Post on 10-Feb-2018
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, 2011
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-
-
-
-
- -
CIP -
004.312(075.8)
-
ISBN 978-608-4504-40-5
COBISS.MK-ID 89142282
.
-.
.
; -
. .
-
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III
- ........................... 221 - ........................................................................ 222 - ................................. 224 - .......................................................................... 225
-............................... 227
........................................ 228 ......................................... 232 ............................................................ 234 ................................... 239 .................. 245 ............................................................. 251
................................................................................. 252 ................................................................................... 256
............................................................................... 262 .................................................................................. 269
............................................................................................. 272
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2
bmnnb PPPPPPPN ).......()( 21011 (1.1)
10 bPi .
m
m
n
n
n
nb bPbPbPbPbPbPN
......)( 22
1
1
0
0
1
1
n
mi
i
ib bPN)( (1.2)
nP
- 0P
- Least Significant Digit).
0123
10 104103102101)1234(
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1. 5
( ) ...N P b P b P bb mm
1
1
2
2
b P b P b P m
1
1
1
2
1( ( ... ( )...)) (1.4)
8
4:8 + 3 = 3,503,50:8 + 5 = 5,43755,4375:8 + 0 = 0,6796875
44:2 = 22 22:2 = 11 11:2 = 5
5:2 = 2 2:2 = 1 1:2 = 0
10=(101100)2.
10
6
10
0,6796875*8 = 5,43750,4375*8 = 3,50
0,50*8 = 4,00 10= (0,534)8.
( ) ( )16 1 7 6 7 1371 0
10
7
13 : 3 = 4 4 : 3 = 1
1 : 3 = 0
(13)10=(111)3
( , ) ( , ...) ( , )0 1 1 3 0 333 0 331
10 10
3
( , ) ( , ...) ( , )0 2 2 11 0 1818 0 18111
10 10
11
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1. 7
0+0=0 0
0+1=1 0
1+0=1 0
1+1=0 1
- - -
1001.011 (9.375)10+1101.101 (13.625)10
________ _________10111.000 (23)10
0-0=0 00-1=1 1
1-0=1 0
1-1=0 0
02 10
- 01___01
8
0112 11000 24
- 10001 -17______ ___00111 7
-
.
.101)2=(6.625)10 2 -2) (1.10101)2=2
-2(6.625)10=(1.65625)10 22 (11010.1)2=2
2(6.625)10=(26.5)10.
0x0=0
0x1=0
1x0=01x1=1
110.10x 10.1________11010
11010___________10000.010
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1. 9
Algori
- 110
2= (24)10 2= (6)10
11000 : 110 = 100
_____= = 00
- 111
2= (46)10 2= (7)10
101110 : 111 = 0110
_____1011
- 111_____=1001
- 111
______
(restoring and nonrestoring algorithm).
10
2:(1111)2 (12)10:(15)10.
1100
-1111 _____ q0=0 -0011restore +1111
_____
11000 -1111
______ q -1=1
-1111_______ q-2=1
-1111
_______ q-3=0 -1001restore +1111
_______01100
- 1111________ q-4=0
- 0011restore + 1111
________11000
- 1111_________ q-5=1
0.q-1q-2q-3q-4q-5
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1. 19
01100 (+12)+11011 (-5)
-------------- 1 00111
10011 (-13)+11001 (-7)--------------
1 01100
11000 (-8)
+00110 (+6)--------------
0 1110 (-
11101 (-3)+11010 (-6)--------------
10111 (-
20
2-(00001001)2 =2310-910
00010111 (+23)+11110111 (-9)--------------
1 00001110 (+14)
-
-
--8 1000 -
-7 1001 1111-6 1010 1110
-5 1011 1101
-4 1100 1100
-3 1101 1011
-2 1110 1010
-1 1111 1001
0 0000
1 0001 00012 0010 0010
3 0011 0011
4 0100 0100
5 0101 0101
6 0110 0110
7 0111 0111
(end around carry) 2-(11110110)2 =2310-910
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1 27 28
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1. 27
0 0 0 0 0
1 0 0 0 1
2 0 0 1 0
3 0 0 1 14 0 1 0 0
5 0 1 0 1
6 0 1 1 0
7 0 1 1 1
8 1 0 0 0
9 1 0 0 1
2
0010
1
0001
10= 0011 0110NBCD 10=1001 0010NBCD
28
0011 0110 36+0110 +0110 +6_________________
1001 1100+1001 0010 +92__________________1 0010 1110
-0110 -6__________________
0001 0010 1000 128
10=0100 0110NBCD 10=1001 0100NBCD
0100 0110 46+0110 +0110 +6
_________________1010 1100
+1001 0100 +94__________________1 0011 1 0000
+1__________________
0001 0100 0000 140
10=1001 0010NBCD 10=0011 0110NBCD
6
01120
1001 0010 92- 0011 0110 -36_________________0101 1100
-0110
__________________0101 10 6
1 29 30
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1. 29
-
a b c d e f g a b c d e f g
0 1 1 1 1 1 1 0 0 0 0 0 0 0 1
1 0 1 1 0 0 0 0 1 0 0 1 1 1 1
2 1 1 0 1 1 0 1 0 0 1 0 0 1 0
3 1 1 1 1 0 0 1 0 0 0 0 1 1 0
4 0 1 1 0 0 1 1 1 0 0 1 1 0 0
5 1 0 1 1 0 1 1 0 1 0 0 1 0 06 1 0 1 1 1 1 1 0 1 0 0 0 0 0
7 1 1 1 0 0 0 0 0 0 0 1 1 1 1
8 1 1 1 1 1 1 1 0 0 0 0 0 0 0
9 1 1 1 1 0 1 1 0 0 0 0 1 0 0
a
b
cd
e
fg
- -
30
3, t2, t1 0 3b2b1b0 3t3+b2t2+b1t1+b0t0.
0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 1 0 0 0 1 0 0 0 1
2 0 0 1 0 0 0 1 0 0 0 1 0
3 0 1 0 0 0 1 1 0 0 1 14 0 1 0 1 0 1 0 0 1 0 0 0
5 0 1 0 1 0 1 1 16 0 1 1 0 1 1 0 07 1 0 1 0 1 0 0 0 1 1 0 1
8 1 0 0 1 1 1 1 09 1 1 0 1 1 0 1 0 1 1 1 1
-2,-
(8,4,-2,-
(8,4,-2,- 0 0 0 0 01 0 1 1 1
2 0 1 1 0
3 0 1 0 1
4 0 1 0 0
5 1 0 1 1
6 1 0 1 0
7 1 0 0 1
8 1 0 0 0
9 1 1 1 1
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1. 33 34
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3 0 0 1 1
9-3=6 1 1 0 0
5 0 1 0 1
9-5=4 0 1 0 0
-2,-
(8,4,-2,-
7 1 0 0 19-7=2 0 1 1 0
-2,-
1 0 1 0 09-1=8 1 0 1 1
b b b b3 2 1 0 0123 tttt .
00112233 tbtbtbtbd .
d
d
b b b b3 2 1 0 .
00112233 )1()1()1()1( tbtbtbtbd
)( 001122330123 tbtbtbtbtttt
dtttt 0123
90123 tttt .
-2,-1).
0 00001 0001
2 0011
3 0010
4 0110
5 0100
6 1100
7 1110
8 1010
9 1000
1. 35 36
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g b b i n
g b
i i i
n n
1 0 1
(1.7)
b i ni , 0 g i ni , 0
x y x y0 0 0
0 1 1
1 0 1
1 1 0
g b b i ni i i ( ) mod 1 2 0 1. (1.8)
1 1 1 0
b3 b2 b1 b0
1 0 0 1
2=(14)10
101
nibbg
gb
iii
nn(1.9)
i i i-1.
0 0000 0000
1 0001 0001
2 0011 0010
3 0010 0011
4 0110 0100
5 0111 0101
6 0101 0110
7 0100 01118 1100 1000
9 1101 1001
10 1111 1010
11 1110 1011
12 1010 1100
13 1011 1101
14 1001 1110
15 1000 1111
g3g2g1g00
b3=g3=1
g2=b3 b2 0=1b2 2=1g1=b2b1 1=1b1 1=0g0=b1b0 1=0b0 0=1
2=(13)10.
