數字系統的轉換

 ummary摘要:

主    題：學習數字系統的轉換                                

一、請將10進位資料: 192、168、219轉換為2進位資料。

192/2=96....0                             168/2=84.....0                         219/2=109.......1

 96/2 =48....0                               84/2=42......0                         109/2=54.........1

 48/2 =24....0                               42/2=21......0                           54/2=27.........0

 24/2=12....0                                21/2=10......1                           27/2=13.........1

 12/2=6......0                                10/2 =5........0                           13/2=6...........1

  6/2 =3......0                                   5/2=2.........1                             6/2=3...........0

  3/2 =1......1                                   2/2=1.........0                             3/2=1...........1

   1/2=0......1                                   1/2=0.........1                             1/2=0...........1

(192) 10=(11000000)2                 (168) 10=(10101000)2                    (219)10=(11011011)2

二、請將2進位資料: 11001101、10101001、11000011轉換為10進位資料。

11001101=1× 2⁷+1× 2⁶+0× 2⁵+0× 2⁴+1× 2³+1× 2²+0× 2¹+1× 2⁰
            = 128  +    64    +  0      +  0      + 8     +     4     + 0      + 1  

                        = (205)10 

10101001=1× 2⁷+0× 2⁶+1× 2⁵+0× 2⁴+1× 2³+0× 2²+0× 2¹+1× 2⁰

                             =  128  +    0    +  32    +    0     +   8     +   0     +  0     +     1

                             = (169)10

11000011=1× 2⁷+1× 2⁶+0× 2⁵+0× 2⁴+0× 2³+0× 2²+1× 2¹+1× 2⁰

                             =  128   +  64    +    0     +  0    +     0    +    0    +    2   +    1

                             = (195)10

 三、請將10進位資料:（2004）₁₀ 轉為16進位資料。

(2004)10=111110101002

轉16進位=0111=7  1101=D  0100=4

(2004)10= (7D4)16

                                                              

                                                                

四、假設布林函數(X, Y, Z)= X'YZ+(X'Y)(Y+Z')+(X'+Z')'，請問F(0,0,1)=?

F(0,0,1) = 0' * 0 * 1 + ( 0'* 0 )* ( 0+1' )+ ( 0'+1' )'
               = 1 * 0 * 1 + ( 1* 0 )* ( 0+0 )+ ( 1+0 )'
               = 0 + (0)*(0)+(1)'
               = 0 + 0 + 0
               = 0