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

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

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

+ (, ) = +

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

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

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

重合定理 + + = + ( + )( + )( + ) = ( + )( + ) + + = + + ( + ) = ( + ) + ( + ) = ( + ) + ( + ) = +

+ + ( + ) + + + + ( + ) = + ( + ) + ( + ) = + ( + ) + ( + ) = ( + ) + + ( + ) = + + ( + ) = + + + + = ( + + ) = (( + )( + ) + ) = ( + + ) = (1 + ) =

1 2 1 2 1 2 1 + 2 + +

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

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

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

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

(,,, ) = (4, 5, 6, 7, 8, 11) 4 = 0100 5 = 0101 6 = 0110 7 = 0111 8 = 1000 11 = 1011 + + + + +

(,,, ) = + + = ( + ) + ( + ) + ( + )( + ) = + + + + + + + = 1101 + 1100 + 1110 + 1010 + 1111 + 0111 + 0110 = (6, 7, 10, 12, 13, 14, 15)

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

(,, ) = + 4 = + + 3 = + + 2 = + + 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 (,, ) = ( + + ) ( + + )( + + )( + + )

101 (,, ) = +... = ( + + ) ( + + ) ( + + ) ( + + )= (0, 2, 4, 5) (,, ) = + = (0, 2, 4, 5) = (1, 3, 6, 7) (,,, ) = ( + + )( + + ) 100 010 000 (,,, ) = ( + + )( + + ) = ( + + + )( + + + ) = 0000 0001 0010 ( + + + ) ( + + + ) ( + + + ) 1010 ( + + + ) = (0, 1, 2, 10)

(,,, ) = + + = ( + )( + ) = + + + = ( + )( + ) = + + + = ( + ) = + (,,, ) = 1111 + 1101 + 1110 + 1100 + 0111 + 0011 + 0110 + 0010 + 1011 = (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) = ( + + + )( + + + )( + + + )( + + + )( + + + )( + + + )( + + + )

{, +, } + = {, }

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

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

{ } = = ( ) ( ) + = ( ) ( ) {} (,, ) = + (,, ) = + = + 0 = (,, ) = + = + 0 = ((,, ),, (,, )) = + = + = +

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

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

.. 2 2 = 2 1.. 1 1 = 1 與 2 = 1 不會同時發生

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

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

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

(,,, ) = +

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

(,, ) = (1, 2, 3, 5, 6, 7) (,, ) (,, ) = + 1 = 001; 2 = 010; 3 = 011 5 = 101; 6 = 110; 7 = 111 (,, ) = +

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

(,,,, ) = (1, 5, 10, 11, 14, 15, 19, 26, 27, 30, 31) = 0 = 1 (,,,, ) = + +

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

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 + + + +

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) = ++ + = +

(,,, ) = (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

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

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

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