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1) X Y(Axy);
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4 (-

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1) X Y(Axy) -
;
2) X Y(Exy) -
;
3) X Y(Ixy) -
;
4) X Y(Oxy) -
.

Exy

" -Y", Oxy -

Ixy.

-
[15]
:
Axy = (xy')' = x'+y
Exy = (xy)'= x'+y'

. -

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Ixy,Oxy,
. -
, Oxy = (Ixy)',
頠 [8]
Oxy
=(Axy)' Ixy = (Exy)',

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_
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XY X X&Y X+Y XY X
X&Y X+Y




Ĵ
00 1 0 0
i0 j 0 i
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ii j i i
01 1 0 1
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j0 i 0 j
10 0 0 1
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,
-
.
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[14].


""[14],





.
Ŀ
xy z0 z1 z2 z3 z4 z5 z6 z7 z8
z9z10z11z12z13z14z15
Ĵ
00 0 0 0 0 0 0 0 0 1 1
1 1 1 1 1 1
01 0 0 0 0 1 1 1 1 0 0
0 0 1 1 1 1
10 0 0 1 1 0 0 1 1 0 0
1 1 0 0 1 1
11 0 1 0 1 0 1 0 1 0 1
0 1 0 1 0 1

y z
-

.
Ŀ
xz y0 y1 y2 y3 y4 y5 y6 y7 y8
y9y10y11y12y13y14y15
Ĵ
00 i i i i 0 0 0 0 1 1
1 1 j j j j
01 j j j j 1 1 1 1 0 0
0 0 i i i i
10 i 0 1 j i 0 1 j i 0
1 j i 0 1 j
11 j 1 0 i j 1 0 i j 1
0 i j 1 0 i




:
y0 = iz'+jz
y1 = xz+ix'z'+jx'z -
y2 = xz'+ix'z'+jx'z
y3 = i(xz+x'z')+j(xz'+x'z)
y4 = x'z+ixz'+jxz
y5 = z
y6 = xz'+x'z
y7 = x'z+ixz+jxz' -
y8 = x'z'+ixz'+jxz
y9 = xz+x'z'
y10 = z'
y11 = x'z'+ixz+jxz'
y12 = i(xz'+x'z)+j(xz+x'z')
y13 = xz+ix'z+jx'z'
y14 = xz'+ix'z+jx'z'
y15 = iz+jz'




Axy,Exy,Ixy. Oxy
-

Ixy, .
x y(Axy).
1.
-

, .

Ŀ
xy
Axy
x x'
Ĵ
===========---------- 00 1
y y'
01 1
==============------- 10 0
11
1



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Axy = (xy')' = x'+y
(Axy)' = xy'
,


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,,
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2. Axy
.-

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x' x
Ŀ
----------=========== xy Axy
y' y Ĵ
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y 01 1
b)===================== 10 0

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b,
,
:" (x) (y)".
,
""()- ,.. -.

Axy :
Axy = y+ix'y'
(Axy)' = xy'+jx'y'
3. Axy
-
.

"x y".
x' x
Ŀ
----------=========== xy Axy
y' y
Ĵ
a)-----================ 00 i
y 01 i
b)===================== 10 0
y' y
11 1
c)----------===========
"c"
" (x)

(y)".
"" - , "" "-

" . -
:
Axy = xy+ix'
(Axy)' = xy'+jx'
4.
[19].
x ===========---------- Ŀ
y1==============------- xy Axy
y2===========---------- Ĵ
00 1
01 i
10 0
11 1

Axy = xy+x'y'+ix'y
(Axy)' = xy'+jx'y
Axy
,

-

.
x y(Exy).
1. Exy
.
Ŀ
x x' xy
Exy
===========---------- Ĵ
y' y 00
1
-------------======== 01 1
10 1
11 0

Exy = (xy)'
(Exy)' = xy



..[17] .
,
-

.
2. Exy
.

Ŀ
x' x xy
Exy
----------=========== Ĵ
y y' 00
i
a)======--------------- 01 1
y y' 10
1
b)==========----------- 11 0


"b"
"

".
:
Exy = x'y+xy'+ix'y'
(Exy)' = xy+jx'y'
3. Exy
.
x' x
Ŀ
----------=========== xy Exy
y y'
Ĵ
a)======--------------- 00 i
y y' 01
i
b)===========---------- 10 1
y' 11 0
c)---------------------
" (x) (y)"
-

"c". ""- ,

.
:
Exy = xy'+ix'
(Exy)' = xy+jx'
x y.
.. " ".
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() ,
-

Ixy .
1. Ixy
.
x x'
Ŀ
================----- xy Ixy
y y'
Ĵ
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y y' 01
i
b)==================--- 10 i
y' y y' 11 1
c)--------==========---

:
Ixy = xy+x'y'+i(xy'+x'y)
(Ixy)' = j(xy'+x'y)
2. Ixy
.

