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  • . . . Boole, , . , Karnaugh, . . , , , . , , . , flip-flop, ROM & RAM. (Verilog, VHDL).

    Mano Morris, Ciletti Michael, " ", 4 , (), , , 2010. J.F.Wakerly, " : & ", 3 ,

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    1947: transistor BellLabs JohnBardeenWalterBrattain(Nobel 1956 WilliamShockley)

  • 1,1 .

    Jack KilbyTexas Instruments(Nobel ,2000)

    transistor ( 1958)

  • (SSI):>10

    (MSI):>100

    (LSI):>1000

    (VLSI):>10000

    2003:

    IntelPentium4mprocessor (55 ) 512Mbit DRAM(>0.5 )

  • Intel4004MicroProcessor

    19711000transistors1MHzoperation

  • Intel Pentium (IV) microprocessor

  • 1. (Supercomputers)

    2. (Mainframes)

    3. (Workstations)

    4. (Microcomputers)

    5. (Microcontrollers)

    (Mainframes)

    (Supercomputers) Workstation: Sun Ultra450

    microcomputer

    Personal Digital Assistant

  • : () () ( ) () ()

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    Top-down

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    die

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    0 1. 0 1 . 2, .

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    :0,1,2,3,4,5,6,7,8,9 (BInary digiT BIT):0,1

  • A . :

    0>1>

    ( bit) .

    bits 2 ? bits 10 ?

    n 2n

    m log2m

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    1/1/0000 ?

    20bit ! ,, =>(5+4+12)=>21 ,,, =>(5+4+12 + 3)=>24

  • ()

    =0=> =1=>

    =0=> =1=>

    , =f()=A!

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    A Z

    AZ

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    Z

    Z

    A B

    A

    B

    .

  • ZCA

    B

    , ,

    1.

    !

    Z

    A

    B

  • ?

    : & &

    {0,1,2,3,4,5,6,7,8,9}, = :+,,*,/ :{,[,(,/,*,,+ : 0 +, 1 *, +, * +,...

    :x+x =2x f(x,y)=3x+5y

  • A Boole

    To1854(!!!)o Georgele : .

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  • Shannon

    (1938), ClaudeShannon """" " " "", le .

    Boole "switchingalgebra". . " " " " "1""0".

    ( ).

  • . {0,1} (')

    =0=>'=1, =1=>'=0 :

    (and/): ( )

    (or/):+ :

    0 0=0, 1+1=1 1 1=1, 0+0=0 0 1=1 0=0, 1+0=0+1=1

    , :{,[,(,',,+

  • +0=, 1= ( ) +1=1, 0=0 ( ) + =, = () (')'= () +'=1 '=0 ()

    ( )

  • + = +, = ()

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

    . w+x+y+z .

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

    1. + ( )+( ). .

    2. 2. x +.

    : (W+Y) (X +) (V+Y) (W +) (X+Y) (V +) =[W+(Y )] [X+(Y )]

    [V+(Y )]=(Y )+(V X W)

    (1/2)( )

  • + =, (X+) = ()

    + '= ( +) ( +')= () : Z' + ' Z'+ Z+ ' Z= Z'+ Z

    =X

    : , , 1 .

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

    ()

    (2/2)( )

  • + +...+ =, ... = ()

    (1 +2 +...+n)'=1' 2' n' (1 2 n)'='1 +'2 +...+'n ( DeMorgan)

    [F(1, 2, ..., n, +, )]'=F('1, '2, ..., 'n, ,+)( DeMorgan)

    : F=(W' )+(X Y)+[W ('+Z')]. T F'=((W')'+X') ('+Y') [W'+( Z)]=

    =(W+X') (X Y)' [W'+(X Z)]

    F(1, 2, ..., n)=X1 F(1, 2, ..., n)+X1' F(0, 2, ..., n) F(1, 2, ..., n)=[X1 + F(0, 2, ..., n) [X1'+ F(1, 2, ..., n)](

    Shannon)

    : F(X,W,Z)=X+W Z. T F(0,W,Z)=W Z F(1,W,Z)=1. A F=X 1+X' W Z F=(X+W Z) (X'+1)

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    4, 7432.

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    :F4(x,y,z)=x' z +y' x

    G(X,W,Y,Z)=[' +] ( +W');

  • F(x,y,z)=x+y+z ? F(x,y,z)=x+y+z =(x+y)+z :

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    =2 ?

    0,1. unary/. .

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    F14 D. D(not AND). F8 OR. OR(not OR). F6 1 1 1 ( , 1 ). OR(eXclusiveOR) XOR.

    F9 1 0 2 1 ( 1 ). (noteXclusiveOR) XNOR.

