-
I.M.
&
&
2006
-
u iJV
, c"' ;. f!-flops, , cp ~',
.. , / .i; . . . , c
.
.
Boo/e .
Karnaugh. ,
, Boo/e. , , .
,
. Karaugh, Quine-McCtuskey
, f , flip-flop. , fli-flops , .
-
a. , , , . , a,
, , a a.
a .
a BCD LEDs ( LCDs) 7-.
.
RAM ROM,
. , .
, , ,
, .
. -,
. .
,
. , , .
/..
-
1 1
1-1 1 1-2 2 1-3 2
3 4
1-4 5 1-5 8 1-6 11
2 1-7 12 1-8 BCD 13 1-9 13 1-10 14
14 1-11 15 1-12 Gray 16 1-13 19 1-14 ASCII 20 1-15 20
-
\/! ,s,. ~~
1-16 r
-
--
vii
Karnaugh 58 Karnaugh 62 Karnaugh 63
2-11 Karnaugh 64 2-12 65 2-13 69 2-14 70
71
3 77
3-1 OR 78 3-2 AND 78 3-3 79 3-4 NAND 80 3-5 NOR 80 3-6 EXOR 81
3-7 EXNOR 82 3-8 83 3-9 NAND NOR 86 3-10 87 3-11 OR AND 91 3-12 RTL
RCTL 93 3-13 DTL 94 3-14 95 3-15 TTL 99 3-16 MOS 102 3-17 CMOS
104
-
&
3-18 TTL CMOS 106 CMOS TTL 106 TTL CMOS 108
3-19 12L ECL 109 3-20 111 3-21 112
113
4 119
4-1 v 120 4-2 120 4-3 121 4-4 Karnaugh 122
4-5 127
Karnaugh 4-6 129
Quine McCiuskey 4-7 135
Karnaugh 136 4-8 141 4-9 144 4-10 149
4-11 152
156
-
ix
5 163
5-1 163
5-2 169 5-3 170
555 170 555 174 74121 176 7 4122 7 4123 178 CMOS 179
5-4 180 5-5 181 5-6 182 5-7 183
185
6 FLIP-FLOP 187
6-1 Flip-flop S-R 190 6-2 Flp-flop S-R 193 6-3 Flip-flop J-K 194
6-4 Flip-flop 197 6-5 Flip-flop D 199 6-6 Flip-flop Master-Siae 201
6-7 Flip-flop 204
209
-
&
7
7-1
7-2
8
8-1
8-2 8-3 8-4 8-5
8-6
9
9-1
Johnson
Flip-flop S-R Flip-flop J-K
BCD
215
215 216 217 219 219 219
223
227
227 228 229 230 232 234 242 243 246 251
254
257
257
-
9-2 263
9-3 BCD 264
9-4 266
9-5 ?- 267 LED ?- 267
(LCDs) 268 9-6 BCD LED ?- 270 9-7 BCD LCD ?- 277
9-8 LED ?- BCD 278
279
10 283
10-1 284 10-2 286 10-3 289 10-4 291 10-5 294
298
11 301
11-1 302 11-2 303 11-3 305 11-4 1-Bit 305 11-5 RAM N-Bits
307
-
&
11-6 DRAM
11-7 RAM 11-8 ROM
12
12-1 12-2 12-3 12-4 12-5 12-6
13
13-1 & 13-2
13-3 - 13-4
Paull & Unger 13-5 13-6 13-7
314
314
318
323
325
325
331
333
335
336
338
339
341
342
346
347
349
350
354
356
361
363
-
13-8 13-9
14
Flip-Fiops S-R
&
Bl
EYPETHPIO
xiii
365 366 366 367
386
389
447
449
-
1 &
, , , . ,
, ,
. , .
1-1 J
, , . , ,
, . , , , 1. ,
, 1, . , ASC/1 (American Standard Code for lnformation
lnterchange) 256
. 8 0-9, ,
.
-
2 1
1-2
1 , ,
, , . , 199 , :
199
, , k k+1 , ( ). , , (k=3) :
k- = 3- 1 =
(1 0), . , (bit), 1, . ,
( ), a 1. 1
, . , byte, 28 =256 .
1-3
, , 2, 1.
n :
-
& 3
, ,n-1 -,-:' 11 _ 1 .:. + 11 _::'.:. + -, ,,+.:. , +r,.:.
+ ,- ! '1- ::' '")'"111 _ 1 .:. + _ ::' .:. + , , + -]ll-
1.1:
1 1 2 1 3 1 1 4 1 5 1 1 6 1 1 7 1 1 1 8 1 9 1 1
10 1 11 1 1 1 12 1 13 1 1 1 14 1 1 15 1 1 1
, i , () () .
, . , 11 011 :
lx2 5 + lx24 + 23 + lx22 + lx2 1 + 2 =54 , 1010.1 :
lx21 +022 +lx2 1 +02 +lxT 1 =10.5 15 1.1.
-
4 1
2 2. 18.35 :
:
18:2 9 () 9:2 4 4:2 2 2:2 1 1:2 ()
, 18 1001 . , :
2
0.352 0.70 0.702 1 0.40 0.402 0.80 0.802 0.60
0.602 0.20 0.202 0.40
, , , 1011 :
, 18.35 .
-
& V, 5
1-4
J ;; . ,
9, 1. , ,
0+0=0
+ 1 = 1
1 += 1
1 + 1 = 1 ,
, :
(7) 10 1 1 1 (5.25) 10 101.01 + + + +
(3) 10 1 1 (11 50)10 1011.10
( 1 ) 10 1 1 =(1 0)10 (16. 75)10 1 . 1 1
. :
- = 1 - = 1
- 1 = 1 - 1 =
1
-
6 1
2 , r . 1 (2-1 = 1) 1 , c:,
.
_ _ 2
( 16) 1 10
(?) 10 1 1 1
(9) 10 1 1 =(9)
(23) 1 1 1 1 10
(4) 10 1 (19)10 1 1 1=(19)10
. , , (1) ,
. , , . ,
k , k .
-
&
t.:J
(13)10
(7)10 (191)10
+
1 1 1
1 1 1
111 1 1 I I
1 1 1 I
1 1 1
(0.34) 10
(5) 10 ( 1 7) 1
1 1 1 1 1=(91 )10
(4.25) 10
(3.25) 10 (13.8125)10
1
+ I 1 . 1
1 00.01
1 1.01
. 1 I
1 1 . 1
1 1 1 . 1 1 1=(13.8125)10
.01011
1 1
1 1 1 +
1 1 1 1 . 1 1 1 1 =(1 7)10
7
, .
. , , ,
. , ( ) 1. , ,
. ,
-
8 1
, , , i , , a , , .
(16) 10
(3) 10
10000
1 ~ I (5 333) 10 1 1
1 1 1
1 1 1
1 1
1 1
>>
1 >>
>>
~(5+0.25+.) 10
1-5 J . ,
-
& 9
, (+) (-). , 1 . , .
1 1
1 1 1
:
+ , ( ) .
+ , ,
:
l l
2 -3
1 1 1 1
lu
1 1 _j_Q_
1
()
> 1 1 -(-1)
, , , (2), ( 1
). , , n , n -. , 3 ( 4 ) :
2n -3 = 24 - 3 = 16 - 3 = 13 = ( 1 1 1 )2 , , (-3)2 1 1 1 1.
, (3)2, . , (3) 2. :
-
1 1
1
1111 1 1 + 1
1 1 1
1
1 1 1 =( -3) 10
L 2 ( 1 1 ) 1. , (3)10 = (00 11 )2 :
1
1111 1 1 + 1
1 1 1
1
1 1 1 =(-3) 10
L :
1. 2 ().
2. , , . 1.
3. .
4. a : ,
. 1,
2. , :
-
&
2
5 --- 1 1 -3 >> 1 1 1
1 ---t>(2) 10 2 1
-3 >> 1 1 1
4 11 1 1=(15)10~2 -15 = (- 1)10
11
, (hardware) . ,
.
1-6 2
, 2, . , m , m
2 . , . ,
(=8), 23= 8, .
2.
1 1 1 1 1 1 4 (m=2) :
-
12 1
1 1 00 1 1 1 1
I I i 2 1 2 3 2
, (1 001001 111 0) 2= (21 0232)~
(m=3) :
100 100 101 110
4 4 5 6
, (1 0010010111 0)2= (4456)8
1-7 , , . , ,
, . , , . , , 1 , .
, ().
)( . , ,
, , a .
- -'\ ,
-
14 1
1.3. . k k+3 BCD. BCD, t , .
, ;J 9
, . . 4 1 1 1. 4 9 5. , 1 1 1 1 , u
5.
1. 3
2 3 1 4 1 5 1 6 7 8 1 1 9
1-10
8 , , 7. , 25 28 1 + 58=21.
3- :
-
- ,
-
16 1
. , 5 ,
. , (7 ),
1.5
1 1
1 1 1 2 1 1 3 1 1 4 1 1
5 1 1 G 1 1 7 1 00100 8 1 1 9
1 1
1-12 GRAY
Gray , ,
. Gray 1. 1.6 Gray 2, 3 4 .
Gray k Gray k-1 :
k-1 . 2k 1 Gray k .
2k 1 Gray k-1 .
