)=300.1011
Мт(4)=1020.0322
Мн(2)=0.1011101111
Мт(2)=0100100000111010
2Мн(2)=1.0111011110
[-Mn]д(2)=1.0100010001
Мн: 0 – 01, 1 – 11, 2 – 10, 3 - 00
Таблица истинности ОЧС
|
À1 |
À2 |
В1 |
В2 |
p |
П |
S1 |
S2 |
Пример операции в четверичной с/с |
|
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
3+0+0=3 |
|
|
0 |
0 |
0 |
0 |
1 |
1 |
0 |
1 |
3+0+1=10 |
|
|
0 |
0 |
0 |
1 |
0 |
1 |
0 |
1 |
3+1+0=10 |
|
|
0 |
0 |
0 |
1 |
1 |
1 |
1 |
1 |
3+1+1=11 |
|
|
0 |
0 |
1 |
0 |
0 |
1 |
1 |
1 |
3+2+0=11 |
|
|
0 |
0 |
1 |
0 |
1 |
1 |
1 |
0 |
3+2+1=12 |
|
|
0 |
0 |
1 |
1 |
0 |
1 |
1 |
1 |
3+3+0=12 |
|
|
0 |
0 |
1 |
1 |
1 |
1 |
0 |
0 |
3+3+1=13 |
|
|
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0+0+0=00 |
|
|
0 |
1 |
0 |
0 |
1 |
0 |
1 |
1 |
0+0+1=01 |
|
|
0 |
1 |
0 |
1 |
0 |
0 |
1 |
1 |
0+1+0=01 |
|
|
0 |
1 |
0 |
1 |
1 |
0 |
1 |
0 |
0+1+1=02 |
|
|
0 |
1 |
1 |
0 |
0 |
0 |
1 |
0 |
0+2+0=02 |
|
|
0 |
1 |
1 |
0 |
1 |
0 |
0 |
0 |
0+2+1=03 |
|
|
0 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
0+3+0=03 |
|
|
0 |
1 |
1 |
1 |
1 |
1 |
0 |
1 |
0+3+1=10 |
|
|
1 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
2+0+0=02 |
|
|
1 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
2+0+1=03 |
|
|
1 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
2+1+0=03 |
|
|
1 |
0 |
0 |
1 |
1 |
1 |
0 |
1 |
2+1+1=10 |
|
|
1 |
0 |
1 |
0 |
0 |
1 |
0 |
1 |
2+2+0=10 |
|
|
1 |
0 |
1 |
0 |
1 |
1 |
1 |
1 |
2+2+1=11 |
|
|
1 |
0 |
1 |
1 |
0 |
1 |
1 |
1 |
2+3+0=11 |
|
|
1 |
0 |
1 |
1 |
1 |
1 |
1 |
0 |
2+3+1=12 |
|
|
1 |
1 |
0 |
0 |
0 |
0 |
1 |
1 |
1+0+0=01 |
|
|
1 |
1 |
0 |
0 |
1 |
0 |
1 |
0 |
1+0+1=02 |
|
|
1 |
1 |
0 |
1 |
0 |
0 |
1 |
0 |
1+1+0=02 |
|
|
1 |
1 |
0 |
1 |
1 |
0 |
0 |
0 |
1+1+1=03 |
|
|
1 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
1+2+0=03 |
|
|
1 |
1 |
1 |
0 |
1 |
1 |
0 |
1 |
1+2+1=10 |
|
|
1 |
1 |
1 |
1 |
0 |
1 |
0 |
1 |
1+3+0=10 |
|
|
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1+3+1=11 |
Минимизируем функцию П использовав алгоритм Рота. Исходные данные
|
L |
N |
|
00001 |
Ø |
В исходных множествах произвели склеивание кубов и получили:
|
L |
N |
|
000x1 |
Ø |
Поиск простых импликант.