Ŀ
x' x
xy Ixy
----------=========== Ĵ
y' y y' 00 i
a)-----==========------ 01 1
y y'
10 1
b)==============------- 11 1



,, :"

(x) - (y)". - .
:"
(x)
(y)". - .

, -
-



.
:
Ixy = x+y+ix'y'
(Ixy)' = jx'y'

. -

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3. Ixy
-
[19].B
Ixy -

x,y,

-
.


.
x' x
----------=========== Ŀ
y y'
xy Ixy
a)==============------- Ĵ
y' y y' 00 i
b)-----==========------ 01 i
y' y
10 i
c)-----================ 11 1
y' y

d)-------------========
Ixy = xy+i(x'+y')
(Ixy)' = j(x'+y')
4.
Ixy.

.
x' x
Ŀ
----------=========== xy Ixy
y' y
Ĵ
a)-------------======== 00 1
y' y y' 01 i
b)-----==========------ 10 1
11
1

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(x) -

(y)"(-

). :
Ixy = x+y'+ix'y
(Ixy)' = jx'y
5. Ixy
.
x' x
Ŀ
----------=========== xy Ixy
y' y
Ĵ
a)-------------======== 00 i
y' y y' 01 i
b)-----==========------ 10 1
y y'
11 1
c)==============-------
""
"
(x) (y)"(-
-
).
- " ".

:
Ixy = x+ix'
(Ixy)' = jx'
6. Ixy
.

Ŀ
xy
Ixy
x' x
Ĵ
----------=========== 00 0
y y'
01 1
==============------- 10 1
11
1


Ixy = x+y
(Ixy)' = x'y'
7. Ixy
:
x =======-------- Ŀ
y1----=====------ xy Ixy
y2=========------ Ĵ
y3---============ 00 i
01
1
Ixy = y+iy' 10 i
Oxy = jy' 11 1



-

Ixy. .
.. ,

Ixy
Ixy',.. Ixy -> Ixy'.

Ixy,

.

:
1)Ixy = x
2)Ixy = x+y+x'y' = 1
3)Ixy = x+ix'

Ixy,-

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x ----------===========
y -----==========------

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Axy-Exy-Ixy.,


()


1-1-2, :
Axy = (xy')' = x'+y
Exy = (xy)' = x'+y'
Ixy = x+y+ix'y' = x+y+i

,..

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-

Ixy.
,
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()

(1-1-8). ,
,
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4*3*8 = 96.
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.
x ===========---------- x ----------===========
y1==============------- y1==============-------
y2===========---------- y2-----==========------
Axy y3-----================

y4-------------========
Ixy
x ===========---------- x ----------===========
y -------------======== y1============---------
Exy y2-----==========------

y3------------=========

Oxy
Ŀ Ŀ Ŀ
Ŀ
xy Axy xy Exy xy Ixy xy Oxy
Ĵ Ĵ Ĵ
Ĵ
00
1 00 1 00
i 00 i
01
i 01 1 01
i 01 i
10
0 10 1 10
i 10 1
11
1 11 0 11
1 11 i
٠ ٠


, -

-:
Axy = xy+x'y'+ix'y
Exy = (xy)' = x'+y'
Ixy = xy+i(x'+y')
Oxy = xy'+i(x'+y)
,
,
.

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Axy,Exy,Ixy

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2.
f(x,y)


xy:00,01,10,11.
3.
f(x,y).
4.
-

.
1.
.
(m) - ()
() - (m) .
--------------------------
() - ()

""
M = AmxAym = (m'+x)(y'+m) = m'y'+xy'+mx
f(x,y) = y'+xy'+x = y'+x = Ayx.

"".
m m' Ŀ
===========---------- xy f(x,y)
x x'
Ĵ
==============------- 00
1
y y' 01
0

=======-------------- 10
1
11 1

,
" Y X"(Ayx).

f(x,y) = y'+x = Ayx.

. ,


" ",..

( ).
2.
(x) -
(m)
(y) -
(m)

____________________________________________________
f(x,y)

AxmAym -> f(x,y)
[8]
.-

.