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1. 41 42
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0 1 1 0 0 0
1 0 0 0 1 1
2 0 0 1 0 1
3 0 0 1 1 0
4 0 1 0 0 15 0 1 0 1 0
6 0 1 1 0 0
7 1 0 0 0 1
8 1 0 0 1 0
9 1 0 1 0 0
( ) !
!( )!
5
2
5
2 5 210
1.19.
0 0 1 0 0 1
1 0 0 0 1 1
2 0 0 1 0 1
3 0 0 1 1 0
4 0 1 0 1 0
5 0 1 1 0 0
6 1 0 0 0 1
7 1 0 0 1 0
8 1 0 1 0 0
9 1 1 0 0 0
-
-
-
(5,0) (4,3,2,1,0)0 01 0 0 0 0 11 01 0 0 0 1 0
2 01 0 0 1 0 0
3 01 0 1 0 0 0
4 01 1 0 0 0 0
5 10 0 0 0 0 1
6 10 0 0 0 1 0
7 10 0 0 1 0 0
8 10 0 1 0 0 09 10 1 0 0 0 0
1. 43 44
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R(N)=N mod p.
2 3 5 70 0 0 0 0
1 1 1 1 1
2 0 2 2 2
3 1 0 3 3
4 0 1 4 4
5 1 2 0 5
6 0 0 1 6
7 1 1 2 0
8 0 2 3 19 1 0 4 2
2 3 5 715 1 0 0 1
5 1 2 0 5______________________
15+5=20 0 2 0 6
2 3 5 78 0 2 3 16 0 0 1 6
______________________8+6=14 0 2 4 0
2 3 5 7
2 0 2 2 28 0 2 3 1
______________________2*8=16 0 1 1 2
N1 321 321 mod 9 = 6N2 248 248 mod 9 = 5
----- ------------------N1+N2 569 569 mod 9 = 2 (6+5=11 mod 9=2)
-
R(N1)=(3+2+1) mod 9 = (6) mod 9 = 6R(N2)=(2+4+8) mod 9 = (14) mod 9 = 5
-checking).
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1. 53 54
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-
-
1111 0001 0010 0110 0101 1101
-
1. 55 56
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-
1.8
16-(256)8
-2), -3,-
(2AC)16=(0010 1010 1100)2=(684)10(256)8=(010 101 110)2=(174)10
10 1010 1100- 0 1010 1110
_________________________
1 1111 1110
(111111110)2=28+27+26+25+24+23+22+21=(510)10
0011.
(4,4,1,-
3 0 1 1 19-3=6 1 1 0 1
-
(8,4,-3,- 3 1 0 1 1
9-3=6 1 0 0 1
-3,-
3 0 0 1 09-3=6 0 1 0 1
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1. 59 60
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8 16 8
3 5 12.
(3EF)16-(1111)2
: 11010010.
-2-
- - -107.
-
-
-3, -2) -6)
14.
-
---n (m-out-of-
1. 61
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-out-of-
18. 7-
-
-
20.
64
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1. -
2. 3. 4. -
(Closure)
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67
68
(( ) )* (( ) )*( )
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x x x x ( ) *1
( ) *( )x x x x
x x x* x 0 x
(Absorption)
x x y x *
x x y x*( )
x x y x x y
* * *1 x y*( )1 x *1 x
(Simplification)
a) x x y x y *
b)x x y x y*( ) *
yxxxyxx **)(* 0 x y*
yx *
(Associative law)
a) x y z x y z x y z ( ) ( )
x y z x y z x y z*( * ) ( * ) * * *
A x y z x y z ( ( )) *(( ) )
( ( )) *(( ) )x y z x y z
( ( )) *( ) ( ( )) *x y z x y x y z z
( ( )) *( )x y z x y z
( ( )) *(( )x y z x y z
(( ) )* (( ) )*( )x y z x x y z y z
(( ) ) *( )x y z x y z
A x y z ( ) A x y z ( )
(Consensus)
a) x y x z y z x y x z* * * * *
b)( ) *( ) *( ) ( ) *( )x y x z y z x y x z
x y x z y z x y x z y z x x* * * * * * *( ) x y x z y z x y z x* * * * * * ( * * * ) ( * * * )x y x y z x z x y z x y z x z y* *( ) * *( )1 1 x y x z* *
(De Morgans law)
a) x y x y *
x y x y*
x y*
x y
. ( ) * ( * )x y x y x x y y
( )x y y x y y( ) x 1 1
yxyyxxyxyx ******)(
0* * *y x y y 0
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73
z z
74
2 5
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z z
z z
)()()()(5 xxyzyyxzzzyxzzyxE
xyzzyxyzxzyxzyxE 6
.
6
zxxyE
zxxyE
))(( zxyxxy
))()()(( zyzxxyxx
))()(( zyzxyx
))(( zyxzyxzzyxyx
))(( zyxzyxzyyxzx
))(( zyxzyxzyxxzy yxx y, zz
))()()(( zyxzyxzyxzyxE
.
2.5
2121 xxxx
2121 xxxx
321321 xxxxxx
321321 xxxxxx
x x1 2 x4 3434 xxxx
21214 xxxxx .
nn xxxxxx ...... 2121
nn xxxxxx ...... 2121 .
E x x x E x x xn n( , ,..., , ,*) ( , ,..., ,*, )1 2 1 2
yzxzyxzyxE
.
))()(( zyxzyxzyxE
75 76
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))(( zyxyzxzyzyyxzxyxE
))(( zyxyzxzx
zxzyxzyxy
E
))()()(( zxzyxzyyxE
))(( zzyzxzzxyxxxzyzxyyx
))(( yzxzzxyxzxy
yzxzyyzxxzyxzzxzyxyzxyyx
zyxzyxyzx
2.6
n
n
n
22n
.
22n
.
-
x y F
0
F
1
F
2
F
3
F
4
F
5
F
6
F
7
F
8
F
9
F1
0
F1
1
F1
2
F1
3
F1
4
F1
5
0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1
0 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 11 0 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1
1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1
F0 0
xyF 1
yxF 2x but not y
F x3
x
yxF 4y but not x
F y5 y
yxyxF 6
F x y7
F x y8
yxxyF 9Equil
F y10 NOT y
F x y11 if y then x (y->x)
F x12 NOT x
F x y13 if x then y (x->y)
xyF 14
F15 1
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81
2112 )1( xxxx
82
2.8
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2112 )(
)( 2212 xxxx
x x1 2
),,,( 4321 xxxxf 3x
4x
)1,0,,()0,0,,(),,,( 214321434321 xxfxxxxfxxxxxxf
)1,1,,()0,1,,( 21432143 xxfxxxxfxx
.
f x x x x f x x x f x xn n n( , ,..., ) [ ( , ,..., )][ ( , ,..., )]1 2 1 2 1 20 1
)......)(...(111210 nnn
xxxbxxxbf
)...)(...( 21122122 1 nn xxxbxxxb n
bi
).
x y x y xy x+y yxyx x y yx yxxy
0 0 1 1 0 0 0 1 1 1
0 1 1 0 0 1 1 1 0 01 0 0 1 0 1 1 1 0 0
1 1 0 0 1 1 0 0 0 1
yxxy
yxyx
xyyxyyxyyxxxyxyxyxyxyx ))((
yxyxyx
yyxxyxyx
)()( yxyyxx
))(( yxyx
83
84
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-
yxxyxy .
x y x y x y .
xxxxx
xyxyxyxy
yyxxyxyxyx .
x x x
x y x y x y x y
yyxxyxxyxy .
zyzxzyxzyxzyx )(
zxyxzyxzyx )( .
zxyzxyzxy
yzxyzx .
85
86
yxyxyx
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yxxy
yxyx
yxxyxy
yxyxyx
))(( yxyx
yxxy
))(( yxyx
yxyx
))(( yxyx :
87
yyxxyxyxyxyx
88
xyxyxyxy
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)()( yxyyxx
))(( yxyx .
yxyx
))(( yxyx :
yxyxyxyx
))(( yxyx
))(( yxyx .
))(( yxyx
yxxy :
))(())(( yxyxyxyx
yxyx
xyyx
yxxy .
xxxxx
yyxxyxyxyx
x x x
x y x y x y x y
yyxxyxxyxy
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91
92
2.10
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-Very Large
Scale Integrated) -
1.