|
C0*C0 |
000x1 |
00x10 |
0x111 |
10x11 |
1x110 |
111x1 |
x010x |
|
000x1 |
- |
||||||
|
00x10 |
0001y |
- |
|||||
|
0x111 |
00y11 |
0011y |
- |
||||
|
10x11 |
y0011 |
y0111 |
- |
||||
|
1x110 |
y0110 |
1011y |
- |
||||
|
111x1 |
y1111 |
1y111 |
1111y |
- |
|||
|
x010x |
00y01 |
001y0 |
001y1 |
101y1 |
101y0 |
1y101 |
- |
|
A1 |
0001x |
0011x |
x0111 |
1011x |
1111x |
1x101 |
Ø |
A1 = { 0001x; 00x11; x0011; 00x01; 0011x; x0110; 001x0; x0111; x1111; 001x1; 1011x; 1x111; 101x1; 1111x; 101x0; 1x101 }
Z0 = { Ø }
B1 = { 000x1; 00x10; 0x111; 10x11; 1x110; 111x1; x010x }
C1 = { 0001x; 00x11; x0011; 00x01; 0011x; x0110; 001x0; x0111; x1111; 001x1; 1011x; 1x111; 101x1; 1111x; 101x0; 1x101; 000x1; 00x10; 0x111; 10x11; 1x110; 111x1; x010x }
|
C1*C1 |
0001x |
00x11 |
x0011 |
00x01 |
0011x |
x0110 |
001x0 |
x0111 |
X1111 |
001x1 |
1011x |
1x111 |
101x1 |
1111x |
101x0 |
1x101 |
|
0001x |
- |
|||||||||||||||
|
00x11 |
- |
|||||||||||||||
|
x0011 |
- |
|||||||||||||||
|
00x01 |
00xy1 |
- |
||||||||||||||
|
0011x |
00y1x |
- |
||||||||||||||
|
x0110 |
- |
|||||||||||||||
|
001x0 |
- |
|||||||||||||||
|
x0111 |
x0y11 |
x011y |
- |
|||||||||||||
|
x1111 |
xy111 |
- |
||||||||||||||
|
001x1 |
001xy |
- |
||||||||||||||
|
1011x |
y011x |
- |
||||||||||||||
|
1x111 |
- |
|||||||||||||||
|
101x1 |
y01x1 |
- |
||||||||||||||
|
1111x |
1y11x |
- |
||||||||||||||
|
101x0 |
y01x0 |
101xy |
- |
|||||||||||||
|
1x101 |
1x1y1 |
- |
||||||||||||||
|
000x1 |
00yx1 |
|||||||||||||||
|
00x10 |
00x1y |
|||||||||||||||
|
0x111 |
yx111 |
|||||||||||||||
|
10x11 |
y0x11 |
|||||||||||||||
|
1x110 |
1x11y |
|||||||||||||||
|
111x1 |
1y1x1 |
|||||||||||||||
|
x010x |
001yx |
x01y0 |
x01y1 |
101yx |
||||||||||||
|
A2 |
00x1x |
00xx1 |
x0x11 |
Ø |
x011x |
x011x |
001xx |
xx111 |
Ø |
x01x1 |
1x11x |
1x1x1 |
101xx |
Ø |
Ø |
Ø |
A2 = { 00x1x; 00xx1; x0x11; x011x; 001xx; x01x0; xx111; x01x1; 1x11x; 101xx; 1x1x1 }
Z1 = { Ø }
B2 = { 0001x; 00x11; x0011; 00x01; 0011x; x0110; 001x0; x0111; x1111; 001x1; 1011x; 1x111; 101x1; 1111x; 101x0; 1x101; 000x1; 00x10; 0x111; 10x11; 1x110; 111x1; x010x }
C2 = { 00x1x; 00xx1; x0x11; x011x; 001xx; x01x0; xx111; x01x1; 1x11x; 101xx; 1x1x1; x010x }
|
C2*C2 |
00x1x |
00xx1 |
x0x11 |
x011x |
001xx |
x01x0 |
xx111 |
x01x1 |
1x11x |
101xx |
1x1x1 |
|
00x1x |
- |
||||||||||
|
00xx1 |
- |
||||||||||
|
x0x11 |
- |
||||||||||
|
x011x |
- |
||||||||||
|
001xx |
- |
||||||||||
|
x01x0 |
- |
||||||||||
|
xx111 |
- |
||||||||||
|
x01x1 |
x01xy |
- |
|||||||||
|
1x11x |
- |
||||||||||
|
101xx |
y01xx |
- |
|||||||||
|
1x1x1 |
- |
||||||||||
|
x010x |
x01yx |
||||||||||
|
A3 |
Ø |
Ø |
Ø |
x01xx |
x01xx |
x01xx |
Ø |
Ø |
Ø |
Ø |
Ø |
A3 = { x01xx }
Z2 = { 00x1x; 00xx1; x0x11; xx111; 1x11x; 1x1x1 }
B3 = { x011x; 001xx; x01x0; x01x1; 101xx; x010x }
C3 = { x01xx }
|
C3*C3 |
x01xx |
|
x01xx |
- |
|
A4 |
Ø |
A4 = { Ø }
Конечное множество простых импликант Z = { 00x1x; 00xx1; x0x11; xx111; 1x11x; 1x1x1; x01xx }
Поиск L-экстремалей.