  • E :(1/2)

  • E :(2/2)

  • ? (2)

  • AB

    CY

    BA CBA

    A

    B

    C

    DY

    BACBA

    DCBA

  • AB

    CY

    A

    B

    C

    DY

  • CBAY =

    ABC

    Y

    B C Y

    X X 0 1

    X 0 X 1

    0 X X 1

    1 1 1 0

    DCBAY =C

    AB

    DY

    A B C D Y

    X X X 0 1

    X X 0 X 1

    X 0 X X 1

    0 X X X 1

    1 1 1 1 0

  • AB

    CY

    ABABCCAB

    A

    B

    CY

    BA +CBACBA ++++

  • A Y

    YAA

    BY

    YA

    B

    A

    BY

    A

    B

    Y

    A

    BY

    A

    B

    Y

  • BAY =AB

    Y

    A

    B

    Y

    ( ) ( )BABABA

    BABBAA

    ABBABAABBABAY

    =+==+++=

    =+==

  • YA

    A

    BY

    A

    BY

    A

    BY

    YA

    BA Y

    A

    B

    Y

    A

    B

    Y

  • BABA =+A

    BY

    B

    Y

    A A

    B

    A

    BY

  • ? . 6inverters 4OR,AND,

    To : . =>.

    : D,NOR . D,OR, ( transistor).

    XOR,XNOR =>

  • , , .

    1: .

    2: .

    3: .

    , , .

  • !

    F3 F4.

    , .

    4 3 F4.

    To ?

    :

  • F3 :F3(,,)= '+' +' '

    :

    ' +' ' =' F3 = '+' =F4.

    H ! , .

    .

  • F(X,Y,Z)=X Y' Z+X' Y Z+Y Z==X Y' Z+Y Z ()= ( Y'+) ()= ( +) (1o )

    F(X,Y,Z)=X Y'Z+X Y' Z+X Y Z'

    F(X,Y,Z)=X Y' Z+X Y' Z+X Y Z'==X Y' Z+X Y Z' (A)= (Y' Z+Y Z') ()= ( ) ( XOR)

  • &

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  • , , .

    .

    .

    2 .

  • ,,

    :,',,'

    AND :, ', ', ' '

    OR :, +',+', +'+' (sumofproducts SOP)

    SOP : + ' + ' + ' ' (productofsums POS)

    . POS : ( +') (+') ( +'+') ,

    ( ) 1. .

    : ' ', +'+' : ' ' , +'+'+

  • , . 2 .

    F(X,Y) :' , , '

    , . 2 .

    F(X,Y) :'+, +, +' +

  • () . () () 1(0) .

    M ( 1 0 ) .

    .. 4=xy'z'.M 5=x'+y+z'

  • .

    .

    1 3 4 5

    F3(x,y,z)=m1 +m3 +m4 +m5 =x'y'z +x'yz +xy'z'+xy'z =(1,3,4,5)

    , . .

  • .

    .

    ( 0) 0 2 6 7

    F'3(x,y,z)='0 +'2 +'6 +'7=>F3(x,y,z)=0 2 6 7 =(x+y+z) (x+y'+z) (x'+y'+z) (x'+y'+z')=

    (0,2,6,7)

    , . .

  • 0 1 .

    .. F(A,B,C)= (1,4,6)=>F= (0,2,3,5,7)G(W,X,Y,Z)= (1,8,11,14,15)=>

    G= (0,2,3,4,5,6,7,9,10,12,13)

    F F' I m'i =Mi 'i =mi

    m'0=(x'y'z')'=x+y+z=M0 A F(x,y,z)= (1,3,4) =>F=m1 +m3 +m4 =>

    F'=(m1 +m3 +m4)'=M1 M3 M4 =(1,3,4)= (0,2,5,6,7)

  • } }

    .

  • Boole .

    : ( Karnaugh /kmap):

    5.

    QuineMcClauskey :

    Espresso:

    , ,D&OR.

  • .

    .

    , 1 . 0.

    ""( / 2 4 8 16 )

  • A B Y0 0 0 1 1 0 1 1

    Karnaugh 2-

  • A B Y0 0 0 1 1 0 1 1

    0 101

    Karnaugh 2-

  • A B Y0 0 0 1 1 0 1 1

    0 10 1

    Karnaugh 2-

  • 0 10 1

    B

  • 0 10 1

    B

    0 10 1

    B

  • 0 10 1

    B

    0 10 1

    B

    0 10 1

    A

  • 0 10 1

    B

    0 10 1

    B

    0 10 1

    A0 1

    0 1

    A

  • A B Y0 0 10 1 11 0 01 1 0

  • A B Y0 0 10 1 11 0 01 1 0

    0 10 1 11

  • A B Y0 0 10 1 11 0 01 1 0

    0 10 1 11

    AY =

  • A B Y0 0 00 1 11 0 11 1 1

  • A B Y0 0 00 1 11 0 11 1 1

    0 10 11 1 1

  • A B Y0 0 00 1 11 0 11 1 1

    0 10 11 1 1

  • A B Y0 0 00 1 11 0 11 1 1

    0 10 11 1 1

    BAY +=

  • 0 10 11 1

    BABABAY =+=

  • (2)

    4, .

    x 0 1.

    y 0 1.

    m0 m1m2 m3

    xy xy

    xy xy

    yx0

    1

    0 1

    1

    yx0

    1

    0 1

    1

    1 1

    yx0

    1

    0 1

    xy =(3)=m3 x+y =(1,2,3)=m1+m2 +m3

  • 00 01 11 1

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