(power dissipation)2.
3. (noise margin).
1. 2.
f =
)()()()(( 321321321321321 xxxxxxxxxxxxxxxf
xyzzyxzyxyzxzyxf
zyzyxxyf .
))()(( zyzyxyxzyzyxxyf
4
cddcabaf .
))()(( dcdcabacddcabaf
))()(( zyzyyx
)()()()()()(
)()()())()((
zyzyxyzyzyxy
zyzyxyzyzyyxzyzyyx
)()()(
()()())()(())()((
zzyzyyyyxx
zyzyyxzyzyyxzyzyyx
))(( zxzyyx
93
94
cz1a
b
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))((*))((*
))(())(())((
zzxxzyyyyxzxzyyx
zxzyyxzxzyyxzxzyyx
)()()()()()(
)()()())(())((
zxzzyyxxzxzzyyxx
zxzyyxzxzyyxzxzyyx
zxyx - - - -
))(( zxyxzxyxzxyx
)()(())(())(( yxzyxzyxzyyxzzyxzxyx
xzxzyyx )( - - - -
zyxxzyxxxzxyxzyxxzxzyyx )()(
zyxzxyxyzzyxzyxzyxyzx
yyzxyyxzzzyxzzxyzzyxzzyx
zxxzyxxyyxyxxxzxxyyyx
)()()()()()(
)()()(
1 2
z2
yxyx *c
z1a
b
z2
cbacbaabccba
cbacbacbaba
cbabacbaba
cbabacbaz
))((
)()(
)()(1
abcbabcaabcbaz )(2
10. 1 2
cz1a
b
z2
95
a) xyyx
96
2.1
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cz1a
b
z2
cbacbaabccba
cbacbacbaba
cbabacbaba
cbabacbaz
))((
)()(
)()(1
bcbaacbacbababacbabaz ))((]))[((2
11. ->,-
qpqp .
qpqppqpq
qpqp
ab c a b c ( ) .
( )( )( )ab ac a b a c
x y w yz x y wz z( ) ( ) a b c uv ( ) .
x y x y
x y x y
xy x y x y .
abc a bc b c a c ( )( )( ) .
E ab ac bc1
E x y y z y z2 ( )( )( )
E x y y z x z3 ( )( )
f x x x( , , )1 2 3 f ( , , , )2 3 5 6
97
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f x x x x x x x x x x( , , ) ( )1 2 3 1 2 2 3 1 1 3 .
( )( )x yz y xz
100
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3.
- - -
1. xy xy y
2. x x y x y
3. xz xy yz xz xy
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3. 105
00 01 11 10 00 01 11 10 00 01 11 10
00 00 00
01 01 01
106
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11 11 11
10 10 10
00 01 11 10 00 01 11 10 00 01 11 1000 00 00
01 01 01
11 11 11
10 10 10
00 01 11 10 00 01 11 10 00 01 11 10
00 00 00
01 01 01
11 11 11
10 10 10
00 01 11 10 00 01 11 10 00 01 11 10
00 00 00
01 01 01
11 11 11
10 10 10
00 01 11 10 00 01 11 10 00 01 11 10
00 00 00
01 01 0111 11 11
10 10 10
00 01 11 10 00 01 11 10 00 01 11 10
00 00 00
01 01 01
11 11 11
10 10 10
00 01 11 10 00 01 11 10 00 01 11 1000 00 00
01 01 01
11 11 11
10 10 10
00 01 11 10 00 01 11 10 00 01 11 10
00 00 00
01 01 01
11 11 11
10 10 10
- -
- - -
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3. 111
3.10.
112
f f ( )( )
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yzyz
x
00 01 11 100 1
1 1 1 1
x z
3.4
f yz xz .
f x y z w( , , , ) ( , , , , ) 0 1 4 5 9
.
zw
xy
00 01 11 10
00 0 0
01 0 0
1110 0
f xz yzw .
f x z y z w ( )( ).
f
f f x z y zw
( )( )x z y z w
xy yz xz z xw zw( )
xy yz z xw zw( ) ( )z zw xy xw
z xy xw
z
zw
xy
00 01 11 10
00 1 1
01 1 1
11 1 1 1 1
10 1 1 1
xy x w
f z xy xw .
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3. 117
118
x3x2x3
00 01 11 10
0 0 0
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x1
x2 x3 f
0 0 0 00 0 1 10 1 0 00 1 1 1
1 0 0 01 0 1 11 1 0 01 1 1 0
f x x x x x x x x x
1 2 3 1 2 3 1 2 3, f x x x x x x x x x x x x x x x ( )( )( )( )( )1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 .
f x x x( , , ) ( , , , , )1 2 3 0 2 4 6 7 .
x1 0 0 0
1 0 0 0
x x1 2
3 x x1 2 f x x x ( )1 2 3.
f x x x 3 1 2
f f x x x x x x 3 1 2 3 1 2( ) .
f x y z w( , , , ) ( , , , , , , , , ) 0 1 2 4 5 6 8 9 10
.
f x y z w( , , , ) ( , , , , , , ) 3 7 11 12 13 14 15 .
f x y z w ( )( ) .
3. 119
zw00 01 11 10
00 0
120
f x x x x x
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xy00 0
01 0
11 0 0 0 010 0
4 =16
NBCD 0 0000 0011
1 0001 0100
2 0010 0101
3 0011 0110
4 0100 0111
5 0101 1000
6 0110 1001
7 0111 1010
8 1000 10119 1001 1100
f x x x x x1 1 2 4 2 3
f x x x x x x x2 2 3 4 2 4 2 3
f x x x x3 3 4 3 4
f x4 4 .
x1x2x3x4 f1f2f3f40 0 0 0 0 0 0 1 1
1 0 0 0 1 0 1 0 02 0 0 1 0 0 1 0 1
3 0 0 1 1 0 1 1 0
4 0 1 0 0 0 1 1 1
5 0 1 0 1 1 0 0 0
6 0 1 1 0 1 0 0 1
7 0 1 1 1 1 0 1 0
8 1 0 0 0 1 0 1 1
9 1 0 0 1 1 1 0 010 1 0 1 0 b b b b
11 1 0 1 1 b b b b
12 1 1 0 0 b b b b
13 1 1 0 1 b b b b
14 1 1 1 0 b b b b
15 1 1 1 1 b b b b
x1x2
f1 x3x4
x1x2
f2 x3x400 01 11 10 00 01 11 10
00 00 1 1 1
01 1 1 1 01 1
11 b b b b 11 b b b b
10 1 1 b b 10 1 b b
1 2
3. 121
x x
f3 x3x4
x x
f4 x3x400 01 11 10 00 01 11 10
00 1 1 00 1 1
01 1 1 01 1 1
122
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x1x2 x1x201 1 1 01 1 1
11 b b b b 11 b b b b
10 1 b b 10 1 b b
f3 4
1x0 1y0
x1 x0 y1 y0 z1 z20 0 0 0 0 0
0 0 0 1 0 0
0 0 1 0 0 0
0 0 1 1 0 0
0 1 0 0 0 0
0 1 0 1 0 1
0 1 1 0 0 1
0 1 1 1 0 11 0 0 0 0 0
1 0 0 1 0 1
1 0 1 0 1 0
1 0 1 1 1 0
1 1 0 0 0 0
1 1 0 1 0 1
1 1 1 0 1 0
1 1 1 1 1 1
1z2
x1x0
z1 y1y0
x1x0
z2 y1y000 01 11 10 00 01 11 10
00 00
01 01 1 1 1
11 1 1 11 1 1
10 1 1 10 1
3.11
1 2
z x y1 1 1z x y x y y x x y2 0 0 1 1 0 1 0 1 .
3. 123
124
f1 zw f2 zw
00 01 11 10 00 01 11 10
00 00
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xyzwwzxywzxyzwyxwzyxf ),,,(1
xyzwwzxywzxyzwyxwzyxwzyxwzyxf ),,,(2
xy xy
00 00
01 01
11 1 1 1 11 1 1 110 1 10 1 1 1
f xy z xzw1
f xz xw2
3.24.
xy
f1 zw
xy
f2 zw
00 01 11 10 00 01 11 1000 00
01 01
11 1 1 1 11 1 1 1
10 1 10 1 1 1
f xy z xzw1 f xz xzw2
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3. 127
x1x2x3x40 0 0 0 0 1 0 0 0 1 2 0 0 1 0
128
00-- 00-- 6,7.