|
z#(Z-z) |
00x1x |
00xx1 |
x0x11 |
xx111 |
1x11x |
1x1x1 |
x01xx |
|
00x1x |
- |
00x01 |
10x11 |
1x111 |
1x11x |
1x1x1 |
101xx |
|
00xx1 |
00x10 |
- |
10x11 |
1x111 |
1x11x |
1x1x1 |
101xx |
|
x0x11 |
00x10 |
00x01 |
- |
11111 |
1111x |
111x1 |
1010x |
|
xx111 |
00x10 |
00x01 |
10011 |
- |
11110 |
11101 |
1010x |
|
1x11x |
00x10 |
00x01 |
10011 |
01111 |
- |
11101 |
1010x |
|
1x1x1 |
00x10 |
00x01 |
10011 |
01111 |
11110 |
- |
10100 |
|
x01xx |
00010 |
00001 |
10011 |
01111 |
11110 |
11101 |
- |
|
Остаток |
00010 |
00001 |
10011 |
01111 |
11110 |
11101 |
10100 |
Далее для расчетов используется исходное множество L (без произведенного склеивания).
|
z#(Z-z) n L |
00001 |
00010 |
00011 |
00100 |
00101 |
00110 |
00111 |
01111 |
10011 |
10100 |
10101 |
10110 |
10111 |
11101 |
11110 |
11111 |
|
00010 |
000yy |
00010 |
0001y |
00yy0 |
00yyy |
00y10 |
00y1y |
0yy1y |
y001y |
y0yy0 |
y0yyy |
y0y10 |
y0y1y |
yyyyy |
yyy10 |
yyy1y |
|
00001 |
00001 |
000yy |
000y1 |
00y0y |
00y01 |
00yyy |
00yy1 |
0yyy1 |
y00y1 |
y0y0y |
y0y01 |
y0yyy |
y0yy1 |
yyy01 |
yyyyy |
yyyy1 |
|
10011 |
y00y1 |
y001y |
y0011 |
y0yyy |
y0yy1 |
y0y1y |
y0y11 |
yyy11 |
10011 |
10yyy |
10yy1 |
10y1y |
10y11 |
1yyy1 |
1yy1y |
1yy11 |
|
01111 |
0yyy1 |
0yy1y |
0yy11 |
0y1yy |
0y1y1 |
0y11y |
0y111 |
01111 |
yyy11 |
yy1yy |
yy1y1 |
yy11y |
yy111 |
y11y1 |
y111y |
y1111 |
|
11110 |
yyyyy |
yyy10 |
yyy1y |
yy1y0 |
yy1yy |
yy110 |
yy11y |
y111y |
1yy1y |
1y1y0 |
1y1yy |
1y110 |
1y11y |
111yy |
11110 |
1111y |
|
11110 |
yyyyy |
yyy10 |
yyy1y |
yy1y0 |
yy1yy |
yy110 |
yy11y |
y111y |
1yy1y |
1y1y0 |
1y1yy |
1y110 |
1y11y |
111yy |
11110 |
1111y |
|
11101 |
yyy01 |
yyyyy |
yyyy1 |
yy10y |
yy101 |
yy1yy |
yy1y1 |
y11y1 |
1yyy1 |
1y10y |
1y101 |
1y1yy |
1y1y1 |
11101 |
111yy |
111y1 |
|
11101 |
yyy01 |
yyyyy |
yyyy1 |
yy10y |
yy101 |
yy1yy |
yy1y1 |
y11y1 |
1yyy1 |
1y10y |
1y101 |
1y1yy |
1y1y1 |
11101 |
111yy |
111y1 |
|
10100 |
y0y0y |
y0yy0 |
y0yyy |
y0100 |
y010y |
y01y0 |
y01yy |
yy1yy |
10yyy |
10100 |
1010y |
101y0 |
101yy |
1y10y |
1y1y0 |
1y1yy |
|
10100 |
y0y0y |
y0yy0 |
y0yyy |
y0100 |
y010y |
y01y0 |
y01yy |
