Bµi 2.7: Bé chuyÓn m·
Bµi 1:
ThiÕt kÕ m¹ch logic thùc hiÖn viÖc chuyÓn ®æi tõ m· nhÞ ph©n
4 bit sang m· Gray.
•
Ph©n tÝch yªu cÇu:
+ §Çu vµo:
M· nhÞ ph©n 4 bit: B
3
B
2
B
1
B
0
+ §Çu ra:
M· Gray 4 bit: G
3
G
2
G
1
G
0
M¹ch
chuyÓn m·
nhÞ ph©n
thµnh Gray
B
0
B
1
B
2
B
3
G
0
G
1
G
2
G
3
•
B¶ng ch©n lý:
•
Tèi thiÓu hãa:
M· nhÞ ph©n M· Gray
B
3
B
2
B
1
B
0
G
3
G
2
G
1
G
0
0 0 0 0
0 0 0 1
0 0 1 0
0 0 1 1
0 1 0 0
0 1 0 1
0 1 1 0
0 1 1 1
1 0 0 0
1 0 0 1
1 0 1 0
1 0 1 1
1 1 0 0
1 1 0 1
1 1 1 0
1 1 1 1
0 0 0 0
0 0 0 1
0 0 1 1
0 0 1 0
0 1 1 0
0 1 1 1
0 1 0 1
0 1 0 0
1 1 0 0
1 1 0 1
1 1 1 1
1 1 1 0
1 0 1 0
1 0 1 1
1 0 0 1
1 0 0 0
B¶ng Karnaugh:
00 01 11 10
00
01
11
10
B
3
B
2
G
3
1 1 1 1
1 1 1 1
B
1
B
0
1 1 1 1
1 1 1 1
G
2
1 1
1 1
1 1
1 1
G
1
1 1
1 1
1 1
1 1
G
0
33
BG =
3223232
BBBBBBG ⊕=+=
2121211
BBBBBBG ⊕=+=
1010100
BBBBBBG ⊕=+=
•
S¬ ®å logic:
B
3
B
2
B
1
B
0
G
3
G
2
G
1
G
0
Bµi 2:
ThiÕt kÕ m¹ch logic thùc hiÖn viÖc chuyÓn ®æi tõ m· Gray 4
bit sang m· nhÞ ph©n .
•
Ph©n tÝch yªu cÇu:
+ §Çu vµo:
M· nhÞ ph©n 4 bit: B
3
B
2
B
1
B
0
+ §Çu ra:
M· Gray 4 bit: G
3
G
2
G
1
G
0
M¹ch
chuyÓn m·
Gray thµnh
nhÞ ph©n
G
0
G
1
G
2
G
3
B
0
B
1
B
2
B
3
•
B¶ng ch©n lý:
•
Tèi thiÓu hãa:
M· Gray M· nhÞ ph©n
G
3
G
2
G
1
G
0
B
3
B
2
B
1
B
0
0 0 0 0
0 0 0 1
0 0 1 1
0 0 1 0
0 1 1 0
0 1 1 1
0 1 0 1
0 1 0 0
1 1 0 0
1 1 0 1
1 1 1 1
1 1 1 0
1 0 1 0
1 0 1 1
1 0 0 1
1 0 0 0
0 0 0 0
0 0 0 1
0 0 1 0
0 0 1 1
0 1 0 0
0 1 0 1
0 1 1 0
0 1 1 1
1 0 0 0
1 0 0 1
1 0 1 0
1 0 1 1
1 1 0 0
1 1 0 1
1 1 1 0
1 1 1 1
B¶ng Karnaugh:
00 01 11 10
00
01
11
10
G
3
G
2
B
3
1 1 1 1
1 1 1 1
G
1
G
0
B
2
1 1 1 1
1 1 1 1
B
1
1 1
1 1
1 1
1 1
B
0
1 1
1 1
1 1
1 1
33
GB =
3223232
GGGGGGB ⊕=+=
++=
1231231
GGGGGGB
123123
GGGGGG ++
321
GGG ⊕⊕=
3211
GGGB ⊕⊕=
++=
012301230
GGGGGGGGB
+++
01230123
GGGGGGGG
+++
01230123
GGGGGGGG
01230123
GGGGGGGG ++
32100
GGGGB ⊕⊕⊕=
•
S¬ ®å logic:
G
3
G
2
G
1
G
0
B
3
B
2
B
1
B
0