-
& 17
1 6 Gray 2, 3 4
i i . . Gray . . Gray . . Gray
00 1 1 1 1 2 1 1 2 1 2 1 3 1 3 1 3
4 1 1 4 5 1 5 1 6 6 1 7 7
8 9 1
10 11 1 12 13 1 14 15
, , Gray 2- Gray 3-:
. Gray 2 . . Gray
. Gray . . Gray
k-1 2 -1. 00 000 1 1 001 2 1 1 k-1 2 1 1 3 1 2 -1 = 3 1
4 1 1 5 1 1 1
. Gray 2
6 1 1 k 1 2 -1 = 7 __ 1
Gray , :
Gray .
-
18 1
. , , Gray =.
,
=1, .
/
:
Gray
Gray
0101100110 0110111011
I I ~w
Gray .
8 Gray
6 4
2
10101111---t> 11111000
15 7 3
1
-
& 19
1-13
(hexadecimal) 16 9 , , C, D, F. A-F 1 15. 1 7 . , 1 16 116 1 +
Ox16a = 16. 31 1 F, 15 .
i 1.7.
3 1 3 9 1 9
10 1 1 16 10 20 14 30 1
, :
1 2 0001 0010 1 1
I 45 . 7 c 0100 1 1 1 1 1 1 1
I 111 I I I I
-
20 1
1-14 ASCII ASC/1 (Amercan Standards Code for lnfor-maton
lnterchange) 8 (1 byte)
. ASCII 4-3-2-1 BCD. 5 ASCII 1 1 1 1. 1.8 ASCII.
i 1.8: i SC
1 1 1 1 1 1 2 1 1 1 3 1 1 1 1 4 1 1 1 5 1 1 1 1 6 1 1 1 1 7 1 1
1 1 1 8 1 1 1 9 1 1 1 1
1 1 1 1 1 1 c 1 1 1 1 D 1 1 1
1 1 1 1 J 1 1 1 1
1 1 1 1 1 1 1 1 + 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1
1-15 .
c1 , ,
-
21
cc { i c r u (._~ ) 4
. , ut r u . , . , 1000. 1100, 111 1111. f: ) 1 \J 1 v iv
, : ' ri l l. , 1100 (),
111 , (). (, i 1101), , . , { , n
, ( 2''), n
. i , n=4 ,
, 2'1= 16
3 . Hammng d ", 4 , ,
Hamrning, d""' , 16 , 3. , e
n , Hamming, , :
d.'"''~::2e+1 (1-1) d,nr,
(1-2)
.
-
22 1
1-16 HAMMING
(J ,
r (J ( ). (1-2)
, Hamming 3. 8 : 000, 001, 010, 011, 100, 101, 110, 111. , ,
d=3, ( 1 1 1). , d=3. ( 1 ), (1 1 0). , ,
, .
d=3
d=3
, , ( ) ( 1 1), d=2. , ( ) ( 1 0). , ( ) ( 1 1). , ( ) (1 1
1)
d=3, . , ( ) ( 1 0), ( 0), (1 1 1) , ( 1 0). ,
, Hamming, .
-
r & 23
1-1
(.., , ) 5 , , , .
25=32 5 dmn=5. , , 00000. d=5, , 11111.
1.9:
'
00000 00001 1 00011 2 00100 1 00101 2 00110 2 01000 1 01001 2
01010 2 01100 2 1 10001 2 10010 2 1 1 2 1 1 2
1 1 1 1 1
1 1 1 2 1 1 1 2
1 1 1 2 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 1 1 1 1 1
2 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1
-
24 1
, 30 I'Jo :1 ccn c , cJ vuc 1 9. v , f: 1. ( 0), , f: , - uv (1
1 1 1 1)
1-17
, r . ( 1) 1, , r'] ,
, . 1.1 BCD .
.
1.1 BCD BCD BCD
1 1 1 1 2 1 1 3 1 1 4 1 1 5 1 1 1 1 6 1 7 1 1 1 1 1 1 8 1 9
1-18 HAMMING
Hamming. Ham-
-
& 25
ming (7,4) 7 . (
), . Hamming (7,4) :
C1 , C2 , C3 ,, 2, 3, 4 .
:
C3=12 13 14 EXOR (Exclussve OR) ,
, :
= = 1
= 1 1 = , Hamming (7,4)
. , , , 2 3 4 = (1 001 ). Hamming (7,4) :
c1 = 11 12 14 = 1 1 = c2 = 1 13 14 = 1 1 =
C3=23 4= 1 = 1 , :
, , :
-
26 1
, () 1. , C1 , C2 C3 ,
:
C 1 =11214=10 1=0 c2 = 11 13 14 = 1 1 =
c3=21314= 1=1 C1, C2 C3
. , C1 , C2 C3 C3 . 1 .
.
( 1), , , . ( 1
), . ,
.
1 1
0011001
0011000
-
& 27
C1, C=' C3 :
c3 c 1
.
, , , .
1-1 , :
) 10010010.001, ) 0.0001, ) 1.00
1-2 : ) 30.45, ) 18567.003, ) 0.33227
1-3 : ) 1011.01 + 110.11
) .001 + 1.0001 ) 11 + 111 + 1111
1-4 :
) 1011.01 +0110.11 ) 1.001 +1.1001 ) 11 + 111 + 1111
1-5 :
) 1011-111 ) 101.001-111
1-6 :
-
28 1
( I 7) IU (8) ]11
( -9) ( -6) ]tl
1-7 :
) 1.00111 101 ) 11.01:0.11
( -13 )]11 (-18) ]()
1-8 :
(11) 111 (5) ]()
(9.9) ]() (3) ]()
( 0.25) 10
(415)10
1-9 BCD : ) 44, ) 67, ) 541.
1-1 : ) (31)8 , ) (124.07)a
1-11 : ) 19, ) 728, ) 12.48
1-12 : ) (222)8, ) (77 .201 )8
1-13 1001-0111-0011 BCD, .
1-14 110110111 Gray .
1-15 10101 Gray.
1-16 : ) 1 F.C, ) 89., ) .ABC
1-17 : ) 10111.01, ) 1100110011.001
-
ii & . 29
1-18 Hamng (7,4) ) 1111, ) 0000 ) 1010
1-19 1027 .
1-20 16 BCD ~J ASCII
1-21 1001 Hamming (7,4).
) 0111001, ) 0001001, ) 0000001 ;
1-22 ,
, , .
Hamming (7,4).
1-23 , 4 , Hamming (7,4) . a .
1-24 , 3 , Hamming (7 ,4 ). a .
-
---,
I I I i j
I
-
r
2
BOOLE
Boole George Boole ,
. 100 Claude Shannon Boole , .
. , ,
1. Boole, , .
2-1
Boole, , . , ... Boole ,
. Boole :
-
32 2
S C (). C C 1.
_ + () . (). (OR) (AND) Ct
[=] .
, S 1. Boole,
, , C ... , 1 , ;', ... , ,,. ,
, = , , ~~ . . , , . + - Boole,
S OR AND
1:
OR (+) AND (.) + = + 1 = 1 1 1 + = 1 1 1 + 1 = 1 1 1
2-2 BOOLE
=
=
=
=
1
Boole, ,
-
r BOOLE 33
1:
+ - a :
+=+ .= .
2:
(+ ) + C = + ( + C) ( . ) . C = . ( . C)
3:
+ ( . C) = (+ ) . ( + C) . ( + C) = . + . C
, OR AND c
4: 1
+= . 1 =
5:
+=1 = :
1:
OR AND , :
-
34 2
+ = 1 + = 1 1 1 = 1
1 =
1 (. 4), 1.
2:
: + 1 = 1 =
+1=(+1)1 . 4 =(+ 1)-( +) . 5
=+(1) . 3
=+ . 4 =1 . 5
=+ . 4 =+ . 5
=(+) . 3
= . 4 =0 . 5
3:
. + = =
-
F
BOOLE
+=(+)1 . 4 =(+) (+) . 5
=+() . 3 =+ 5 = . 4
=+ . 4 =+ . 5
=(+) . 3 =1 .2 = . 4
4:
: + . = (+ ) =
+ =1+ =(1+)
= ( +1) = 1 =
-(+) =(+) -(+) =+(-)
=+ =
. 4 . 3
. 2 2 . 4
. 4 . 3
2 . 4
35
-
36 2
5:
:
+=+ (+ )=
+ = ( + ) . ( +) . 3 =1(+)) . 5 = + . 4
( +)= + . 3 =+ . 5
= . 4
6:
: =
=() =
p 7: De Morgan
:
01 02
+= -- --
=+
-
BOOLE 37
1, 5, :
(+)+ =-=(+ )+ -
=++ = +1 =1
:
()(+)= + =0+0
=0
, (+), 5, , :
+=
. :
-
++=(+)(+)+ -- -
=1(+)+
=++ =+1 =1
()(+)=-+ =0+0
=0
, () + , :
-
38 2
2-1
:
: =-=---==------
ABC+A+B+C=ABC ABC --- --- ---= ABC+BBAC+C CAB
=0 B-C+OAC+OAB =0+0+0 =0
2-2
( + C) .
: (AB+C)A = AB+AC
=(AA)B+AC =AB+AC =A(B+C)
2-3
:
+
: +=
-
r t
BOOLE
=(+)(+) -
=+ + + =+ ++ =+
,.