"" "".
M = AxmAym = (x'+m)(y'+m) = m+x'y'
f(x,y) = x'y'+i = Ix'y'(3)
Ŀ
x ===========---------- xy f(x,y)
m ================----- Ĵ
y1 -----------====------ 00 1
y2 -----==========------ 01 i
y3 ========------------- 10 i
y4 =============-------- 11 i

( -

): f(x,y) = x'y'+i =
Ix'y'(3).
3-()
:" x'
y'".
.
3.
(m) - (x)
(m) - (y)

____________________________________________________
f(x,y)

AmxImy -> f(x,y)
M = AmxImy = (m'+x)(y+m+im'y') =
mx+m'y+xy+im'y'
f(x,y) = x+y+iy' = Ixy
Ŀ
m ===========---------- xy f(x,y)
x ================----- Ĵ
y1 -------===========--- 00 i
y2 -----================ 01 i
y3 -----========-------- 10 1
11 1

f(x,y) = x+ix' = Ixy(5) =
IxyIxy',.. "
- -
,
- ". ""

,
"".
4.
.
(m) - (y)
(m) - (x)

____________________________________________________
f(x,y) = IxyIx'y.
M = AmyImx = (m'+y)(m+x+im'x') =
m'x+my+xy+im'x'
f(x,y) = x+y+ix' = Ixy
""
:
f(x,y) = y+iy' = Ixy(7) = IxyIx'y.
5.
[10,.27] "" :
() (m)
(y) (m)
----------------------------------
-
,
-
.
.
M = AxmIym = (x'+m)(y+m+im'y') =
m+x'y+im'x'y'
f(x,y) = x'y+i = Ix'y(3),
.. " - -
".
""
. -

Ixy(3).
,
64
4-
(2- ).

.
1- :
AAA,AEIxy'[3],AIIxy[5],AOOxy[7],EAE,EEIx'y'[3],EIIx'y[5],
EOOxy[7],IAIxy'[3],IEIxy'[2],IOOxy[7],OAOxy[2],OEOxy[5],
OIOxy'[2],OOOxy[2].
2- :
AAIx'y'[3],AEE,AIIx'y[3],AOOxy[2],EAE,EEIx'y'[3],EIIx'y[5],
EOOxy[7],IAIxy'[3],IEIxy'[2],IOOx'y[2],OAOxy[2],OEOxy[5],
OIOxy'[2],OOOxy[2].
3- :
AAIxy[3],AEIxy'[3],AIIxy[5],AOOxy[7],EAIx'y[3],EEIx'y'[3],
EIIx'y[5],EOOxy[7],IAIxy[7],IEIxy'[7],IOOx'y[2],OAOxy[5],
OEOxy[5],OIOxy'[2],OOOxy[2].
4- :
AAA,AEE,AIIx'y[3],AOOxy[2],EAIx'y[3],EEIx'y'[3],EIIx'y[5],
EOOxy[7],IAIxy[7],IEIxy'[7],IOOx'y[2],OAOxy[5],OEOxy[5],
OIOxy'[2],OOOxy[2].

:
1- :
AAA,AEI[3],AII[3],EAE,EEI[3],EII[3],IAI[3],IEI[3].
2- :
AAI[3],AEE,AII[3],EAE,EEI[3],IAI[3],IEI.
3- :
AAI,AEI[3],AII[3],EAI[3],EEI[3],EII[3],IAI,IEI[3].
4- :
AAA,AEE,AII[3],EAI[3],EEI[3],EII[3],IAI[3],IEI[3].

. -

.
-(3- )
-

( ).
1- :
AAA,AEO,AII,AOI,EAE,EEI,EII,EOI,IEO,OEI.
2- :
AAI,AEE,AII,AOI,EAE,EEI,EII,IEO,OAO.
3- :
AAI,AEI,AII,AOO,EAI,EEI,EII,EOI,IAI,IEO,OAI,OEI.
4- : AAA,AEE,EAI,EEI,EII,EOI,IAI,IEI.
.
1.


, -
,
().
2.
-
,
Axy,Exy,Ixy.
3. , ,
-

. .
4.
-

.
5.
-

[13,15], -

,


-
[14].
6.
.
7.
( -
)
.
8. .

1.. . 4- . -
:1978.

2. .. .
- :1986.
3. ..
-
.- ..
..13.
4. ..
-
.-  .


..19,,1982.
5. ..
. - :"
",1998.
6. .. . -
:1910.
7. . . - :1979.
8. .. .. . -
:1995.
9. .. . - -.:1997.
10. . . - :1973.
11. .. .-
:1977.
12. ..
-

. - . N54-87,: -
,1987.
13. ..
.// :
,

( V ) -
:1998.
14. .. .//-
..2.N%9,1998,.34-40.
15. ..
.//-
-
..2.N%10,1998,.27-36.
16. ..
. - :1973.
17. ..

.
- ,1881.
18. .. . -
:1997.
19. ..
. - :1967.
20. ., . . -
.:1997.
21. .. . -:1991.

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