yy1yy |
10yyy |
10100 |
1010y |
101y0 |
101yy |
1y10y |
1y1y0 |
1y1yy |
|
10100 |
y0y0y |
y0yy0 |
y0yyy |
y0100 |
y010y |
y01y0 |
y01yy |
yy1yy |
10yyy |
10100 |
1010y |
101y0 |
101yy |
1y10y |
1y1y0 |
1y1yy |
|
x0100 |
00y0y |
00yy0 |
00yyy |
00100 |
0010y |
001y0 |
001yy |
0y1yy |
10yyy |
10100 |
1010y |
101y0 |
101yy |
1y10y |
1y1y0 |
1y1yy |
Множество L-экстремалей E = { 00x1x; 00xx1; x0x11; xx111; 1x11x; 1x1x1; x01xx }
Z´ = Z - E = { Ø }
Минимальное покрытие - множество L-экстремалей E = { 00x1x; 00xx1; x0x11; xx111; 1x11x; 1x1x1; x01xx }
Минимизация функции S1 с помощью алгоритма Рота.
Исходные данные
|
L |
N |
|
00011 |
Ø |
В исходных множествах произвели склеивание кубов и получили:
|
L |
N |
|
01100 |
Ø |
Поиск простых импликант.
|
C0*C0 |
01100 |
11111 |
0x011 |
0010x |
x0110 |
x1001 |
x1010 |
1x000 |
101x1 |
|
01100 |
- |
||||||||
|
11111 |
- |
||||||||
|
0x011 |
- |
||||||||
|
0010x |
0y100 |
- |
|||||||
|
x0110 |
001y0 |
- |
|||||||
|
x1001 |
010y1 |
- |
|||||||
|
x1010 |
0101y |
- |
|||||||
|
1x000 |
1100y |
110y0 |
- |
||||||
|
101x1 |
1y111 |
y0101 |
1011y |
- |
|||||
|
A1 |
0x100 |
1x111 |
010x1 |
001x0 |
1011x |
1100x |
110x0 |
Ø |
Ø |
A1 = { 0x100; 1x111; 010x1; 0101x; 001x0; x0101; 1011x; 1100x; 110x0 }
Z0 = { Ø }
B1 = { 01100; 11111; 0x011; 0010x; x0110; x1001; x1010; 1x000; 101x1 }
C1 = { 0x100; 1x111; 010x1; 0101x; 001x0; x0101; 1011x; 1100x; 110x0; 0x011; 0010x; x0110; x1001; x1010; 1x000; 101x1 }
|
C1*C1 |
0x100 |
1x111 |
010x1 |
0101x |
001x0 |
x0101 |
1011x |
1100x |
110x0 |
|
0x100 |
- |
||||||||
|
1x111 |
- |
||||||||
|
010x1 |
- |
||||||||
|
0101x |
- |
||||||||
|
001x0 |
- |
||||||||
|
x0101 |
- |
||||||||
|
1011x |
- |
||||||||
|
1100x |
- |
||||||||
|
110x0 |
- |
||||||||
|
0x011 |
|||||||||
|
0010x |
|||||||||
|
x0110 |
|||||||||
|
x1001 |
|||||||||
|
x1010 |
|||||||||
|
1x000 |
|||||||||
|
101x1 |
|||||||||
|
A2 |
Ø |
Ø |
Ø |
Ø |
Ø |
Ø |
Ø |
Ø |
Ø |
A2 = { Ø }
Конечное множество простых импликант Z = { 0x100; 1x111; 010x1; 0101x; 001x0; x0101; 1011x; 1100x; 110x0; 0x011; 0010x; x0110; x1001; x1010; 1x000; 101x1 }
Поиск L-экстремалей.