2-4
+ + = 1 .
:
+ + =(+)+ - -
=(+)(+)+ = 1-(+)+ =(+)+
=(+)+ =1+ =(1+)1 =(1+)(+) =+1 =+ =1
2-3
39
(relays), : . 1 ,
.
.2-1 , , C . , . , Y=A+B+C. , , , C 1 , ,
1. . 2-2.
-
40 2
c
. 2-1 .
i
=(+ C) D
i
t:~~y ~ '
'---------""
=((+ C) + D)
. 2-2. .
. . 2-3. :
= AB+CD+ADE+CBE
:
= ( +C)(B+ D)E +( +CD)E =ABE+ADE+CBE+CDE+ABE+CDE
- -
= ( +)+ ADE +CBE +CD(E +)
-
BOOLE 41
= AB+CD+ADE+CBE
c
= AB+CD+ADE+BCE
. 2-3. .
, , , ,
Boole, . .
2-4
= f(A, , C, ... ), Boole, + (OR) . (AND). , , C, ... , -
- - - , , , C ... , . , , .
n , 2n n 1 , n
22n. 2.1 5 . , , , 4
: , , , . , (AND), : (=0), , ,
.
-
42 2
2.1: n .
n ~n n 2 2~
2 4
2 4 16
3 8 256
4 16 65536
5 32 :::::. 4 3 10 9
(OR), : + (=1 ), +, + , + + .
, : + , + .
2.2: f f
+
+
+
+
+ +
2.2 16 . ,
, .
-
"
BOOLE
2-5
43
, . , , C
f(A,B,C) = + ABC + BC (0, 1) , 2.3.
, . , .
, , , Q . , , w
, , C, , {./
. 2.3:
ABC ABC BC f(A, , C) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1
, (). . , :
f(A,B,C) = -B-(C + C) + A-B-C t (+ ) B-C , =ABC+ABC+AB
C+A-B-C+A-B-C
, ,
-
44 2
. . -cril
, , . , 2.3,
f(A,B,C)=O : -
f(A,B,C) = ABC+ C+A BC , :
f(A, , C) = ABC + ABC + ABC = ABC+ ABC+ ABC
- --
=(+ + C) (+ + C) (+ + C) .
2-6 I I , .
OR AND.
Boole , AND. , , , 2, ; , 4 234, 1 2
2 ,, 1 234 , ... .
__ , . 4 , , 2 , 3 4
2,4 2,4' 234' ... .
-
BOOLE 45
Boole, n .2' 1 ( n ).
24
1
. 2.4 :
123
1 2 3 mo a 1 1 2 3 m1 a 1 2 1 2 3 m2 a 2 1 3 - 1 2 3 m3 a 3
4 1 2 3 m4 a 4 1 5 1 2 3 m5 a 5
6 1 2 3 m6 a 6 7 1 2 3 m7 a 7
, .
2-5
:
-
f(x1,x 2 ,x3 =1 + 1 (2 + 3 )
-
f(x 1,X 2 ,x3 )=X1 + 1 (2 + 3 ) =1(2 +2)(3 +3)+12 +13 = 123 + 12
3 + 1 23 + 1 2 3
+12+13
-
------------~-------
- -~ -
+12(3 +3)+1(2 +2)3
2.4, , m,_ :
2 -1 f(x 1,x 2 , .. ,xn) = a1m 1
~
m, = i, i = , 1, _ , .2n -1 a, = 1 , , ,
m,.
, : - - - --
f(x1,X2,x3)=X1X2X3 + 1 7 3 +1 2 3 + 1 2 3 =m4 +m5+m3+Hl =
(3,4,6,7)
: F I = (l, 3, 4, 7) , ,
1, 3, 4, 7_ :
m 1
rn 3 1
m 4
m 7 1 1
-
:,
:
BOOLE 47
-
F3 = 123 + 123 + 123 + 123
2-7
n [ OR , , 1, 2, 3, 4 ( 1 + 4 ),
( 1 + 2 + 3 + 4 ) .
, . , , C + + C , + + C, + + C . . n 2n
, . ~
( , , 'a ,
. n1i
, , mi , 1 . , 3 m3 ,
: - -
m3 = 3 = 1 2 3 = 1 + 2 + 3
,
,
-
48 2
, 61. ,
- - -
f(X 1,X 2 ,X 3 )=(X 1 +2 + 3 ) (1 + 2 +3)( 1 + 2 +3) = (01 0,1
01,001) = ~ 1\1 :i J\1 1 = fl ( ~, J\1 :i , 1 )
=]( , 2, )) , .
2-6
:
-
=(1 +3)(2 +3)
:
-
= (1 + 3). (2 + 3) - - -
=(1 +22 +3)(11 +2 +3) =(1 +2 +3)(1 +2 +3)
- - -
(1 +2 +3)(1 +2 +3)
, , , :
l 1
-
BOOLE
: --- -
mo 1 2 3 4
m4 1 2 3 4 -
m5 1234
-
m6 1 2 3 4 -
m7 1 2 3 4 - --
ms 1234
m10 1 2 3 4 -
m14 1 2 3 4
m15 1 2 3 4 :
-
+ 1234 + 1234 + 1234 + 1234 + 1234 + 1234
-------
f = f = mo m4 ms m6 m7 ms m1o m14 m15 - -
=(1 +2 +3 +4)(1 +2 +3 +4)(1 +2 +3 +4)
- - -
(1 +2 +3 +4)(1 +2 +3 +4)(1 +2 +3 +4) - - - -
(1 +2 +3 +4)(1 +2 +3 +4)(1 +2 +3 +4)
:
49
.
(.) (+).
-
50 2
2-7
:
- -
= 12 (3 + 3) + 1 (2 + 2 )3
= (1 1,1 ,11,1)
, :
,
= = -
=(1 +2 +3)(1 +2 +3) - - -- - -
(1 +2 +3)(1 +2 +3) -
= (1 + 2 + 3). (1 + 2 + 3) - - - - -
(1 +2 +3)(1 +2 +3)
,, =, 2, 6, 7 .
-
'
BOOLE 51
2-8
. 2-4, .
. 2-4. .
2.5, . :
Z=ABCO+ABCO+ABCO+ABCO
, :
-
= = C + C + C + CO
= C C C CO
=======-
( + + C + D )( + + C + D)
=(+ + C +)( + + C + D)
(+ + C +)( + + C + D)
-
52 2
. 2.5 .2-4.
I /0 1/0 ABCD z ABCD 0000 1 0001 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1
2-8
z
, ,
(). , (1)2 , 21 ai-1, ai-2, .... , a2, a1, ao, .
. ,
(3)1=44 :
87 86 85 a4 83 a2 a1 ao
(~) = 44 = ( 1 1 1 )2 10
I m5 m3 m2
, : f(x1,x2 ,x3 ) = (m5 ,m 3 ,rn 2 )
-
BOOLE 53
= (11, 11, 1)
2-9
(},,=200 .
:
(~) = 200 =( 1 10 I 1 1
m 7 m 6 ,
f(x 1,x2 ,x3 ) = (m7 ,m 6 ,m 3 ) = (111, 11 , 011)
2-10
(2)1=14 .
:
(2 ) 10 = 14 = 1 1 1 )2
m3 m2 m1 mo ,
-
-54 2
-
f(x 1,x 2 )=m 0 =12
2-11
:
f (1, 2, 3) = ~ >2 + ~3
: -
f(x1,x2,x3) = ~>2 + ~3
1
= (196)10
2-9 , ,
-
BOOLE 55
, . 2-5 (). , = ,
. , . 2-5(). ,
, . 2-5().
~ () ()
to ~ ~ 1
() () 011 111
010
I 101 000 ~ 100
() . 2-5. -.
. 2-5() =+ . , . 2-5().
, . . 2-6, Z=ABCD +
- -- - -- --
ABCD + CD + CD + C . , ,
, .
-
56 2
1111
. 2-6. .
, , ,
( ).
2-10 KARNAUGH
1, Karnaugh. 2n ()
( n>1). Karnaugh 2n f; .-.
Karnaugh 6 , . 6 , Karnaugh
, .
rv Kamaugh
, Karnaugh :
-
--------------------------
BOOLE
5J ~ ~ 57
f(x) = f(x) = Karnaugh :
~ ~ f ()=
~ ~ f ()=
Kamaugh
1
mo m2
1 m1 m3
, , :
Karnaugh : 1 2 1
1
1 1 1
-
58 2
Karnaugh
-
1 c l,J m4 c 00 mo m4
m1 ms 01 m1 ms
mJ my 11 m3 m?
m2 m5 10 m2 m c
:
Kamaugh :
1 1 3 00
01 1
11
10 1
Kamaugh
, ( ) Karnaugh . 4 , .
-
r ---------- ---------------------
BOOLE 59
c D 00 01 11 10
mo m4 m 12 ms D 00 mo m4 m 12 ms
m1 ms m13 mg 01 m1 ms m13 mg
m3 m m1s m 11 11 m3 m m1s m11
m2 m6 m14 m1o D 10 m2 m6 m14 m1o
2-12
Kamaugh : = f(x1, 2, 3, 4) = 124 + 234
:
Karnaugh :
-
r 60 2
Karnaugh, , . (
). . , Karnaugh , m0 m_ 3 . ,
. m4 m13 , , . :Q . .. 1, , , .
