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Позиционни бройни системи PowerPoint PPT Presentation


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Позиционни бройни системи. Урок за нови знания и упражнение. Представяне на данните. Данните, които обработват цифровите машини, се делят на три вида: логически символни цифрови Единственото средство за представяне на данните в електронните изчислителни машини са

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Позиционни бройни системи

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5934774


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  • , , . (). , , .


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  • . . () .


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  • (), : 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. 10 . .


5934774

  • :

    35187 = 3.104 + 5.103 + 1.102 + 8.101 + 7.100 .

    , N :

    N = ak.10k+ a-1.10k-1+ + a1.101+ a0.100.

    ak, a-1, .... a1, a0

    0i 9, i=0,1,2,,k, ak0.


5934774

  • . :

    5,2187 = 5.100 + 2.10-1 + 1.10-2 + 8.10-3 + 7.10-4 .

    , N :

    N =am.10m++a1.101+ a0.100+a-1.10-1++a-q.10-q.

    am,,a1, a0, a-q

    0i 9, i=0,1,2,,q, aq0.


5934774

  • 10 -

    b, b>=2.

    b=2

    . . - 0 1.


5934774

  • 0 1, 10010011101. 0 1 , , : 10111001001(2)


5934774

  • :

    10111001001(2) = 1.210+1.28+1.27+1.26+1.23+1.20.

    :

    1. :

    101101, 1001110, 101.1, 0.1, 1101.01


5934774

  • N , :

    N = ak.10k+ ak-1.10k-1+ ...+ a1.101+ a0.

    ai {0,1,2,3,4,5,6,7,8,9}; i = 0,1,2,...k,ak 0 :

    N = bm.2m+ bm-1.2m-1+ + b1.21+ b0.

    bi {0,1}; i = 0,1,2,..m ; bm 0


5934774

  • N 2 : N/2 = N1+ b0/2 ,

  • N1 = bm-1.2m-1+ bm-2.2m-2+ + b2.21+ b1 N 2. b0 N N.


5934774

  • - N1, N1. , .


5934774

  • 73(10) :

    73 / 2 => 36 + 1 , b0 = 1

    36 / 2 => 18 + 0 , b1 = 0

    18 / 2 => 9 + 0 , b2 = 0

    9 / 2 => 4 + 1 , b3 = 1

    4 / 2 => 2 + 0 , b4 = 0

    2 /2 => 1 +0 , b5 = 0

    1 /2 => 0+1 , b6 = 1


5934774

  • , 73 1001001(2) :

  • 1001001(2) = 1.26 + 1.23 + 1.20 = 64 + 8 + 1 = 73.


5934774

  • 2 . 2 , 0;

  • . , .


5934774

  • 57.25(10) .

  • 57(10) = 111001(2)

  • 0.25*2 = 0.5 - >

    0.5 *2 = 1.0 - >


5934774

:

0.2510 = 0.012

57.2510 = 111001.012

: , - 0.


5934774

1. :

  • 512, 901, 1024,46, 999, 1024.001

  • 0.541, 0.125, 25.179, 64.267, 512.378, 202.074


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  • - . - . , , , 0 1. .


5934774

  • :

  • 16.42, 12.368, 731.268, 43,69

  • (OCT Octal )

  • , 8

    0,1,2...7 , 8


5934774


5934774

  • :

  • :

  • 101011101, 111000011011101,11101011

  • 101010.0110111101, 111110101.1100111


5934774

  • (HEX Hexadecimal ) , 16 . , : 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. , .


5934774

  • , . , (16 = 24).


5934774

  • , , (). () . :


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5934774

  • ( ) , . 101100100100111110(2) : 0010 1100 1001 0011 1110 (2) = 3 C 9 3 E - 3C93E(16)


5934774

1. :

  • A01, 30B7, FFAB, ABBA, C59D

  • 10010111011010, 10101111010101 111111101010101111, 11101.01010111


5934774

  • . , , . , .


5934774

:

0 + 0 = 0

0 + 1 = 1

1 + 0 = 1

1 + 1 = 10

100101 37

10110 22

11101159

:

0 0 = 0

1 - 0 = 1

1 - 1 = 0

0 1 = 1

101101 45

10100 20

11001 25

5. :


5934774

:

  • 1. :

  • 0111 + 1011 , 100101 + 10110,

  • 101.111 + 11.101, 1101.1011 + 1011.0111

  • 101101 10100, 11010011 110110, 1111101 101111, 101.011 11.110


5934774

  • , . , .

  • :

  • ) :


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  • :


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, , , . 0, : (000...0) (100...0), . +0 -0 .


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, , ..

, . , .


5934774

, , , . () - , - ( -) , . :

7 6 5 4 3 2 1 0

1 0 0 1 1 1 0 1 0


5934774

()

  • , .

    7 6 5 4 3 2 1 0

    1 1 1 0 0 0 1 0 1


5934774

()

  • 8086 , , . . 0, 1.

  • , , .

  • . , () 1.


5934774

  • - "1 - (-).

  • : - 510 = 11012

  • 1010

  • 1 1 1011


5934774

1. Z=X+Y X=30, Y=45, n=8[b], .


5934774

4. Z=X+Y X=30, Y=-30, n=8[b], .


5934774

5. Z=X+Y X=30, Y=-30, n=8[b], .


5934774

13. Z=X+Y X=-96, Y=-32, n=8[b], .


5934774

  • = -96-32 = -128, 8 . , . 1 0000000.


5934774

14. Z=X+Y X=-96, Y=-96, n=8[b], .


5934774

2. Z=X+Y X=-30, Y=45, n=8[b], .


5934774

3. Z=X+Y X= -30, Y= -45, n=8[b], .


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  • , . (BCD)

  • BCD - , .. () .

  • BCD


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  • 4- .

  • 7095 <cd7><cd0><cd9><cd5>, 2, .. 4 (cd).


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  • , 4- ( ), (ddd ddd). .


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  • , , (,) ., .


5934774

BCD

  • 4 , 3 ( 4) . 7095, ASCII , :


5934774

BCD

  • 0011 0111 0011 0000 0011 1001 0011 0101

  • K3 K3 K3 K3

  • 7 0 9 5

  • K3 :

  • K3 = 0011 = 0 011


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