|
z#(Z-z) |
0x100 |
1x111 |
010x1 |
0101x |
001x0 |
x0101 |
1011x |
1100x |
110x0 |
0x011 |
0010x |
x0110 |
x1001 |
x1010 |
1x000 |
101x1 |
|
0x100 |
- |
1x111 |
010x1 |
0101x |
00110 |
x0101 |
1011x |
1100x |
110x0 |
0x011 |
00101 |
x0110 |
x1001 |
x1010 |
1x000 |
101x1 |
|
1x111 |
0x100 |
- |
010x1 |
0101x |
00110 |
x0101 |
10110 |
1100x |
110x0 |
0x011 |
00101 |
x0110 |
x1001 |
x1010 |
1x000 |
10101 |
|
010x1 |
0x100 |
1x111 |
- |
01010 |
00110 |
x0101 |
10110 |
1100x |
110x0 |
00011 |
00101 |
x0110 |
11001 |
x1010 |
1x000 |
10101 |
|
0101x |
0x100 |
1x111 |
01001 |
- |
00110 |
x0101 |
10110 |
1100x |
110x0 |
00011 |
00101 |
x0110 |
11001 |
11010 |
1x000 |
10101 |
|
001x0 |
01100 |
1x111 |
01001 |
01010 |
- |
x0101 |
10110 |
1100x |
110x0 |
00011 |
00101 |
10110 |
11001 |
11010 |
1x000 |
10101 |
|
x0101 |
01100 |
1x111 |
01001 |
01010 |
00110 |
- |
10110 |
1100x |
110x0 |
00011 |
Ø |
10110 |
11001 |
11010 |
1x000 |
Ø |
|
1011x |
01100 |
11111 |
01001 |
01010 |
00110 |
x0101 |
- |
1100x |
110x0 |
00011 |
Ø |
Ø |
11001 |
11010 |
1x000 |
Ø |
|
1100x |
01100 |
11111 |
01001 |
01010 |
00110 |
x0101 |
10110 |
- |
11010 |
00011 |
Ø |
Ø |
Ø |
11010 |
10000 |
Ø |
|
110x0 |
01100 |
11111 |
01001 |
01010 |
00110 |
x0101 |
10110 |
11001 |
- |
00011 |
Ø |
Ø |
Ø |
Ø |
10000 |
Ø |
|
0x011 |
01100 |
11111 |
01001 |
01010 |
00110 |
x0101 |
10110 |
11001 |
11010 |
- |
Ø |
Ø |
Ø |
Ø |
10000 |
Ø |
|
0010x |
01100 |
11111 |
01001 |
01010 |
00110 |
10101 |
10110 |
11001 |
11010 |
00011 |
- |
Ø |
Ø |
Ø |
10000 |
Ø |
|
x0110 |
01100 |
11111 |
01001 |
01010 |
Ø |
10101 |
Ø |
11001 |
11010 |
00011 |
Ø |
- |
Ø |
Ø |
10000 |
Ø |
|
x1001 |
01100 |
11111 |
Ø |
01010 |
Ø |
10101 |
Ø |
Ø |
11010 |
00011 |
Ø |
Ø |
- |
Ø |
10000 |
Ø |
|
x1010 |
01100 |
11111 |
Ø |
Ø |
Ø |
10101 |
Ø |
Ø |
Ø |
00011 |
Ø |
Ø |
Ø |
- |
10000 |
Ø |
|
1x000 |
01100 |
11111 |
Ø |
Ø |
Ø |
10101 |
Ø |
Ø |
Ø |
00011 |
Ø |
Ø |
Ø |
Ø |
- |
Ø |
|
101x1 |
01100 |
11111 |
Ø |
Ø |
Ø |
Ø |
Ø |
Ø |
Ø |
00011 |
Ø |
Ø |
Ø |
Ø |
10000 |
- |
|
Остаток |
01100 |
11111 |
Ø |
Ø |
Ø |
Ø |
Ø |
Ø |
Ø |
00011 |
Ø |
Ø |
Ø |
Ø |
10000 |
Ø |
Далее для расчетов используется исходное множество L (без произведенного склеивания).