2-13
Karnaugh :
Karnaugh. 4 ( 4 ),
1 ( ) 3 ( 3 ).
-
BOOLE 61
2-14
. Karnaugh
24 . 1 3 .
:
2-15
Karnaugh :
:
, Karnaugh f :
-
62 2
1 2
4 00 01 11 10
00 1 1 1
01 1 1 1
11 1 1 1 1
10 1 1 1 1
, ,
(4= 0100, 1 =0001 ).
Karnaugh
Karnaugh 5 4 , :
BC 00 01 11 10 D
BC 00 01 11 10
mo m4 m12 ms m1s m2o m2s m24
01 m1 ms m13 mg 01 m17 ~1 m29 m2s
11 m3 m7 m1s m11 11 m19 m23 m31 m27
10 m2 ms m14 m1o 10 m1s m22 ~ m2s
16 .
2-16
Karnaugh : Z=AB+CD+DE
-
BOOLE 63
s_ 1:
BC DE 00 01 11 10 00 01 11 10
00 1 1 1 1 1
~ v 1 1 1 1 1 CD DE JJ. .(1 1 1 1 1 1 1 v
10 1 1
:
= + CD += (m3 , m 4 ,m 5 ,m 7 ,m 11 ,m 12 ,m13 , + m1s ,m19
,m2o,m21,m23, m24, m2s,
+ m26,m27,m2s,m2g,mJo,m31
Karnaugh
a 6 Karnaugh, Karnaugh 5
.
F CD 00 01 11 10
CD F 00 01 11 10
00 mo m4 m12 ms 00 m16 m2o m2s m24
01 m1 ms m13 mg 01 m17 1:>1 m29 m2s
11 m3 m m1s m 11 11 m1g m23 m31 m27
10 m2 m6 m14 m1o 10 m1s m22 11:3 m26
-
64 2
CD 00
F 01 11 10 F CD 00 01 11 10
00 m32 m36 m44 m4o 00 m4a ms2 mGo msG
01 m33 m37 m4s m41 01 m49 ms3 m61 ms7
11 m3s m39 m47 m43 11 ms1 mss m 63 msg
10 m34 m3a m46 m42 10 mso ms4 m62 msa
26=64 6 .
. , m5 , m7, m13 m15 m21, m23, m2g m31
2-11 KARNAUGH
, Karnaugh, , , , 1. ,
,
. , , (don't care)
d . , Karnaugh, 1, 1.
2-17
Karnaugh:
-
BOOLE 65
L ~
4 00 01 11 10 4 00 01 11 10
00 ~ 00 '1 01 ~ 01 1
11 GJ 11 /-_ 1 10 G) 10 1
'--"'
1, 1. ,
: f(x1, 2, 3, 4) = 12 + 24 + 1234
2-12
/-. 49 ~ . OR AND .a AND OR . f , f 0 . Kamaugh, 1 (
) , , 1 .
1.
2. d - -
-d - =
-
66 2
3. . =+, :
= , :
, =:\,
, , Z=AC+ BC' : =(A+C')(B+C').
2-18
: f(x 1,x2 )=x1+x 2
: fd(x1,x2) = 12 = m3 :
a3 a2 a1 ao
1
m3
f(x 1.x2 ). :
f(.2) =
a3 a2 a 1 ao
(2 )10 = 1 1 )2 =(14)10
m3 m2 m1
l
-
BOOLE 67
a, (. 1, 1, 1, ) ( 1, , , 0). , :
2-19
Kamaugh. .
Karnaugh :
,
, Kamaugh 1, Karnaugh . :
-
68 2
1 1 3 1 1 3
00 1 11 1 .L_
01 1 1 10
11 1 00 1L-
10 1 1 01
, :
1 , .
n& 2-20
f(x1, 2 , 3 ) = 12 + 1 3 (. 2.7).
: fd(x 1,x2,x3)=(x1 +2 )( 1 +3 )
,
- -=13 +12 +23 =1(2 +2)3 +12(3 +3)+(1 +1)23 = 123 + 123 + 123 +
123
f(x 1,x2,x3)=(fd(x1,x2,x3))d =( 1 +2 + 3 )( 1 +2 +3 ) .(1 +2
+3)(1 +2 +3)
-
69
2-13
;.; Ue Morgan cJ c . ( c i C cc
2-21
t\i! f(x1,x2,xJ) c:: 1(2 +3)
(J i
f':J(X1, 2,3) :::: 1 1-- 23 1 , - f: / .. -"
f(x1,x2,x3) = 1 + 2 3
2-22
Karnaugh
4 00 01 11 10
00 1
01 1
11 1 1
10 1 1 1
-
70 2
1. 1,
:
1 = 3~ 00 01
00
01
11
, :
, :
2-14
f , f, ,
f 1, f 2 1. f , f.,
. =>. , f 1 f 2 , f => f 2 . li
I
-
,
:,
J f 1
f
BOOLE 71
f f:', f 1 ::::::> f::o, 1 + f.:: = I. , f 1 1, , f::> 1.
, f 1 , f 1 1. , f 1 f 2 1. , f1 + f 2 = .
2-23
:
, :
- - - -
= 1 + 2 + 3 + 4 + 13 + 24
=(1 +1 3 )+(2 ++24)+3 +4 = 1 + 3 + 2 + 4 + 3 + 4
=1 +( 3 + 3 )+2 +(4 +4) = 1 + 1 + 2 + 1 = 1
2-1 : - -
f(x, y,z, W) = ++ +W + xy + XW
2-2 .2-1.
-
72 t 2 ----------------------.. --------------------
2-1
2-3 f(x1,x 2,x3)=X 1+x2(x1+x3) .
2-4 1 = ~ ( 1.2 .. )) .
2-5 1:1 = .L ( 1.3.\ 9)
2-6 :, = ( 1.2,4) .
2-7 : f(x1. 2. 3) =(,+ 2 )(2 + 3) ~~ .
2-8 r:, = (0.2.4). .
2-9 , = ( 1.4.6). .
2-1 ri:
f(x1,x2,x3)=x1x3 +x2x1 F3 = 1 (0,2.C1)
2-11 ( 2 ) = I 5, .
1
-
)
:
)
BOOLE 73
2-12 ( 3 ) 10 = , .
2-13 Karnaugh :
. z = 12 + 34 . z = 123 + 23 + 123
2-14 Karnaugh : f(x 1,x2 ,x3 ,x4 ,x5 )=X1X2 +24 +3 4 +5
2-15 Karnaugh:
4 00 01 11 10 4 00 01 11
00 1 00 1
01 1 1 1 01 1 1
11 1 1 1 11 1 1 1
10 1 1 10
2-16 : . z = 12 + 1 + 3
10
1
. = (123 + 2 )4
2-17 F3 = (,1,2).
2-18 F3 = (0,2,6).
2-19 :
-
-....... ------------------------
74 2
2-20 Karnaugh
4 ~ 00 01 11 10
00 1 1 1 1
01 1 1
11 1 1
10 1 1 1 1
2-21 :
2-22 Karnaugh:
~
4 00 01 11 10 4 00 01 11 10
00 1 1 1 1 00 1 1
01 1 1 1 01 1 1 1 1
11 1 1 11 1 1 1
10 1 1 1 1 10 1 1
2-23 (3) = 71 (~) =53.
2-24 (3) = 27 ((3) = 45)d.
-
--
BOOLE 75
2-25 .
" '-----------" c
. 2-2
-
3
, V(O) V(1) (LOW) 1 (HIGH) Boole.
1 1. 1
(, V(1)>V(O)), . , V(O) >V(1 ), .
, 1, . ,
, , MOSFET .
, :
-RTL -RCTL -DTL -ECL -1 2L -TTL -CMOS
Resistor-Transistor Logic Resistor-Capacitor-Transistor Logic
Diode-Transistor Logic Emmiter-Coupled Logic lntegrated-lnjection
Logic Transistor-Transistor Logic Complementary MOS Logic
-
78 3
, , , ,
. , TTL CMOS.
3-1 OR
OR, , , C, ... W, , , :
Y=A+B+C+ .. W (3-1) , OR, ,
1, 1.
:=D-y OR
OR
=+
. 3-1. OR , .
OR , , . OR . 3-1.
3-2 AND
AND, , , C, ... W, :
-
79
= 3 ... \V (3-2)
AND. , 1, 1. AND
3-2.
AND
=
. 3-2. AND.
, OR , AND OR . ,
AND, , OR .
3-3
,
() . , , 1
1, . . 3-3. ,
. .
-
80 3
=
--{>-
------------
. 3-3.
3-4 NAND
NAND ( -AND) AND .
NAND
. 3-4. NAND.
NAND . 3-4. , NAND , , 1. , NAND , , C, ... W, :
Y=ABCW (3-3)
3-5 NOR
NOR OR, . NOR . 3-5.
-
81
, , C, ... W NOR :
= + + C + + \V
D~y
NOR
=+
. 3-5. NOR.
3-6 EXOR
(3-4)
EXOR (Exclusie OR) 1, 1. , EXOR, :
= + = EtJ (3-5)
EXOR . 3-6.
