0 0 = 1 0 = 0 1 = = 1 1 = 0 0 = 1

Transcription

1

2 0 0 = 1 0 = 0 1 = = 1 1 = 0 0 = 1

3 : = {0, 1} : 3 (,, ) = + (,, ) = +

4 + (, ) = +

5 (,,, ) = ( + )( + ) + ( + )( + ) +

6

7 = + = = + + = + = ( + ) + = + ( + ) () = () ( + ) = + + = ( + )( + ) + = = + 0 = + 1 = 1 0 = 0 1 = + = 1 = 0 + = ( + ) =

8 + = 1 + = (1 + ) = 1 = ( + ) = ( + 0)( + ) = + 0 = + 0 =

9 + + ( + ) ( + ) ( + ) = + ( + ) + ( + ) = + ( + ) + ( + ) = ( + ) + + ( + ) = + + ( + ) = + + ( + ) = + + ( + ) = = ( + ) + ( + ) + = = + +

10

11 (,, ) 1 (,, ) = 2 (,, ) = 3 (,, ) = 4 (,, ) = { 1 (,, ) = (1, 1, 1) 1 = 0 { 1 (,, ) = (1, 1, 0) 2 = 0 { 1 (,, ) = (0, 1, 1) 3 = 0 { 1 (,, ) = (0, 0, 1) 4 = 0 (,, ) = 1 (,, ) + 2 (,, ) + 3 (,, ) + 4 (,, ) = (,, ), 2 (,, ), 3 (,, ), 4 (,, ) (,, )

12 1, 2,, 1 2 = ( 1, 2,, ) , 2,, 2 1, 2,, (,, ) = = ( + ) + ( + ) = (1) + (1) = (,, ) = +

13 (,, ) = + = (,, ) = + = (1) + (1) = ( + ) + ( + ) = + + +

14 (000) 2 = 0 (001) 2 = 1 (010) 2 = 2 (011) 2 = 3 (100) 2 = 4 (101) 2 = 5 (110) 2 = 6 (111) 2 = 7 (,, ) = +... = = 001 (1, 3, 6, 7)

15 (,,, ) = (4, 5, 6, 7, 8, 11) 4 = = = = = =

16 (,,, ) = + + = ( + ) + ( + ) + ( + )( + ) = = = (6, 7, 10, 12, 13, 14, 15)

17 1, 2,, = ( 1, 2,, ) 1 2 1, 2,, 2 1, 2,,

18 (,, ) = + 1 = = = = + + { 0 (,, ) = (1, 0, 1) 1 = 1 { 0 (,, ) = (1, 0, 0) 2 = 1 { 0 (,, ) = (0, 1, 0) 3 = 1 { 0 (,, ) = (0, 0, 0) 4 = 1 (,, ) = 1 (,, ) 2 (,, ) 3 (,, ) 4 (,, ) = ( + + ) ( + + )( + + )( + + )

19 101 (,, ) = +... = ( + + ) ( + + ) ( + + ) ( + + )= (0, 2, 4, 5) (,, ) = + = (0, 2, 4, 5) = (1, 3, 6, 7) (,,, ) = ( + + )( + + ) (,,, ) = ( + + )( + + ) = ( )( ) = ( ) ( ) ( ) 1010 ( ) = (0, 1, 2, 10)

20 (,,, ) = + + = ( + )( + ) = = ( + )( + ) = = ( + ) = + (,,, ) = = (15, 13, 14, 12, 7, 3, 6, 2, 11) = (2, 3, 6, 7, 11, 12, 13, 14, 15) = (0, 1, 4, 5, 8, 9, 10) = ( )( )( )( )( )( )( )

21

22 {, +, } + = {, }

23 = + {+, } {+, } () = {+, }

24 +

25 { } = = ( ) ( ) + = ( ) ( ) { } = = ( ) ( ) + = ( ) ( )

26 = = + = (1, 2) = (0, 3) = ( + )( + ) = ( + ) + = = ( + )

27

28 = = 1 與 2 = 1 不會同時發生

29 (, ) = = ( + ) = 1 = + = ( + ) = 1 = (, ) = + (, ) = + + = ( + ) + ( + ) = +

30 (,, ) = = ( + ) = + = ( + ) = (, ) = + (,, ) = + + = ( + ) + ( + ) = +

31 (,, ) = = ( + ) + ( + ) = (1) + (1) = + = ( + ) = (1) = (,, ) =

32 (,,, ) = +

33 + = ( + ) = (,, ) = = ( + ) + ( + ) = + (,, ) = + +

34 (,, ) = (1, 2, 3, 5, 6, 7) (,, ) (,, ) = + 1 = 001; 2 = 010; 3 = = 101; 6 = 110; 7 = 111 (,, ) = +

35 (,,, ) = (0, 1, 2, 3, 8, 9, 10) (,,, ) = + + (,,, ) = + + +

36 (,,,, ) = (1, 5, 10, 11, 14, 15, 18, 26, 27, 30, 31) = 0 = 1 (,,,, ) = + +

37 + ( ) + ( ) ( ) = + 含項 函數 在卡諾圖中 任何單一個 或任何一組 可以被合併在一起而形成一個積項 被稱為 的含項

38 質含項 若一個積項不能再和其它項合併而消去變數則稱為質含項 基本質含項 如果一個項只被一個質含項包含, 則包含此項的質含項稱為基本質含項

39 有些布林函數對於某些特定的輸入值, 不在乎其輸出值為 或, 換句話說, 其函數值到底是 還是, 均無所謂 這些無所謂的輸入組合可展開成最小項的形式, 我們將其在卡諾圖所對應的位置, 記成 用 表示一月到 月 用,,, 表示 = (1, 3, 5, 7, 8, 10, 12) + (0, 13, 14, 15) = ++ +

40 (,,, ) = (0, 1, 2, 5, 6, 7, 8, 9, 10, 14) 左列中 表示其二元表示法中沒有 表示各項中只有一個 表示有二個 表示有三個 若只有一個 不一樣 則此二項可以合併 因此相鄰的 可以比較 不相鄰的 或同 中的二項是不可以合併 因為至少有二個 不一樣

41

42 (,,, ) = + + }{{} (1,5) }{{} (5,7) }{{} (6,7) + }{{} (0,1,8,9) + }{{} (0,2,8,10) + }{{} (2,6,10,14) (,,, ) = + +

43

44 (,,, ) = (0, 3, 5, 6, 7, 10, 12, 13) + (2, 9, 15)

45

46 (,,, ) = }{{} (0,2) }{{}}{{}}{{}}{{} (2,10) (9,13) (12,13) (2,3,6,7) + }{{} (5,7,13,15) (,,, ) =