|
z#(Z-z) n L |
00011 |
00100 |
00101 |
00110 |
01001 |
01010 |
01011 |
01100 |
10000 |
10101 |
10110 |
10111 |
11000 |
11001 |
11010 |
11111 |
|
01100 |
0yyyy |
0y100 |
0y10y |
0y1y0 |
01y0y |
01yy0 |
01yyy |
01100 |
yyy00 |
yy10y |
yy1y0 |
yy1yy |
y1y00 |
y1y0y |
y1yy0 |
y11yy |
|
11111 |
yyy11 |
yy1yy |
yy1y1 |
yy11y |
y1yy1 |
y1y1y |
y1y11 |
y11yy |
1yyyy |
1y1y1 |
1y11y |
1y111 |
11yyy |
11yy1 |
11y1y |
11111 |
|
00011 |
00011 |
00yyy |
00yy1 |
00y1y |
0y0y1 |
0y01y |
0y011 |
0yyyy |
y00yy |
y0yy1 |
y0y1y |
y0y11 |
yy0yy |
yy0y1 |
yy01y |
yyy11 |
|
10000 |
y00yy |
y0y00 |
y0y0y |
y0yy0 |
yy00y |
yy0y0 |
yy0yy |
yyy00 |
10000 |
10y0y |
10yy0 |
10yyy |
1y000 |
1y00y |
1y0y0 |
1yyyy |
Множество L-экстремалей E = { 0x100; 1x111; 0x011; 1x000 }
Z´ = Z - E = { 010x1; 0101x; 001x0; x0101; 1011x; 1100x; 110x0; 0010x; x0110; x1001; x1010; 101x1 }
|
L#E |
00011 |
00100 |
00101 |
00110 |
01001 |
01010 |
01011 |
01100 |
10000 |
10101 |
10110 |
10111 |
11000 |
11001 |
11010 |
11111 |
|
0x100 |
00011 |
Ø |
00101 |
00110 |
01001 |
01010 |
01011 |
Ø |
10000 |
10101 |
10110 |
10111 |
11000 |
11001 |
11010 |
11111 |
|
1x111 |
00011 |
Ø |
00101 |
00110 |
01001 |
01010 |
01011 |
Ø |
10000 |
10101 |
10110 |
Ø |
11000 |
11001 |
11010 |
Ø |
|
0x011 |
Ø |
Ø |
00101 |
00110 |
01001 |
01010 |
Ø |
Ø |
10000 |
10101 |
10110 |
Ø |
11000 |
11001 |
11010 |
Ø |
|
1x000 |
Ø |
Ø |
00101 |
00110 |
01001 |
01010 |
Ø |
Ø |
Ø |
10101 |
10110 |
Ø |
Ø |
11001 |
11010 |
Ø |
|
Остаток |
Ø |
Ø |
00101 |
00110 |
01001 |
01010 |
Ø |
Ø |
Ø |
10101 |
10110 |
Ø |
Ø |
11001 |
11010 |
Ø |
Множество кубов, непокрываемых L-экстремалями, L´ = L # E = { 00101; 00110; 01001; 01010; 10101; 10110; 11001; 11010 }
|
Z´i n L´ |
00101 |
00110 |
01001 |
01010 |
10101 |
10110 |
11001 |
11010 |
|
010x1 |
0yy01 |
0yy1y |
01001 |
0101y |
yyy01 |
yyy1y |
y1001 |
y101y |
|
0101x |
0yyy1 |
0yy10 |
010y1 |
01010 |
yyyy1 |
yyy10 |
y10y1 |
y1010 |
|
001x0 |
0010y |
00110 |
0yy0y |
0yy10 |
y010y |
y0110 |
yyy0y |
yyy10 |
|
x0101 |
00101 |
001yy |
0yy01 |
0yyyy |
10101 |
101yy |
1yy01 |
1yyyy |
|
1011x |
y01y1 |
y0110 |
yyyy1 |
yyy10 |
101y1 |
10110 |
1yyy1 |
1yy10 |
|
1100x |
yyy01 |
yyyy0 |
y1001 |
y10y0 |
1yy01 |
1yyy0 |
11001 |
110y0 |
|
110x0 |
yyy0y |
yyy10 |
y100y |
y1010 |
1yy0y |
1yy10 |
1100y |
11010 |
|
0010x |
00101 |
001y0 |
0yy01 |