EXOR
=
. 3-6. EXOR.
-
82 3
EXOR
'' =(+)(:\ )= (3-6)
, r .
+
(+) ( )
. 3-7. EXOR.
. (3-5) (3-6) . 3-7. EXOR
, .(3-5) (3-6), De Morgan.
3-7 EXNOR
EXNOR (Exc/usive NOR) , 1 . , EXNOR ( coinci-dence gate). ,
EXNOR, :
= (+ ) ( )= + = (3-7) , EXNOR EXOR (.
-
83
EXNOR . 3-8. . 3-9 EXNOR AND, OR .
EXNOR
=
~J>--
. 3-8. EXNOR.
+
. 3-9. EXNOR.
3-8
3.1 .
/ (Drver/Buffer), , . , . , , . , , = AC + BC.
AND , OR .
. 3-1 . ,
( ).
-
84 3
3.1 :
n
~=D- = ~ =D- =+
-
-{>- =
~=(>- -= ~- --=+ ~ =dD- =
--~=- = -(>- =
AC + BC
. 3-1 . .
3-1
:
= AB+BC
( ), . 3-11 ()
.
-
85
--- ~ \6 + EJC
c
()
()
. 3-11. () p! () .
, Boole. :
= +C = C' =(+ ) BC~ = C
, . 3-11 (), AND .
3-2
, , , , = =.
=1, , = =.
-, = , - = . . 3-12
. 3-12. .
-
86 3
3-9 NAND NOR
01 AND, OR NAND NOR. , . 01 3.2 01 3.3 1
. 3.2: NAND , AND OR.
. 3.3: NOR , OR AND
=D-
-
t 87
3-1
,
3.1, . 34
.
. 3.4:
=D- = -=D- = --D- = v-=[)- = =D- , :
+ ( EXOR EXNOR) ( ). , .
+ AND OR OR
AND. .
-
. \.
{jJ , , 3-13(), ,
1. , c --1 (active-high).
c
()
c
()
c
()
. 3-13. : () , ()
() .
. 3-13()-(), = 1,
1. , C, D . , ' .
= ( --, active-low), .
3-3
. 3-14 NOR.
l !
-
89
r r 3.4 . 3-15()-().
c D
+ CD
. 3-14. r r . -
- -
+ CO + CO - -c c
() ()
AB+CO
c
() . 3-15. NOR.
3-4
Y=AB+BC NAND.
r:
= + BC = + BC = BC
-
90 3
, NAND, . 3-16.
. 3-16. = + BC NAND.
3-5
EXOR ) NAND ) NOR.
1. NAND
EXOR : =-==
= + = + =
, NAND, . 3-17.
R
. 3-17. EXOR NAND.
2. NOR
EXOR :
= (+ ) =(+ )
I
-
91
=(+ )+:\ 3 =(:\+)+
=(+)+(+)
3-18 .
. 3-18. EXOR NOR.
3-11 OR AND
OR AND . , , (fan-in) . (fan-out) ( )
(, ) . OR (DL, Diode Logic) . 3-19()-(). ,
, , =. ,
1 (. . 3-19()), ( ). , :
()- ]) - V(O) =. (R 13 + R 1 + R) (3-8)
, V0 Rr a .
-
92 3
c C=O
V(O) R
~ () V(O) () V(O)
c
V(1) R
~ V(O) ()
. 3-19. OR ()-() () .
.(3-8) :
= _V_(I_) -_Y:..:_r) _-__( _) R 13 +R+R
:
(3-9)
Vy = R + V(O) = R( ()- - V(O)J + V(O) (3-1 ) RB+Rt"+R R>>
RB + Rr, .(3-1 ) :
-
93
(3-11)
, OR 1. () 1. 3-19() OR , , 3-20()-() AND DL,
3-20() , ,
, . , , AND 1, , V(1 ), 1.
. 3-20()
c c
V(O) V(1)
~ -~ V(1) V(1) () ()
. 3-20. AND () () .
3-12 RTL RCTL
, , . , RTL, RCTL DTL, , , . , RTL (Resistor- Transistor Logic),
. 3-21 ().
-
r 94 3
OV . V =V':_; , 1. , ( 1). , , (V"=V_ s,1, OV). NOR RTL 3-21 ().
, , =1, 1, . , ,
RCTL (Reslstor-Capac/tor- Trans/stor Logic).
() ()
. 3-21. () () NOR RTL (RCTL).
3-13 DTL
NAND DTL (Diode-Transistor Loglc), , . 3-22. , ( 0), 1 - . ,
( ) 5 V ( 1). , 1 (+5 V), ( 1 ), -
-
95
( )
. 3-22. NAND DTL.
3-14 TTL
L (ransistor-Transistor ogic 2),
(J. 5V, 5% (4.75-5.25 V). , DTL,
, . TTL :
- (Standard )
- (High-speed , -)
- (ow-power -)
-Schottky (S-)
- Schottky (S-- )
. 3-23 NAND TTL. ,
-
96 3 ------------
. NAND (LOW), pn ,
, 0.6V, V, . , ut 5 (HIGH)
c
. 3-23. NAND TTL.
. 3-24() NAND (Standard L), ()
. NAND, . 3-24(). , 1 -.
, (LOW-HIGH) NAND, . 3-24 ()-(). . 3-24(), 1, 1 2 . , 4 , 2
D1 3 , 3 . .3-24(). (otem-Po/e Output)
3 4 , , . , LOW, 3 .
, HIGH, 3 . ,
-
97
, . , (rsetime). , LOW HIGH, ~
3 , ns, ,
(30-40 mA) . (!)- () LOW (L) HIGH ()
=40 , =-1.6 mA, loH=-400 =16 mA
c
c
()
()
()
()
. 3-24. () NAND, () TTL ()-() NAND .
TTL , . 3-25, Schottky (
-, ) - , . . 3-26 NAND Schottky TTL. - TTL
-
98 3
3.5 I (lnput) (Output), L LOW HIGH.
. 3-25. Schottky S-TTL.
. 3-26. Schottky TTL NAND.
3.5. TTL
Vcc (Volts (ma >>
VH(min >> Vo~max >> VOH >>
- = - = S- =
Standard
5 0.8 2 0.4 2.4 9 25 10
LS-T =
L-TTL H-TTL S-TTL
5 5 5 0.8 0.8 0.8 2 2 2 0.3 0.4 0.5 2.4 2.4 2.7 33 6 3 3 40 80 1
23 23
LS-TTL
5 0.8 2 0.5 2.7 9.5 30 2
-
99
3.6 7400, . 3-27
' jJ
3.6: ' . 7400 ~ _r_ Q~
2 3 4 5 8 12 13
:[)- 7408 7411 7420 7409 7415 7421 D- 7432 - 7400 7410 7420 7430
74134 74133 7401 7422 D- 7402 74260 7433
74128
~D- 7486 74135 74136 74386
~ 74135 74266 3- 15 TTL
TTL ,
-
100 3
. , .
7400 7430
7401 7432
7402 7486
7404 74135
7408
. 3-27. 7400.
-
" 101
. HIGH LOW, . TTL vv (OC. ope-co//ector),
(pull-up resistor), R, , LOVV, 16 mA . . , .
c
+5
R (Pu-up)
. 3-28. NAND .
. 3-28 NAND . , (,
), TTL. ,
. 3-29, (pu/1-up resistor), AND. vv AND (wired AND).
, NOR , v OR (wired-OR). 3. 7 7 400
.
-
102 3
\
l I)
c ])
Y.\l~lJ)
ll!)
. 3-29. () AND () AND.
3.7: OC 7400
Fan-in
7401,7403 NAND 2 4 7405 1 6 7409 AND 2 4 7412 NAND 3 3 7415 AND
3 3 7422 NAND 4 2 74136 EXOR 2 4 74266 EXNOR 2 4
3-16 MOS
TTL , MOS MOSFET - (PMOS) - (NMOS), a VMOS (Vertica/ MOS) HMOS
(High-Performance MOS). , PMOS NMOS, -
-
jii>
103
COS!MOS (Complementary Symmetry MOS) CMOS.
()
()
. 3-30. () , () NAND () NOR NMOS.
, MOSFET , , , s.
PMOS NMOS, NMOS , PMOS. ,
. , NMOS PMOS.
-
104 3
VMOS , . . ( NMOS () 3-30(). ~ (pull-up transistor) LOW,
~ HIGH. , HIGH, , LOW
. 3-30()-() NAND NOR NMOS.
3-17 CMOS
MOSFET, MOS , CMOS (Complementary Symmetry MOS), MOSFET. MOS, ,
. ,
. , . , CMOS, , , .
CMOS MOSFET ,
, , .
CMOS 3-15V ( 4000) 3-18V ( 40008), (
). , CMOS TTL. , , . 3.8 NMOS, CMOS TTL CMOS (, .3-31.
.
-
. 3.8: NMOS, CMOS TTL
NMOS CMOS
+ + ++ + ++
++ +
---,.----+ V DD
=
. 3-31. CMOS.
. 3-32. NOR CMOS.
105
. 3-31, HIGH (), 2 , 1 ( LOW).
-
106 3
. , , . NOR CMOS . 3-32. , HIGH, FET (-n) .
LOW, FET - , HIGH.
. 3-33. NAND CMOS.