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3 0 0 1 1
6 0 1 1 0 9 1 0 0 112 1 1 0 0 7 0 1 1 1 11 1 0 1 113 1 1 0 1 14 1 1 1 0
x1x2x3x4
0,1 0 0 0 -0,2 0 0 - 0 1,3 0 0 - 1 1,9 - 0 0 12,3 0 0 1 - 2,6 0 - 1 0
3,7 0 - 1 13,11 - 0 1 1 6,7 0 1 1 -6,14 - 1 1 0 a
9,11 1 0 - 1 9,13 1 - 0 1 b12,13 1 1 0 - c12,14 1 1 - 0 d
x1x2x3x40,1,2,3 0 0 - - e
1,3,9,11 - 0 - 1 f
2,3,6,7 0 - 1 - g
x x x2 3 4 , x x x1 3 4, x x x1 2 3 , x x x1 2 4 , x x1 2 , x x2 4 x x1 3. -
0 1 2 3 6 7 9 11 12 13 14a x x
b x x
c x x
d x x
e x x x x
f x x x x
g x x x x
3.13
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3. 135
x1x2x3x49,13 1 - 0 1 b12,13 1 1 0 - c
136
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7,15 - 1 1 1 d
13,15 1 1 - 1 e
0 9 13 15
a* x
b* x x
c x
d x
e x x
f x x x x x x x x x x 1 2 3 4 1 3 4 2 3 4f x x x x x x x x x x 1 2 3 4 1 3 4 1 2 4 .
-
3.10:
0 4 16 12 24 28
a x x
b x x
c x x
d x x
e x x
f x x
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3. 139
x1x2x3x4
140
-
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x1x2x3x4
4,5,12,13 - 1 0 - d
3.17
4 5 10 11 12 13 14a* x x
b x x
c x x
d* x x x x
f x x x x x x x x ( )( )( )1 2 3 2 3 1 3 4 f x x x x x x x x ( )( )( )1 2 3 2 3 1 2 4
.
f x x x x b( , , , ) ( , , , , , ) ( , )1 2 3 4 3 4 6 9 10 15 8 11
.
41.
x1x2x3x44 0 1 0 0 8 1 0 0 0
3 0 0 1 16 0 1 1 0 9 1 0 0 110 1 0 1 0
11 1 0 1 1 15 1 1 1 1
3 4 6 9 10 15
a x x
b x
c x
d x x
x1x2x3x4
4,6 0 1 - 0 a8,9 1 0 0 -8,10 1 0 - 0 3,11 - 0 1 1 b9,11 1 0 - 110,11 1 0 1 - 11,15 1 - 1 1 c
x1x2x3x48,9,10,11 1 0 - - d
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3. 143
144
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2 11 12 13 14 15
a xb
c
d x x
e
f x x x x
3 7 11 12 13 14 15a
b x x
c x x
d x x
e x x x x
f x x x x
3 7 12 13 14 15
a
b x x
c x x
d
e
f x x x x
1,
2 3
p adf d f adf1 ( )p b e b c e d e f c d e f e bd f2 ( )( )( ) ( ) ( )
p b b c f c f bf3 ( ) ( )
p p p p adf e bd fbf abdf e bd abdf 1 2 3 ( ) ( )
2 11 12 13 14 15
a x
b
d x x
f x x x x
1
1.
2142143211 xxxxxxxxxfdaf .
3 7 11 12 13 14 15
a
b x x
d x x
f x x x x
2
3. 145
2
214314312 xxxxxxxxfdbf .
3 7 12 13 14 15
146
1x0 1y0
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3 7 12 13 14 15
ab x x
d
f x x x x
3
214313 xxxxxfbf .
x1x0y1y0 f1f2f3f40 0 0 0 0 0 0 0 0
1 0 0 0 1 0 0 0 0
2 0 0 1 0 0 0 0 0
3 0 0 1 1 0 0 0 0
4 0 1 0 0 0 0 0 0
5 0 1 0 1 0 0 0 1
6 0 1 1 0 0 0 1 0
7 0 1 1 1 0 0 1 1
8 1 0 0 0 0 0 0 0
9 1 0 0 1 0 0 1 0
10 1 0 1 0 0 1 0 0
11 1 0 1 1 0 1 1 0
12 1 1 0 0 0 0 0 0
13 1 1 0 1 0 0 1 1
14 1 1 1 0 0 1 1 0
15 1 1 1 1 1 0 0 1
x1x0
f1 y1y0
x1x0
f2 y1y000 01 11 10 00 01 11 10
00 00
01 01
11 1 11 1
10 10 1 1
x1x0
f3 y1y0
x1x0
f4 y1y000 01 11 10 00 01 11 10
00 00
01 1 1 01 1 1
11 1 1 11 1 1
10 1 1 10
0111012
01011
yyxyxxfyyxxf
004
0110010101013
yxfyyxyxxyyxyxxf
3. 147
1, x0, y1 0 1,x0 y=(y1,y0
148
3.6
f x x x x( , , , ) ( , , , , , , )1 2 3 4 0 2 5 6 7 8 10 .
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x1x0y1y0 f1f2f30 0 0 0 0 0 1 0
1 0 0 0 1 1 0 0
2 0 0 1 0 1 0 0
3 0 0 1 1 1 0 0
4 0 1 0 0 0 0 1
5 0 1 0 1 0 1 0
6 0 1 1 0 1 0 0
7 0 1 1 1 1 0 0
8 1 0 0 0 0 0 1
9 1 0 0 1 0 0 1
10 1 0 1 0 0 1 0
11 1 0 1 1 1 0 0
12 1 1 0 0 0 0 1
13 1 1 0 1 0 0 1
14 1 1 1 0 0 0 1
15 1 1 1 1 0 1 0
x1x0
f1 y1y0
x1x0
f2 y1y000 01 11 10 00 01 11 10
00 1 1 1 00
01 1 1 01
11 11 1
10 1 10 1 1
f3 y1y0
x1x0
00 01 11 10
00
01 1
11 1 1 1
10 1 1
01010101010101012
010001111
yyxxyyxxyyxxyyxxf
yyxyxxyxf
010001113 yyxyxxyxf
f x x x x( , , , ) ( , , , , , )1 2 3 4 1 3 5 7 13 15 .
f x x x x x b( , , , , ) ( , , , , , , , , , , , , , ) ( , , , )1 2 3 4 5 0 1 5 6 8 9 12 15 17 20 21 22 25 28 3 14 27 30
)18,10,8()31,30,28,27,25,22,20,19,17,15,12,11,9,6,4,3,1( bf
-
f x x x x( , , , ) ( , , , , , , , )1 2 3 4 1 4 5 6 7 9 11 12 .
-
f x x x x b( , , , ) ( , , , , , , , ) ( , )1 2 3 4 0 1 2 5 7 12 13 14 8 11 .
-
f x x x x( , , , ) ( , , , , , )1 2 3 4 1 3 5 7 13 15 .
-
f x x x x b( , , , ) ( , , , ) ( , , , , )1 2 3 4 2 4 8 15 0 7 10 12 13
9.
f
f
f
1
2
3
0 2 4 5 9 10 11 13 15
2 5 10 11 12 13 14 15
0 2 3 4 9 11 13 14 15
( , , , , , , , , )
( , , , , , , , )
( , , , , , , , , )
3. 149
-
f
f
1 2 3 5 7 8 9 10 11 13 15
2 3 5 6 7 10 11 14 15
( , , , , , , , , , )
( )
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f
f
2
3
2 3 5 6 7 10 11 14 15
6 7 8 9 13 14 15
( , , , , , , , , )
( , , , , , , )
f a b c d b( , , , ) ( , , , , ) ( , , , , , ) 2 6 8 10 11 3 4 5 9 12 15 .