0yyy0 |
y0101 |
y01y0 |
yyy01 |
yyyy0 |
|
x0110 |
001yy |
00110 |
0yyyy |
0yy10 |
101yy |
10110 |
1yyyy |
1yy10 |
|
x1001 |
0yy01 |
0yyyy |
01001 |
010yy |
1yy01 |
1yyyy |
11001 |
110yy |
|
x1010 |
0yyyy |
0yy10 |
010yy |
01010 |
1yyyy |
1yy10 |
110yy |
11010 |
|
101x1 |
y0101 |
y011y |
yyy01 |
yyy1y |
10101 |
1011y |
1yy01 |
1yy1y |
Могут быть получены следующие тупиковые формы:
Fmin1 = { x0101; x0110; x1001; x1010; 0x100; 1x111; 0x011; 1x000 }
Минимизация функции S2 с помощью алгоритма Рота.
Исходные данные
|
L |
N |
|
00001 |
Ø |
В исходных множествах произвели склеивание кубов и получили:
|
L |
N |
|
01001 |
Ø |
Поиск простых импликант.
|
C0*C0 |
01001 |
01010 |
10011 |
11000 |
000x1 |
00x10 |
x0100 |
x1111 |
1x101 |
1x110 |
|
01001 |
- |
|||||||||
|
01010 |
- |
|||||||||
|
10011 |
- |
|||||||||
|
11000 |
- |
|||||||||
|
000x1 |
0y001 |
y0011 |
- |
|||||||
|
00x10 |
0y010 |
0001y |
- |
|||||||
|
x0100 |
001y0 |
- |
||||||||
|
x1111 |
- |
|||||||||
|
1x101 |
1010y |
111y1 |
- |
|||||||
|
1x110 |
y0110 |
101y0 |
1111y |
- |
||||||
|
A1 |
0x001 |
0x010 |
x0011 |
Ø |
0001x |
001x0 |
1010x |
111x1 |
Ø |
Ø |
A1 = { 0x001; 0x010; x0011; 0001x; 001x0; x0110; 1010x; 101x0; 111x1; 1111x }
Z0 = { 11000 }
B1 = { 01001; 01010; 10011; 000x1; 00x10; x0100; x1111; 1x101; 1x110 }
C1 = { 0x001; 0x010; x0011; 0001x; 001x0; x0110; 1010x; 101x0; 111x1; 1111x; 000x1; 00x10; x0100; x1111; 1x101; 1x110 }
|
C1*C1 |
0x001 |
0x010 |
x0011 |
0001x |
001x0 |
x0110 |
1010x |
101x0 |
111x1 |
1111x |
|
0x001 |
- |
|||||||||
|
0x010 |
- |
|||||||||
|
x0011 |
- |
|||||||||
|
0001x |
- |
|||||||||
|
001x0 |
- |
|||||||||
|
x0110 |
- |
|||||||||
|
1010x |
- |
|||||||||
|
101x0 |
y01x0 |
- |
||||||||
|
111x1 |
- |
|||||||||
|
1111x |
- |
|||||||||
|
000x1 |
||||||||||
|
00x10 |
||||||||||
|
x0100 |
x01y0 |
|||||||||
|
x1111 |
||||||||||
|
1x101 |
||||||||||
|
1x110 |
||||||||||
|
A2 |
Ø |
Ø |
Ø |
Ø |
x01x0 |
x01x0 |
Ø |
Ø |
Ø |
Ø |
A2 = { x01x0 }
Z1 = { 11000; 0x001; 0x010; x0011; 0001x; 1010x; 111x1; 1111x; 000x1; 00x10; x1111; 1x101; 1x110 }
B2 = { 001x0; x0110; 101x0; x0100 }
C2 = { x01x0 }
|
C2*C2 |
x01x0 |
|
x01x0 |
- |
|
A3 |
Ø |
A3 = { Ø }
Конечное множество простых импликант Z = { 11000; 0x001; 0x010; x0011; 0001x; 1010x; 111x1; 1111x; 000x1; 00x10; x1111; 1x101; 1x110; x01x0 }
Поиск L-экстремалей.