NAND . 3-33. 3.9 CMOS
40008.
3-18 TTL CMOS
TTL +5V CMOS +3 +15V ( 40008 +3 +18 V). CMOS,
V00 , , 1 (HIGH), VrH=0.7V0 o. , Vcc=5V
V 1H=3.5V. , , VoH. TTL, HIGH, 2.4 3.6
.
CMOS TTL
TTL CMOS, TTL. ,
-
107
(pu/1-up), . 3-34. TTL, HIGH, 5V. , TTL LOW (0.2 0.4 V), ,
CMOS,
+1.5 V, LOW. TTL CMOS (.. 401 04) TTL CMOS.
. 3.9: CMOS ( 40008)
2 3 4 8
~ 4/4081 3/4073 2/4082 =D- 4/4071 3/4075 2/4072 [)-- 4/4011
2/4012 1/4068 =D- 4/4001 3/4025 2/4002 1/4078
~D- 4/4070 =}D- 4/4077 ,
.
-
108 3
+5
VoH V 2.4-3.6V 3.5V
. 3-34. CMOS TTL.
TTL CMOS
TTL CMOS, . 3-35.
CMOS, HIGH, .
r---------~-+Voo
CMOS
n
. 3-35. CMOS TTL.
, CMOS 5 10 TTL, 1 40 =400 ,
, HIGH,
-
109
V>=5V-400AxR;::r,. R:.: P-MOSFET . , R;=r:=1 k, : VaH=4.6
V.
, TTL (2V) HIGH. CMOS,
TTL, LOW , . 3-36, V~; CMOS ,,R:, , V 1 ,
(O.BV). , =-1.6m R,=1k, CMOS V:::;=1 6V. , , CMOS TTL, (.. 7
4LS04 40508) CMOS TTL.
+5
I +-- I J
---------
l . 3-36. CMOS TTL.
3-19 12L ECL fL MTL
(lntegrated Jnjection Logic Merged-Transistor Logic) (BJT,
),
npn . , npn -
-
11 3
. i . , ,
(VLSI). , TTL CMOS.
. 3-37. OR/NOR ECL.
ECL (Emitter-Coupled Logic) CML (Current-Mode Logic) (J ,
TTL, .
( 120 MHz). , () . . ,
. . 3-37 OR NOR ECL. LOW, 1 2 . ,
. , 3 ( VREF). . , 4 5 ,
LOW (-1, NOR) HIGH (-2, OR).
-
111
, HIGH. R,, Tc . . Tc (-1 LOW) 1
(-2 HIGH)
3-20
. , . ( Hi-Z). TTL
(SL, Tri-State ), MOS CMOS . , 1 , (Gate Control, GC).
-f'>r- -f'>r- GC ~ GC~ Gate Contro (Active-High)
AGC
z 1 z
1 1
()
Gate Contro (Active-Low)
AGC
1 z 1 1 z
()
~=C>- GJ
Gate Contro (Active-High)
GC
1 1 1 1
z
()
. 3-38. () , () -- (actie-low) () NAND
. 3-38 . . 3-38, 1.
-
112 3
, (data) (bus). , ,
. TTL 3-39, (). GC=1,
( , GC=O. - .1 , 0 2 3 ,
, 3.1 TTL CMOS.
GC
. 3-39. (L).
.3.10:
Fan-in
74366 1 6 74368 1 6 4502 1 6
74134 NAND 12 1
3-21
(transmission gates bi/ateral switches) ,
-
113
CMOS, . , . FETs , p n.
(, . , - . (LOW), -, . , 1 (HIGH),
. -
. . 3-40 , 4016 4066. -, 1, 4016 300 , 4066 80 .
1/0 Voo
/ c
1/0= lnput-Output 1/0 c
C=Control / 1/0
c 1/0
c 1/0
Vss 1/0 4016 I 4066
. 3-40. 4016 4066.
3-1 , , C C=O = , C=1 =+.
-
114 3
3-2
C f (. .C)
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
3-3 , , C , , :
ABC
1 1 1 1 1
1 1 1 1 1 1 1 1 1
1 1 1 1 1
3-4 :
f1(A,B,C)= ( ++ C)
f2(A,B,C,D)= (AC ++ C)
3-5 2--3. HIGH, 2 HIGH.
3-6 OR - NAND .
3-7 , NAND.
-
...
.
115
:=.\+.\
3-8 3-1 NAND
. 3-1
3-9 , Karnaugh , NOR .
4 00 01 11 10
00
01 1 1 1
11 1 1 1
10
3-10 2-bits, a1ao b1 bo. 7400, bit 1, .
3-11 , , :
-
116 3
= ( ) .. ( ) 3-12 t
-
117
,
1, 2 LED, .
r---~~~-----~~====5V .----2 1
. 3-4
-
4
, , , . , , ,
, . , ,
. , ,
, .
, AND/OR OR/AND, , w ,
. ,
-
120 [/\ 4 -----------------------------
.
4-1
: f, n , . u f , , m .- n , =c> f,
, , , f, p' .: f.
:
f(x 1,x 2 ,x 3 ) = 1 + 1 2 3 , 1 = 1 J>2 = 1 2 3 . :
, 1 , 2 3 2 , f.
4-2
, , , :
, ,
-
121
.
f. , f=f1+f_, f1
() , . f:, , t~ , , ( ,), f2 =x,f; ( f 2 :=Xi f;) ; =-> f.
f:, c.-> 2* , f] 1, t:;' 1. , f = 1 + r; , AND, f:, f.
.
4-3
, f . () f,
f, f . , , f. , , , . :
, 1 . 1 ~ _1
-
~ ..................................... .
122 4
. .
, Pj, f f, f. , , 2 , . , Pk , ' , Pj , :
, .
, . , ,
, .
4-4 KARNAUGH
Karnaugh . 4 5 , .
,
Karnaugh. () Karnaugh, (. 2-12). , Karnaugh 4
. , .
-
123
. , , AND, . , Karnaugh ( ):
- 00 01 11 10 .,
00 1
01 1 1 1
11 1 1 1
10 1 1 1
() ()
4 00 01 11 10 00 1
01 1 1 1
11 1 1 1
10 1 1 1
()
, 1 ,
( 2 ~). , () . , ()-(),
. , ,
, 4 . , (), . , Karnaugh ,
, .
, , . .
-
124 r,F 4
4-1
uv ;J vvr vc rov (J ivcu f
-
-.J 125 ------------------------ --- ----------
--------------------------
4 00 01 1 1 10 ,---00 1 1
-~ ( 1 1 ) 11 ( 1 \ ) 10 1 (1 1 )
-
126 4
u ,
u-
, r,
3~. 00 01 11 10 4 ~
00 1 1
= 1 ,-, 1 L 01 1 (1 1 '
11 1 1 1
10 ~ 1
t-;:==1===::::-t-----t---== /+-- 3= 2 4
00 01 11 10
00 1 1
01 1 1 ~ 11 1 1 1
'---"" = 7 2 "3 10 11 1
-
128 4
1 2
4 00 01 11 10
00 I( 1 1 ) 1 01 1 1
11 ) 10 1 L :
--- -134, 134, 23, 24, 12
2 , . ,
134, 134, 23 24
4-4
Karnaugh:
-
4 00 01 11 10 r--.
00 1
01 1 1
11 r 1 1 1 ... ~
10 1 1 r---'-..._./ ~
I ,.,
" 1 1 . .
, . i .
-
~. 129
4-5
r1 ( 1') F(::
Karaugh
00 01 _,
1 10 00 1 1 w 1
---....,
01 1
11 ( ' J ,..----...
10 1 1 I'. ./
1
, . Karnaugh,
, :
4-6 QUINE-McCLUSKEY
, , Karnaugh, , QuneMcCiuskey ci
Quine-McCiuskey
1.
2. .
-
130 4
1 , () c: 1 f: :J
' 1 ~~; 1 0101
3. 1,
c: , ,, i=O, 1, 2, ... , n, i 1, n .u.
4. ,, =, 1, 2, ... , n-1, , ,, 1 . , # . ,
(0, 1) , , (-). , ,
,, 1 , ; . , (J, ...
5. 4, ;. , , . 5 ;' .
6. 5 ( ) . #
.