152
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)
-
- -
2n
4. 153
-
154
i
iiiiiiiiiiiiiiiiiiiiiii CyxyxCyxyxCyxCyxCyxCyxS )()(
iiiiiiiiiiiii CyxCyxyxCyxyx )()()( (4.3)
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xi
i i Ci i i+1-
yi Ci Si Ci+1 Si: Ci+1:
0 0 0 0 0 xi xi0 0 1 1 0 0 1 0 1
0 1 0 1 0 00 1 00
0 1 1 0 1 yiCi 01 1 yiCi 01 1
1 0 0 1 0 11 1 11 1 1
1 0 1 0 1 10 1 10 11 1 0 0 11 1 1 1 1
a) )
i i+1
iiiiiiiiiiiii CyxCyxCyxCyxS
(4.1)
)(1 iiiiiiiiiiii yxCyxCyCxyxC (4.2)
i i
p
- p.
)()(1 iiiiiiiiiiiii yxCyxyxyxCyxC . (4.4)
i i+1 --
- -
- -
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4. 157
i i+1 Ci
158
i i+1 i+2, Bi, Bi+1, Bi+2 i.
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Carry-
iiiiii
iiiii
iiii
CPPGPG
CPGPG
CPGC
111
11
1112
)(
(4.7)
i+1 =1 i Pi+1=1
i i=Pi+1=1.
-
4- -
- i -
-
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4. 163 164
2n
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4. 167
- i.
168
1 0 i.
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f x y z x yz xy z x y z xyz( , , ) ( , , , ) 1 2 4 7
. (4.9)
3- f s s D s s D s s D s s D 1 0 0 1 0 1 1 0 2 1 0 3. (4.10)
s x1 s y0 . f x yD xyD x yD xyD 0 1 2 3. (4.11)
D D z D D z0 3 1 2 . (4.12)
f x y z x yz xy z x y z xyz( , , ) ( , , , ) 1 2 4 7
f xzD xzD xzD xzD 0 1 2 3
1=z 0
. (4.13)
3
D y D y D y y0 1 2 D3 .
wx
yz
00 01 11 10
00 1
01 1
11 1 1
10 1
f w x y z( , , , ) ( , , , , ) 0 1 6 7 11
-
1 0
f s s D s s D s s D s s D 1 0 0 1 0 1 1 0 2 1 0 3. (4.14)
4. 169
1s0 0 yz yz y z z y ( ) . D y0 .
yz yz y s
170
D D x D xw x w0 1 2 w D3 .
-
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yz yz y 1s0
f D 1. D y1 .
D3 0 D yz2 .
f w x y z( , , , ) ( , , , , ) 0 1 6 7 11
f w x y z( , , , ) ( , , , , ) 0 1 6 7 11
1 0
.
3
C2 C1 C0 D0 D1 D2 D3 D4 D5 D6 D70 0 0 x 0 0 0 0 0 0 0
0 0 1 0 x 0 0 0 0 0 0
0 1 0 0 0 x 0 0 0 0 0
0 1 1 0 0 0 x 0 0 0 0
1 0 0 0 0 0 0 x 0 0 0
1 0 1 0 0 0 0 0 x 0 0
1 1 0 0 0 0 0 0 0 x 0
1 1 1 0 0 0 0 0 0 0 x
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4. 173
- - -
174
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6 3
12
-
- AB AB AB, , AB
ABC ABC ABC ABC, , ,
-
- - i -
-
- w x y z s1 s2 s3 s4 s5 s6 s7
0 0 0 1 1 1 1 1 1 1 1 0
1 0 1 0 0 0 0 0 1 1 0 0
2 0 1 0 1 1 0 1 1 0 1 1
3 0 1 1 0 0 0 1 1 1 1 1
4 0 1 1 1 0 1 0 1 1 0 1
5 1 0 0 0 0 1 1 0 1 1 1
6 1 0 0 1 1 1 0 0 1 1 1
7 1 0 1 0 0 0 1 1 1 0 0
8 1 0 1 1 1 1 1 1 1 1 1
9 1 1 0 0 0 1 1 1 1 0 1
- 6.
4. 175
6 s6 3 5 6 8 9 11 ( , , , , , )
176
s5 3 4 6 7 8 9 10 11 12 ( , , , , , , , , )s6 3 5 6 8 9 11 ( , , , , , )s7 5 6 7 8 9 11 12 ( , , , , , , ) .
n
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s6 ( , , , , , ) .
-
-
-
s1 3 5 9 11 ( , , , )s2 3 5 6 8 10 11 12 ( , , , , , , )s3 3 5 6 8 10 11 12 ( , , , , , , )s4 3 4 5 6 7 10 11 12 ( , , , , , , , )
n
n -
4.5 ROM (Read Only Memory)
n n
n
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4. 179
(PLA-Programmab (PAL-
180
4.
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n n
Array).
n
f xz xz1
-
f yz xz2
f xz yz3
f x y yz4
xz xz yz, , x y.
1, f2, f3 4
f1 x
yz
0 1
00
01 1
11 1
10 1
f2 x
yz
0 1
00
01 1 1
11 1
10
f3 x
yz
0 1
00 1
01 1 1
11
10 1
f4 x
yz
0 1
00 1
01 1 1
11
10
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4. 183
184
-
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1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 61 1
2 1
3 1
4 1
5 1
6 1
7x x x x x x1 2 5 7 11 12 1 0 - - 1 - 1 - - - 0 11
8 1
9 1
10 1
11 112 1
13 1
14 1
15 1
16 1
A
-
B S P
0 0 0 0
0 1 1 0
1 0 1 0
1 1 0 1
-
S: A P: A0 1 0 1
B0 1
B0
1 1 1 1
S A B AB AB
P AB -
S AB AB
AB AB AA BB
( ) ( )A B A A B B
AB A ABB
( )( )AB A AB B
4. 185 186
( ) ( )A B A A B B
( )( )A B A B
( )( )A B A B
A B A B
A A B B A B
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-
P AB
AB
AB AB .
-
-
S AB AB AB AB AA BB
P AB
AB
A B
A A B B .
-
-
S ABC ABC ABC ABC
-
C AB AB C AB AB( ) ( )
4. 187
C AB A B C A B AB( ) ( )
C AB A B C A B AB( ) ( )
C AB AB C AB AB( ) ( )
CS CS 1 1
1 -
188
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P ABC ABC AB C ABC
C AB AB AB( )
CS P1 1 1 -
B C S P0 0 0 0 0
0 0 1 1 00 1 0 1 00 1 1 0 11 0 0 1 01 0 1 0 11 1 0 0 11 1 1 1 1
-
S ABC ABC ABC ABC
3
P ABC ABC AB C ABC .
4. 189
x0
i i k=1.
x1 x2 x3 x4 x5 x6 x7 z0 z1 z2
190
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0 1 2 3 4 5 6 7 0 1 2
1 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 10 0 1 0 0 0 0 0 0 1 00 0 0 1 0 0 0 0 0 1 10 0 0 0 1 0 0 0 1 0 00 0 0 0 0 1 0 0 1 0 1
0 0 0 0 0 0 1 0 1 1 00 0 0 0 0 0 0 1 1 1 1
z x x x x0 4 5 6 7
z x x x x1 2 3 6 7
z x x x x2 1 3 5 7
y x x I x x I x x I x x I 1 2 0 1 2 1 1 2 2 1 2 3
y x x x x x x1 1 2 1 2 1 2
y x x x x x x2 3 4 3 4 3 4 .
4.35.
C0 C1 C2 C3 v1 v2 w
0 0 0 0 0 0 01 0 0 0 0 0 10 1 0 0 0 1 10 0 1 0 1 0 10 0 0 1 1 1 1
4. 191
v C C1 2 3 v C C2 1 3 w C C C C 0 1 2 3.
C x x0 2 4 C y x x1 1 1 2 C x x2 1 3 C y x x3 2 3 4 .
192
z x x x x x x x x1 1 2 1 2 3 4 3 4 z2
z x x x x x x2 1 2 1 3 3 4 ( )
x x x x x x x x1 2 1 3 3 4 3 4( )
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v C C x x x x1 2 3 1 3 3 4 v C C x x x x2 1 3 1 2 3 4 .
F x x I 0 1 2 F x x I 1 1 2 F x x I 2 1 2 F x x I 3 1 2 .
1 z2 3 z F x x v x x x x x x2 1 1 2 1 1 2 1 3 3 4 ( )z F x x v x x x x x x3 3 1 2 1 1 2 1 3 3 4 ( ) .