|
z#(Z-z) |
11000 |
0x001 |
0x010 |
x0011 |
0001x |
1010x |
111x1 |
1111x |
000x1 |
00x10 |
x1111 |
1x101 |
1x110 |
x01x0 |
|
11000 |
- |
0x001 |
0x010 |
x0011 |
0001x |
1010x |
111x1 |
1111x |
000x1 |
00x10 |
x1111 |
1x101 |
1x110 |
x01x0 |
|
0x001 |
11000 |
- |
0x010 |
x0011 |
0001x |
1010x |
111x1 |
1111x |
00011 |
00x10 |
x1111 |
1x101 |
1x110 |
x01x0 |
|
0x010 |
11000 |
0x001 |
- |
x0011 |
00011 |
1010x |
111x1 |
1111x |
00011 |
00110 |
x1111 |
1x101 |
1x110 |
x01x0 |
|
x0011 |
11000 |
0x001 |
0x010 |
- |
Ø |
1010x |
111x1 |
1111x |
Ø |
00110 |
x1111 |
1x101 |
1x110 |
x01x0 |
|
0001x |
11000 |
0x001 |
01010 |
10011 |
- |
1010x |
111x1 |
1111x |
Ø |
00110 |
x1111 |
1x101 |
1x110 |
x01x0 |
|
1010x |
11000 |
0x001 |
01010 |
10011 |
Ø |
- |
111x1 |
1111x |
Ø |
00110 |
x1111 |
11101 |
1x110 |
001x0 |
|
111x1 |
11000 |
0x001 |
01010 |
10011 |
Ø |
1010x |
- |
11110 |
Ø |
00110 |
01111 |
Ø |
1x110 |
001x0 |
|
1111x |
11000 |
0x001 |
01010 |
10011 |
Ø |
1010x |
11101 |
- |
Ø |
00110 |
01111 |
Ø |
10110 |
001x0 |
|
000x1 |
11000 |
01001 |
01010 |
10011 |
Ø |
1010x |
11101 |
11110 |
- |
00110 |
01111 |
Ø |
10110 |
001x0 |
|
00x10 |
11000 |
01001 |
01010 |
10011 |
Ø |
1010x |
11101 |
11110 |
Ø |
- |
01111 |
Ø |
10110 |
00100 |
|
x1111 |
11000 |
01001 |
01010 |
10011 |
Ø |
1010x |
11101 |
11110 |
Ø |
00110 |
- |
Ø |
10110 |
00100 |
|
1x101 |
11000 |
01001 |
01010 |
10011 |
Ø |
10100 |
Ø |
11110 |
Ø |
00110 |
01111 |
- |
10110 |
00100 |
|
1x110 |
11000 |
01001 |
01010 |
10011 |
Ø |
10100 |
Ø |
Ø |
Ø |
00110 |
01111 |
Ø |
- |
00100 |
|
x01x0 |
11000 |
01001 |
01010 |
10011 |
Ø |
Ø |
Ø |
Ø |
Ø |
Ø |
01111 |
Ø |
Ø |
- |
|
Остаток |
11000 |
01001 |
01010 |
10011 |
Ø |
Ø |
Ø |
Ø |
Ø |
Ø |
01111 |
Ø |
Ø |
00100 |
Далее для расчетов используется исходное множество
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