4-6
Quine-McCiuskey, (
-
~--- ~~~--~-~~~~---
131
Karnaugh, 4.2 ):
f(x 1,x2 ,x3 ,x 4 )=x1x2x3x4 + 1 2 3 4 + ,234 + ,234
+ ,234 + ,234
+ ,234 + ,234 - -
+ ,:?34 + ,234
: f(x1, 2 , 3 , 4 ) = (m0 , m1, m2 , m3 , m5 ,m8 ,m10 , m11 ,
m13 , m15 ) :
1
'
' 1
4.1: Quine-Mc Cluskey ( 4.6)
ma 0000
m1 0001 m2 1 ms 1
m3 1 1 ms 1 1 m1o 1 1
m11 1 1 1 m13 1 1 1
m1s 1 1 1 1
(m , m 1) -
(m , m 2) - (m , m s) -
(m1, m3) - 1
(m 1, m s) - 1
(m 1, m 1)
#
# # #
# # #
# #
#
#
# #
#
* 134
-
132 4
' 2
(m:c,mc) (l2. l'.) (m:.n!) (lF, l?) (m,m) (m 8. rn c) (m,,m,) (m
3, m 11) (m 5, m 11) (m , m 13) (m 1, m 11) (m , m ) ' 3 (m 11, m
15)
(m 13, m 1s)
" (mo,m1,m2,m3)
(mo,m2, m 1,m3) (m o,m 2,m s,m 10) (m o,m s,m 2.m ) " 1 (m 2,m
1o,m 3.m 11)
1 - #
- 1 #
1 - # - 1 1 #
- 1 1 * 2 3 4 1 1 - #
1 - 1 1 134 1 1 - 1 *124
-- * 1 2 -- #
-0-0 * 2 4 -0-0 #
- 1 - * 2 3
(* ), :
-- -- -134, 234,134,124,12,24,23
4-7
:
- -- ---------~
1 ? 3 4 f(x1, 2, 3, 4) 1 1 1 1
i 1 1 1
1 1 1 1 1 I Q__ .__1_ ~- _1_____ c_ ___ o _____ j
-
133
---
-; 1 1 ! --
--- -- -----------< 1 1 1 1 1 I
--
1 1 1 I
1 1 1 1 1 I
I 1 1 1 I [ 1 1 1 1 1 i
---- - ------ ----'
.
f(x 1,x.:-,x,,x1) = :2.:(n 11 ,11;z,1 1 ,(,,s,)
Quine-McCiuskey
4.2: Quine-Mc Cluskey ( 4.7) mo 0000 #
1 m2 1 # m4 1 # ms 1 #
2 m6 1 1 # m1o 1 1 # ' mo, ? - #
mo, 1114 - # mo, ms - # ' 1 (m2, mG) - 1 #
(m2 m) - 1 # (m4, m6) 1 - # (m4, m1o) (ms, mG) (ma, m) 1 - # "
(mo, m2, m4, m6) -- *14
(mo, m2, n1s, m1o) - - * 24
(mo, m4, n, m6) -- # (mo, ms. m2, m) -- #
-
134 4
14 24
4-8
Karnaugh Quine-McCiuskey, Karnaugh:
12 3 4
00
01
11
10
Karnaugh:
00
1
01 11 10
1 1
1 1 1
Karnaugh, .
00 01 11 10
00
01 I( 1 1 "' ./
r 1 11 1 ( 1) 1
10
-
.....
135
2. Quine-McCiuskey:
Quine-McCiuskey - :
4.3: Quine-Mc Cluskey ( 4.8) 1 m1 0001 #
2 ms 1 1 # mg 1 1 # 3 m? 1 1 1 #
m11 1 1 1 # 4 m1s 1 1 1 1 #
' 1 (m1, ms) - 1 * ,34 (m1, mg) - 1 * 234 ' 2 (ms, m?) 1 - 1 *
124
(ms, m11) (mg, m) (mg, m11) 1 - 1 * 124 ' 3 (m?, m1s) - 1 1 1 *
234
(m11, ~:} 1 - 1 1 * ,34
: 134, 234, 124, 124, 234,134
4-7
, (. )
. , ,
Karnaugh Quine-McCiuskey.
-
136 4
, , , .
, . , Karnaugh, .
Kamaugh
, , Karnaugh:
~
4 00 01 11 10
00 1 1 1
01 1 1 1
11 1 1
10 1
: mo, m 1, m 3, ms, m7, m, m1o, m12 m13 :
~
4 00 01 11 10 4 00 01 11 10
00 1 (1 1 ) 00 1 1 ( 1
01 1 1 1 01 1 1 1 ./
11 1 1 11 1 1
10 1 10 1
-
--------------------
t-. 137
"
4 00 01 11 10
'1' ~ 00 1 1 01 1 1 1
"-......__/ \....._.1
11 1 1 ~
10 1
:
- -- --- - -
14,134,234,234,123,123,124
Karnaugh .
11 10
00 : 1 : 1 : 1
w , vayv- , . v" , , :
-
138 4
00 1
01
11
10
11
1
10 01 11 10
, . , ,
~~v .9v. 4.4 . 1 () . -
. 4.4.:
0000 0001 0011 0101 0111 1000 1010 1100 1101
, ( 4.5) ,
, 23 (m 12 , m13), .
-
.. -...... -~~-----~-~~----------
""""""
. 4.5.:
m0
134
234
234
123
0000 1100 1101
139
, m0 . 3 .. 1 23 ,
( AND , NOR ).
4-9
Karnaugh :
4 00 01 11 10
00 1 1 1
01 1
11
10 1 1 1
m0, m2 , m4, m6 , m8, m10 , m13 . Karnaugh :
-
140 4
4 00 01 11 10
00 1 1 1
01 GJ 11
10 1 1 1
2 4 , 4 2 ,4 , . . 4-1.
. 4-1. 4.9.
, . 4-1, 8 15 (
.
4-10
, AND/OR, , , C, D, 1, (ABCDE)~ 21.
-
f
-
142 4
1. . , wVi)L;"j'v , , , .
4-11
, , C D 1, (ABCD) 2 1 , 9.
1, :
---- --- - -- - ---
f(A,B,C,D)-:cA C D+A BCD+ABC D+ABCD+AB C D
, : f(A,B,C,D) = CD + BCD + ABCD + ABCD + CD , ABCD, ABCD, ABC D
, ABCD, ABCD ABCD . , 1, Karnaugh (= 1 ):
c ~
oc
01
11
1f
00 01 1 1
1 1
11
10
--
~ ...
{
---
-
AC
.__ D
Karnaugh , , AC D . , ,
' . ,
-
143
f(A, , C, D) = D. , ,
-- ---
f(A,B,C,D)=A D~B C D , .
4-12
Karnaugh:
~
4 00 01 11 10
00
01
11 1 1 1
10 1 1
(00 00) , (01 01), (11 01)
(10 11) 1 . :
L L
4 00 01 11 10 4 00 01 11 10
00 00 ~-01 01 ~ ? 11 1 1 1 11 IC 1 1 1 " J
10 1 1 .............
_,/
I 10 oJ 1 1
I 123 123 34 ,
:
-
144 4
f(x 1,x 2 3 . 4 )= 1 2 3 + 1 2 3 + 2 4 + 3 4 , :
( ) .:
4-9
( OR AND),
, .
f, , DeMorgan, f. . , ,
() , , , DeMorgan, , . (OR) . , ,
Karnaugh , (OR/AND).
1" ~
4 00 01 11 10
00 1 1 1
01
11
10 1 1 1
,
-
145
2 00 01 11 10
4 ~"' 00 1 1 1
01 r--
11
10 1 1 1
f , :
. 4-2.
. 4-2. OR/AND.
5 7 ( ,
(AND/OR). , ( 1,
). , Karnaugh :
-
146 4
, :
f
. 4-3. AND/OR.
AND/OR . 4-3, 6 9
. , OR/AND.
4-13
Karnaugh.
-
f
147
~
4 00 01 11 10
00 1 1
01 1 1
11 1 1
10 1 1
1 , Karnaugh, :
~
4 00 101
00 1 01 1
11 1
10 1 I
f= 24 + 24 f, :
f = ( 2 + ~c~ }( 2 +~ )
11 1 10
oj 1 ,___
-
1
1
ol 1 I
, ' . 1
4-14
Karnaugh.
-
148 4
~
4 00 01 11 1
00
01 1 1 1
11 1 1 1
10 1 1 1
1, , : . '
-
1 ()() 11 10
1 ()() 01
()() () () 00 ()
01 I 1 1 01 I
11 () l 1 1 11 1
10 \J. 1 1 10 I '---"
: [= 24 + xlx4 + 23 + xlx3 . 4-4.
11 10
) 1 1
I I
I I
. 4-4. 4.14 AND/OR.
-
! 149
, ,
- I .' j. ~ -1 = ( +::)( ,+ 1 )
. 4-5, ,
AND/0~~
f
. 4-5. 4.14 OR/AND.
4-1
, Karnaugh, , 5-6
. , Quine-McCiuskey,
, , , .
.
4-15
AND/OR Karnaugh:
-
150 4
..
00 01 11 10 4
00
01 1 1 1
11 1 1 1
10
4.8, Karnaugh Quine-McCiuskey. :
134, 234, 124, 124, 234, 134 , , , .
4.6,
.
. 4.6.:
m1 ms m? mg m11 m1s 0001 01010111100110111111
1 13~
2 23~
3 124
4 124
5 234
6 134
. ,, i=1,
-
151
2, ... 6, , =1 , ,
, : 4.6 . , m , , ,
1+=,::>1 , , :
1+c::' 1 1+:~ 1 3+5 ::' 1 c+4::' 1 4+G ::' 1 ~+c::' 1
, , :
1+2=1 1+3=1 3+5=1 2+4=1 4+6=1
s+6=1
, 1. , :
(1+2) (1+3) (3+,,) (:,+4) (4+) (s+c)=1
, , () ,.
, 1, . ,
, . ='36 =1,
:=1, J=1, 6=1,
-
------------------~------
152 4
AND/OR, 4 15, , (
4-11
n k , . 4-6, f1, f2, ... fk . ,
, .
1 -------r--------~------f1 2 f 2
. 4-6. .
, , . , , . .
+ f1, f2, ... fk, .