1, z2 3
z v x x x x1 2 1 2 3 4
x x x x x x x x1 2 1 2 3 4 3 4.
z XX XX XX XX11 10 01 11 00( ) { , , , }
x3x4
x1x2
00 01 11 10
00 1 1
01 1 1 1 1
11 1 1
10 1 1 1 1
x x x x x x x x1 2 3 4 1 2 1 3
3
z x x x x x x3 1 2 1 3 3 4 ( )
x x x x x x x x1 2 3 4 3 4 1 3( )
x x x x x x x x x x x1 2 3 4 1 2 3 4 1 2 3.
1z X3 1 1100 1111 111( ) { , , }
x3x4
x1x2
00 01 11 10
00
01
11 1 1 1
10
z x x x x x x3 1 2 4 1 2 3 .
-
-
4. 193
f1 f2 f3A B AB A=B
0 0 0 0 10 1 1 0 0
1 0 0 1 01 1 0 0 1
194
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-
1, f2 3
f AB1f AB2
f A B AB A B AB A B AB3 .
-
-
-
f yz xy x yz
f s s D s s D s s D s s D 1 0 0 1 0 1 1 0 2 1 0 3.
s x1 s y0 .
f x y z x y f z xyf z x y f z xyf z( , , ) ( , , ) ( , , ) ( , , ) ( , , ) 0 0 0 1 1 0 1 1 .
f i i z( , , )1 2
ij { , }0 1
z z 3-1
f i i z( , , )1 2 j 1i2.
D D D z0 1 20 1 , , D z3 .
4. 195
f yz xy x yz
f
D00MUX
4x11 D1
196
f x x x x x x x x x x( , , , )1 2 3 4 1 2 3 4 3 4
.
3 4 1 2
f x x f x x x x f x x x x f x x x x f x x 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 20 0 0 1 1 0 1( , , , ) ( , , , ) ( , , , ) ( , ,
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f
X y
4x1z
z
D2
D3
f yz xy x yz
f x y z yz f x yzf x yz f x yzf x( , , ) ( , , ) ( , , ) ( , , ) ( , , ) 0 0 0 1 1 0 1 1 .
D x D D x0 1 20 , , D3 1 .
f yz xy x yz
f
D0x
y z
MUX
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x
1
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D D x x0 3 1 2
x x x x x x1 2 2 2 1 1( ) ( )
x x x x x x1 2 1 2 1 2
D D x x1 2 1 2 1 1 1 2
x x x x x x1 2 1 2 1 2
f x x x x x x x x x x( , , , )1 2 3 4 1 2 3 4 3 4
6:
4. 197
3
0
1
2
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3
0
1
2
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x1 x2
x1
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MP1:
31131131331331 xxxxxxxxxxxxxxa
MP2:
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210
D
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2
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2
3
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1
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7:
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0
1
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3
0
1
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3
0
1
2
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3
0
1
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4. 199
a) DC:430 xxD 431 xxD 432 xxD 433 xxD
DP:3210 xxxF 3211 xxxF 3212 xxxF 3213 xxxF
MP1:2320320321 0 DxxFxxDxxz
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200
1x0y1y0
x1x0y1y0 z1z2z30 0 0 0 0 0 0 0
1 0 0 0 1 0 0 1
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3323321321322z
433232132321324332 xxxxxxxxxxxxxxxxxx
432432 xxxxxx
30
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II
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1
x1 x4
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1
0
0
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0
30
4324322
II
xxxxxxz
1010 41414141430 xxxxxxxxxII
1
x1 x4
MUX
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0
0
x2 x3
MUX
z2
0
1 0 0 0 1 0 0 1
2 0 0 1 0 0 0 1
3 0 0 1 1 0 1 0
4 0 1 0 0 0 0 1
5 0 1 0 1 0 1 0
6 0 1 1 0 0 1 0
7 0 1 1 1 0 1 18 1 0 0 0 0 0 1
9 1 0 0 1 0 1 0
10 1 0 1 0 0 1 0
11 1 0 1 1 0 1 1
12 1 1 0 0 0 1 0
13 1 1 0 1 0 1 1
14 1 1 1 0 0 1 1
15 1 1 1 1 1 0 0
0
x0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
x1
y0
y1
z2z1 z3
4. 201
x1x0
z1 y1y0
x1x0
z2 y1y000 01 11 10 00 01 11 10
00 00 1
01 01 1 1 1
11 1 11 1 1 1
10 10 1 1 1
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202
01011 yyxxz
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x1x0
00 01 11 10
00 1 1
01 1 1
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0 0 0 0 0 0 0 01 0 0 0 1 0 0 1
2 0 0 1 0 0 1 0
3 0 0 1 1 0 1 1
4 0 1 0 0 0 0 1
5 0 1 0 1 0 1 0
6 0 1 1 0 0 1 1
7 0 1 1 1 1 0 0
8 1 0 0 0 0 1 0
9 1 0 0 1 0 1 1
10 1 0 1 0 1 0 0
11 1 0 1 1 1 0 1
12 1 1 0 0 0 1 1
13 1 1 0 1 1 0 0
14 1 1 1 0 1 0 1
15 1 1 1 1 1 1 0
2, z1 0
4. 203
0
x0
1
2
3
4
5
6
7
8
9
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204
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10
11
12
13
14
15
y0
z2 z1 z0
x1x0
z2 y1y0
x1x0
z1 y1y000 01 11 10 00 01 11 10
00 00 1 1
01 1 01 1 1
11 1 1 1 11 1 1
10 1 1 10 1 1
010001112 yyxyxxyxz
010101011010110111011 yyxxyyxxxyyxxyxxyxyyz
x1x0
z0 y1y000 01 11 10
00 1 101 1 1
11 1 1
10 1 1
00000 xyyxz
x0x1 y0y1z2 z1 z0
x1y1
x1x0y0
x0y1y0
y1y0x1
y1x1x0
y1x1x0
y1y0x1
y1y0x1x0
y1y0x1x0
4. 205
0 0000 0000 0
1 0001 0001 1
206
f x x x( , , ) ( , , , )1 2 3 0 4 6 7
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1 0001 0001 1
2 0010 0011 3
3 0011 0010 2
4 0100 0110 6
5 0101 0111 7
6 0110 0101 5
7 0111 0100 48 1000 1100 12
9 1001 1101 13
10 1010 1111 15
11 1011 1110 14
12 1100 1010 10
13 1101 1011 11
14 1110 1001 9
15 1111 1000 8
0
b
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
a
d
c
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
0
y
x
w
z
f x x x x x x x x x x x x x( , , )1 2 3 1 3 1 2 1 2 3 1 2 3
f x x x x b( , , , ) ( , , , , , ) ( , )1 2 3 4 3 4 7 8 11 13 0 5
4. f x x x x b( , , , ) ( , , , , ) ( , , )1 2 3 4 3 4 6 8 9 10 11 15
-
x x1 0 y y1 0 4
-
x x1 0 y y1 0
- -
4. 207
8
208
f1 2
f1 3 5 6 7 ( , , , )f2 1 2 4 7 ( , , , ) .
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f w x y z wx yz wxyz wxyz wx yz1( , , , )
f w x y z wx yz wxyz wx yz2 ( , , , )
f w x y z wxyz wx yz3( , , , ) .
x y z w f 1 f20 0 0 0 0 00 0 0 1 0 0
0 0 1 0 0 00 0 1 1 0 1
0 1 0 0 0 00 1 0 1 0 1
0 1 1 0 0 10 1 1 1 1 01 0 0 0 0 0
1 0 0 1 0 11 0 1 0 0 11 0 1 1 1 01 1 0 0 0 11 1 0 1 1 01 1 1 0 1 0
1 1 1 1 1 0
-
-
f1 f2 f3 4
210
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n
5. 211
m
212
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m (finite state machine).
-
SR (Set-
0
1
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5. 215
Q
Q
Q
Q Q Q
Q =1
216
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Q
S R Q Q
1 0 0 1
1 1 0 1 0 1 1 0
1 1 1 0 0 0 - -
t+1=Qt
Q
Q
Q S RQt t 1 .
5. 217
Qt S R Qt+1 S R Qt+10 0 0 0 0 0 Qt0 0 1 0 0 1 0
0 1 0 1 1 0 1
0 1 1 - 1 1 -
1 0 0 11 0 1 0
1 1 0 1
1 1 1
218
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1 1 1 -
8:
SR
Qt
00 01 11 10
0 b 1
1 1 b 1
Q S RQt t 1
S
R
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5. 221
-
t1 t2 t1
222
- - - -
Q Q
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-
-
-
- -s - - -
-
0
1
t1 t2
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t1
Q
D
C
Q
t3
0
1
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Q
D
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Q
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SR master- -
1 1 Q1 Q1
Q1 Q1
Q2 Q2 .
-
- - - - - - -
5. 223
JK master- -
224
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-
Qt J K Qt+1 J K Qt+10 0 0 0 0 0 Qt
0 0 1 0 0 1 00 1 0 1 1 0 1
0 1 1 1 1 1 Qt1 0 0 1
1 0 1 0
1 1 0 1
1 1 1 0
-
-
- -
-
- Q J Q KQt t t 1 .
JK
Qt
00 01 11 10
0 1 1
1 1 1
Q J Q KQt t t 1
-
-
- -
-
5. 225
226
- - -
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-
-
-
- - -
- -
- -
- -
-
Qt Qt+1 Qt+10 0 0 0 Qt0 1 1 1 Qt1 0 1
1 1 0
-
- TQQTQ ttt 1
TQQTQttt 1
-
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0 1
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5. 227
-
-
228
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-
Qt Qt+1 S R Qt Qt+1 J K
0 0 0 b 0 0 0 b
0 1 1 0 0 1 1 b
1 0 0 1 1 0 b 1
1 1 b 0 1 1 b 0
Qt Qt+1 D Qt Qt+1 T
0 0 0 0 0 0
0 1 1 0 1 1
1 0 0 1 0 11 1 1 1 1 0
-
-
-
1 2 1 2. - n
-
S x Q1 2 2 , R x Q1 1 1 - S x Q x Q2 2 1 1 1 ,R x x2 2 1 -
z x Q Q 2 1 2 .
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5. 233
-
234
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1
x =0 x =1
A A,0 B,0B A,0 C,0
C D,0 C,0
D A,0 B,1
1101
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5. 237
-
x =0 x =1
238
x =0 x =1
a
A b,0 a,0
D b,0 a,0
G c,0 a,0
H c,0 a,0
b B b,1 a,1
cC d,1 a,0
E d,1 a,0
d F d,0 c,1
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x 0 x 1A B,0 G,0
B B,1 H,1
C F,1 D,0
D B,0 H,0
E F,1 D,0
F F,0 C,1
G E,0 A,0
H E,0 A,0
-
1={ADGH, B, CE, F}:
x =0 x =1
a
A B,0 G,0
D B,0 H,0
G E,0 A,0
H E,0 A,0
b B B,1 H,1
cC F,1 D,0
E F,1 D,0
d F F,0 C,1
2={AD,GH, B, CE, F}.
x =0 x =1
aA b,0 D b,0
G c,0 a,0
H c,0 a,0
b B b,1
cC d,1 a,0
E d,1 a,0
d F d,0 c,1
5. 239
x =0 x =1
a b,0 e c,0 a,0
b b,1
c d,1 a,0d d,0 c,1
240
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-
- .
-
- -
0110
x =0 x =1
A B,0B C,0C D,0D D,0
0110
Q1Q2
x =0 x =1Q1
+Q2+,z Q1
+Q2+,z
0 0 0 0,0 01,0
0 1 0 0,0 10,0
1 1 0 0,0 11,0
1 0 0 0,1 11,0
5. 241
- - -
Qt Qt+1 J K
0 0 0 b0 1 1 b
1 0 b 1
1 1 b 0
242
K1 x
Q1Q2
0 1
00 b b
01 b b
11 1
10 1
J1 x
Q1Q2
0 1
00
01 1
11 b b
10 b b
J2 x
0 1
00 1
K2 x
0 1
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- 1, K1, J2 2 1Q2.
Q1Q2
x =0 J1K1 J2K2
x =1 J1K1 J2K2
0 0 0 b 0 b 0 b 1 b
0 1 0 b b 1 1 b b 1
1 1 b 1 b 1 b 0 b 0
1 0 b 1 0 b b 0 1 b
.43: -
1, K1, J2K2
J xQ1 2 , K x1 , J x2 , K x Q2 1 z xQ Q 1 2 .
-
-
Q1Q2
00 1
01 b b
11 b b
10 1
Q1Q2
00 b b
01 1 1
11 1
10 b b
z x
Q1Q2
0 1
00
01
11
10 1
5. 243
- - -
Qt Qt+1 D
0 0 00 1 1
1 0 0
1 1 1
244
D1 x
Q1Q2
0 1
00
01 1
11 1
10 1
D2 x
Q1Q2
0 1
00 1
01
11 1
10 1
z x
0 1
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-
Q1Q2
x =0 x =1
D1D2 D1D20 0 00,0 01,0
0 1 00,0 10,0
1 1 00,0 11,0
1 0 00,1 11,0
-
-
D xQ xQ1 1 2
, D xQ xQ
2 1 2
z xQ Q
1 2 .
-
-
Q1Q2
0 1
00
01
11
10 1
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5. 247
x =0 x =1
A B,0 C,0B D,0 E,0
C F,0 G,0
D H,0 H,1
E H,0 H,1
1a DE,DF,DGEF,EG,FG
2 FG,BC,DE
3 DE FG
248
-
Q1Q2Q3
x =0 x =1Q1
+Q2+Q3
+,z Q1+Q2
+Q3+,z
A 0 0 0 1 1 1 1 1 1 1 0
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F H,1 H,0
G H,1 H,0
H A,0 A,0
3 DE,FG
Q1
Q2Q3
0 1
00 A H
01 B C
11 G E
10 F D
A 000
B 001
G 011
F 010
H 100
C 101
E 111
D 110
A 0 0 0 1 1 1,1 1 1 1,0
G 0 0 1 1 1 1,0 1 1 1,0
- 0 1 1 - -
C 0 1 0 1 0 0,1 1 0 1,0
E 1 0 0 0 0 1,0 0 0 0,0F 1 0 1 0 0 0,0 0 0 1,0
B 1 1 1 0 1 0,0 1 1 0,1
D 1 1 0 1 0 1,0 1 0 0,1
x=0 x=1
Q1Q2Q3 Q1Q1+ Q2Q2
+ Q3Q3+ Q1Q1
+ Q2Q2+ Q3Q3
+
0 0 0 0 1 0 1 0 1 0 1 0 1 0 1
0 0 1 0 1 0 1 1 1 0 1 0 1 1 1
0 1 1 0 - 1 - 1 - 0 - 1 - 1 -
0 1 0 0 1 1 0 0 0 0 1 1 0 0 1
1 0 0 1 0 0 0 0 1 1 0 0 0 0 0
1 0 1 1 0 0 0 1 0 1 0 0 0 1 1
1 1 1 1 0 1 1 1 0 1 1 1 1 1 0
1 1 0 1 1 1 0 0 1 1 1 1 0 0 0
5. 249
X=0 x=1
Q1Q2Q3 J1K1 J2K2 J3K3 J1K1 J2K2 J3K30 0 0 1 1 b 1 b 1 b 4 1 b 1 b 1 b
0 0 1 1 b 1 b b 0 1 b 1 b b 0
0 1 1 b b b b b b b b b b b b
0 1 0 1 b b 1 0 b 1 b b 1 1 b
1 0 0 2 b 1 0 b 1 b 3 b 1 0 b 0 b1 0 1 b 1 0 b b 1 b 1 0 b b 0
1 1 1 b 1 b 0 b 1 b 0 b 0 b 1
1 1 0 b 0 b 1 1 b b 0 b 1 0 b
250
J2 xQ1
Q2Q3
00 01 11 10
00 1 1
01 1 1
11 b b b b
10 b b b b
K2 xQ1
Q2Q3
00 01 11 10
00 b b b b
01 b b b b
11 b b
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1
J1 1 , K Q xQ1 2 3 , J Q2 1 , K Q2 3 , J x Q Q x Q3 1 2 1 ( )( ),
K x Q Q3 2 1 ( ) z xQ Q xQ Q 1 3 1 2 .
1 2 3 4J1 xQ1
Q2Q3
00 01 11 10
00 1 b b 1
01 1 b b 1
11 b b b b
10 1 b b 1
K1 xQ1
Q2Q3
00 01 11 10
00 b 1 1 b
01 b 1 1 b
11 b 1 b
10 b b
11 b b
10 1 1 1 1
J3 xQ1
Q2Q3
00 01 11 1000 1 1 0 1
01 b b b b
11 b b b b
10 0 1 0 1
K3 xQ1
Q2Q3
00 01 11 10
00 b b b b
01 0 0 011 b b
10 b b b b
z xQ1
Q2Q3
00 01 11 10
00 1
01
11 b 1 b10 1 1
5. 251
252
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- -
-
0, D1, D2 3 -
- -
5. 253
-
i
i
- i(i=0,1, 3).
254
- -
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-
- -
-
Shift - - - -
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5. 257
- 64.
-
258
0 1 0 2 1 Q3 2
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000 000 0000
001 001 1000
010 011 1100
011 010 1110
100 110 1111
101 111 0111
110 101 0011
111 100 0001
- - -
- - - -
4-
Q3Q2Q1Q00 0 0 0
0 0 0 1
0 0 1 0
0 0 1 1
0 1 0 0
0 1 0 1
0 1 1 0
0 1 1 1
1 0 0 0
1 0 0 1
1 0 1 0
1 0 1 1
1 1 0 0
1 1 0 1
1 1 1 01 1 1 1
-
-
-
5. 259
- -
-
260
Q1Q2
x =0 x =1D1D2 D1D2
0 0 10 01
0 1 00 11
1 1 01 10
1 0 11 00
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4-
0: -
5.68.
D Q x Q x Q x1 2 2 2 D xQ xQ Q x2 1 1 1 .
-
D2 x
Q1Q2
0 1
00 101 1
11 1
10 1
D1 x
Q1Q2
0 1
00 101 1
11 1
10 1
5. 261
-
262
5.8
- + Q.
-
L G Q Q+
0 0 0 00 0 1 10 1 0 0
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0 1 0 00 1 1 01 0 0 0
1 0 1 11 1 0 11 1 1 1
L G Q+
0 0 Q
0 1 0
1 0 Q
1 1 1
GQ
L
00 01 11 10
0 1
1 1 1 1
LGQGQ
L G Q Q+ T
0 0 0 0 00 0 1 1 00 1 0 0 00 1 1 0 11 0 0 0 01 0 1 1 01 1 0 1 1
1 1 1 1 0
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5. 265
-
Q1Q2Q3Q4 Q1+Q2
+Q3+Q4
+
0 0 0 0 0 0 0 1 0
1 0 0 0 1 b b b b
2 0 0 1 0 0 1 0 03 0 0 1 1 b b b b
4 0 1 0 0 0 1 1 0
5 0 1 0 1 b b b b
6 0 1 1 0 1 0 0 0
7 0 1 1 1 b b b b
266
5. -
Q3Q2Q1Q0 Q3+Q2
+Q1+Q0
+
0 0 0 0 0 0 0 0 1
1 0 0 0 1 0 0 1 0
2 0 0 1 0 1 0 0 13 0 0 1 1 b b b b
4 0 1 0 0 b b b b
5 0 1 0 1 b b b b
6 0 1 1 0 b b b b
7 0 1 1 1 b b b b
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8 1 0 0 0 1 0 1 0
9 1 0 0 1 b b b b
10 1 0 1 0 1 1 0 0
11 1 0 1 1 b b b b12 1 1 0 0 1 1 1 0
13 1 1 0 1 b b b b
14 1 1 1 0 0 0 0 0
15 1 1 1 1 b b b b
Q1Q2
D1 Q3Q4
Q1Q2
D2 Q3Q400 01 11 10 00 01 11 10
00 b b 00 b b 101 b b 1 01 1 b b
11 1 b b 11 1 b b
10 1 b b 1 10 b b 1
Q1Q2
D3 Q3Q400 01 11 10
00 1 b b
01 1 b b
11 1 b b
10 1 B b
21313211 QQQQQQQD 32322 QQQQD
33 QD 04 D
8 1 0 0 0 b b b b
9 1 0 0 1 1 0 1 0
10 1 0 1 0 1 0 1 1
11 1 0 1 1 1 1 0 012 1 1 0 0 1 1 0 1
13 1 1 0 1 1 1 1 0
14 1 1 1 0 1 1 1 1
15 1 1 1 1 0 0 0 0
Q1Q2
D3 Q3Q4
Q1Q2
D2 Q3Q400 01 11 10 00 01 11 10
00 b 1 00 b01 b b b b 01 b b b b
11 1 1 1 11 1 1 1
10 b 1 1 1 10 b 1
0123133 QQQQQQD 012023122 QQQQQQQQD
Q1Q2
D1 Q3Q4
Q1Q2
D0 Q3Q4
00 01 11 10 00 01 11 1000 1 b 00 1 b 1
01 b b b b 01 b b b b
11 1 1 11 1 1
10 b 1 1 10 b 1
013011 QQQQQD 00 QD
5. 267
a b c d x y z w
0 0 0 1 1 3 0 0 0 0 0
1 0 1 0 0 4 1 0 0 0 8
2 0 1 0 1 5 0 1 0 0 4
3 0 1 1 0 6 1 1 0 0 12
4 0 1 1 1 7 0 0 1 0 2
5 1 0 0 0 8 1 0 1 0 10
6 1 0 0 1 9 0 0 0 1 1
7 1 0 1 0 10 1 0 0 1 9
268
Q1
LSB
Q1
Q2
Q2
D1 Q3
Q3
D2 D3
x
C
MSB
Q4
Q4
D4
0123456789101112131415
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7 1 0 1 0 10 1 0 0 1 9
8 1 0 1 1 11 0 1 0 1 5
9 1 1 0 0 12 1 1 0 1 13
0
b
1
2
3
4
5
6
78
9
10
11
12
13
14
15
a
d
c
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
0
y
x
w
z
-
z
5. 269
270
x =0 x =1
A A,0 C,0
B D,1 A,0
C F,0 F,0
D E,1 B,0
E G,1 G,0
F C,0 C,0
G B,1 H,0
H H,0 C,0
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1 2
-
-
-
- J xQ1 2 , K xQ1 2 , J x Q x Q2 1 1 ( )( ) , K x Q x Q2 1 1 ( )( )
z Q1 2 z Q2 1 .
Q1Q2x1x2,z
00 01 10 11
0 0 1 0,0 1 1,0 0 0,1 1 1,0
0 1 1 0,1 1 1,0 0 0,1 1 1,1
1 0 0 0,0 0 1,1 0 0,1 0 1,0
1 1 0 0,1 0 1,0 0 0,1 0 1,1
5. 271
L M Q Q+
0 0 0 00 0 1 0
0 1 0 00 1 1 01 0 0 1
1 0 1 11 1 0 1
1 1 1 0
- 1 2 1 z2
1. Balabanian N., Carlson B.: Digital logic design principles, John Wiley& Sons, New York, 2001
2. Balch M.: Complete digital design: A comprehensive guide to digital
electronics and computer system architecture, McGraw-Hill, New York,2003
3. Mano M., Ciletti D.: Digital design, Prentice Hall, New York, 2007
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1 2 1 2
Q1Q2x1x2,z1z2
00 01 10 11
0 0 00,00 01,00 11,00 00,00
0 1 01,00 01,00 11,00 01,00
1 0 10,11 01,11 11,10 10,10
1 1 11,10 01,10 11,10 11,10
Beograd, 1994
projektovanja digitalnih sistema, Nauka - Beograd, 1995
6. cCluskey E.: Logic design principles: With emphasis on testablesemicustom circuits, Prentice Hall Englewood Clifs, New Jersey, 1986
7. ull L., Lobur J.: The essentials of computer organization and
architecture, Jones and Bartlett, Boston, 2003
digitalne elektronike, II deo- knjiga, Beograd, 1985
9. anenbaum A.: Structured computer organization, 3rd edition, Prentice
Hall Englewood Clifs, NJ, 1990