, t1 n t2 , f1 n t3 , , t,- n f..:, f, f2 t,, f, f2 f4 , ... ,
f..:_ 2 f..:_ 1 fh ... , t (~ n ..... f,;.
+ , f1, f2, .. fk . 01
, ,
-
153
.
+ , .
+ .
:
f1= m3+ms+m7+m13+m14+m1s f2= ms+m7+m1o+m13+m14+m1s f3= mo+m4+m1o
+m14+m1s
, :
34 00 01 11 10
00
01 1 1
11 1 1) r:j"" 10 1
00 01 11 10
00
01 1 1
11 1 ,--.,
1
10 1 1 ' J -
-
154 4
~.< 00 01 11 10 ."
00 (1 1) 01
r----.. 11 1
10 L( 1 1). ~
4.7, f,1
f, f1. , ( 4.8).
4.7.: .
f1 24 123 134
f2 24 123 134
f3 134 123 134
f12 123 24
f13 123
f23 123 134
f123 123
, 2 , , . 2 .1 f1 fc , . .
-
....
155
4.8 : : : :
. . 4-7 :: : : AND/OR. 12 : 26 .
. 4.8.:
.
f f2 f3 1
m3 ms m m13 m14 m,s ms m m m13 m14 m1s mo m4 m10 m14 m1s 0011
0101 0111 1101 1110 1111 0101 0111 1010 1101 1110 1111 0000 0100
1010 1110 1111
123 1 1 1 1 1 1
24 1 1 1 1 1 1 1 1 ~
134 1 1 1 1 ~
134 1 1 ~ ~ ~
134 1 1
. 4-7. .
-
156 4
4-1 Karnaugh
\I\ .
\:.\ .j
()(I II 11 10 4 00 01 11 10 ()() I I () () 00 1 1
() I () 01 1 1
I I I () 11 1 1 1 1
() () () () 10 1
4-2 Karnaugh :
, 2
4 00 01 11 10 4 00 01 11 10
00 1 1 00 1 1
01 1 1 01 1 1
11 1 1 1 11 1 1
10 1 10 1 1 () ()
4 00 01 11 10 4 00 01 11 10
00 1 1 00 1 1 1
01 1 1 01 1
11 1 1 11 1 1
10 1 1 10 1 1 1 () ()
-
157
4-3 Karnaugh,
Quine-McCiuskey.
.~ I
~ 00 01 11 10
00 1 1 1
01 1 1
11 1
10 1
4-4 AND/OR i Karnaugh:
4 00 01 11 10
00 1 1 1
01 1 1
11 1 1
10 1 1
4-5 OR /AND i Karnaugh:
4 00 01 11 10
00 1 1 1
01 1
11 1 1
10 1 1
-
158 4
4-6 Karnaugh, .
[) .~
' "
.1 00 01 11 10 4 00 01 11 10
00 1 1 00 1 1 1
01 1 1 01 1 1
11 1 1 11 1 1
10 1 1 10 1 1
4-7 (~)=199.
4-8 (3)=28.
4-9 Karnaugh:
2
4 00 01 11 10
00 1 1 1
01 1
11 1 1
10 1 1
4-1 Karnaugh ()-().
.
-
159
. -
-
"
00 01 11 10 00 01 11 10
00 1 1 1 00 1
01 1 01 1 1
11 1 1 1 11 1 1 1
10 1 1 10 1 1
() ()
4-11
f1= (, 1, 7, 11) f2= (1, 5, 7, 11) f 3= (2, 7, 11, 15)
4-12 , , C, D . bit , , , bit C, D W, C. NAND, , , 1 W.
4-13 , , C, D . bit
, ,
, , 1 (8).
4-14 , , C, D . bit , , , , 1 (5) 1rJ. ,
(5) 10 (9):.
-
160 4
4-15 , C :., ,., , , bit 1 bit . bit ,
111, 000
4-16 1 2 , :,1 , bit. 1, bit .
.
4-17 . 4-1 () , . , 8
.
II.L .. - ~- .\
(\
~!. jj,j.J
-
/ I 161
Sr S 2 , 1, . , 1,
4-1 (). 1, . 4-1 (). ,
. 4-1 () . 4-1 (), S 1, , . ,
. .
-
5
, , , .
. , . , ,
, .
. , , flip-flop , .
.
5-1
, 5-1,
-
164 5
, ;, ( )
.
. 5-1. .
. , 1 2
. - 2 , R8 , 2
(IB2(sat = lc2(sat ). 1, . , 1 2 , 1 . , 1
, 2 . 2 , 1 Ru R1 . ~, (, ), C V0 - V1112 "" ( . , , , R8 ,
-Vcc. , R8
-
'
165
=' , : i i ,
c- ,- ( )1 -e tR,c) (5-1) c i i R, c , i ,:
t=T c i i , (= 0.6), . , i i . (5-1)
c=, ,=-cc 1=: , :
-V+(V+V)[-~ !~,,]=u (5-2) , i:
(5-3)
i ( 2 i ) ccR 1 /(R 1 +RL2), 2 i .
]{ 1.1
. 5-2. .
. 5-2 i i , i
-
166 5
:, (Vrrr,) (V.-",) . 5-2 .
R~ Vrrn -~R _t::R-~- V,~c (5-4) ' L2
.
1. Vcc R. . R .
2. RE .
3. RR 2
4. C, .
5. R1 R2 ( R1c) 1, , 1, .
5-1
1 ms 5 k, 9 V.
=50, lca=O, V,= V (s.,:1=0 12 V
-
167
5-2
1. , R =Rc~=R, = 5 k
2 V,=2 V, (V:=-V,-Vc:"''c: 12-2-02;98 V)
( R1 R2).
3. VE - VccRE /(R - RE) RE. , :
4. lc2(sat) 2 :
Vcci(R+RE)=2mA. , 2 , , :
l(sat)=lc2(sat) I = 40
2 , 1.5, 2.
, l82=1.5x40 =60 :
Vcc- Vs2 I 2 = __:::_:::___.:::::..::::_ Rs
R0 167 k. T=0.693xRsC=1 ms, . :
C=0.0087 F.
5. 1 , . , 1 5-3() 1 VE=2 V,
-
168 5
, 0.6 . 1 , R1=R=.
R L1
RE
-=-
()
Vcc RL1 R2
Vou
1 2
()
. 5-3 1, () () .
6. 1 , 01 R1 , R~ 1 (1 81 =60 ) , . 5-3() :
cc ~ 1 1 I 1 =- l1 - 2 == -=--=----"--'-
R + R1 R2
---
-
169
6. 5 6 R1 R~. ,
5-2
. 5-4 TTL CMOS. NOR, . , 1.
+V
. 5-4. NOR .
( NOR), NOR . , , C, , R. , 1, (0). 1, RC, =0.693RC sec. , NAND,
. 5-5.
-
-------------
170 5
c
Gu~ IL
. 5-5. NAND .
5-3
.
TTL, CMOS (IC mers).
74121, 74122 74123 (). CMOS, 4047 (
), 4098 74C221. (timers), 555 556 ( ).
555
+4 +18 . ,
TTL CMOS. . 5-6, 555 , , , , flip-flop . flip-flop ( )
(HIGH-LOW). flip-flop , . flip-flop . 5-7 555
(099 DIP).
-
7
1-----+----{ 4
3
.5-6. 555.
99
1: 2: (rgger) 3 4: (ReseQ
DIP
8
2 7
3 6
4 5
5 (Control Voltage) 6 (hreshold) 7: (Discharge) 8: (V cc)
171
5-7. 555 ( ) 99 DIP
-
172 5
(2) (6) 555 (2) , 5-6, Vcc)3
, (6) , 2V/3, ,
, .
. 5-1.: . 555
(2) VmG
VRG < cc 3 RG < cc
3 RG > cc
3 RG > cc
3
(6)
Vcc
2V::c/3
V/3
V
< 2cc --
3 2cc > --
3 2cc < --
3
> 2cc 3
(3)
::. 1s ()
::. ()
. 5-8. - 555.
-
173
, 5 1. ..;J . . V /3 2V /3, (3)
0.5 V, a V . ,
c , (0.1 V).
(2) (6). . 5-8.
V:/3, , , Vcc
2V)3. , Vcc/3
2Vcc/3. , flip-flop, ,
. , . 5-8,
, Vcc/3 2Vcc/3, . ,
Vcc/3 2Vcc/3, 555 .
(3)
, 1 , , .
, , V;. 40 mA.
(4) 0.4 V, (3) (7) . ,
4 ,
..
-
174 \i :.
u . bur!
(5) ;> . , ,
5 k. 5 , OAV::. 8\1 , _ , ! ,
5 0.01 F, .
(7) . 555 ,
, .
555
555 (non-retriggerable) (retriggerab/e) . , . , , 555, , .
5-9.
, (7) . , R 2V. 13,
ri
-
175 ---- -----------------------
'"''' l-d I lJ- - L - 55:) ~
4 ~)
R
_ 5-9 555
:
- ln3RC --- 1_1xRC (5-6)
r. 15 min, _
~ ,_
555 l 6
4 5
_ 5-1 r. 555.
-
176 5
c.. ( 5 ), XR2240,
555 a 5-1
555 , (Reset), .
74121
TTL 7 4121.
, 1 , :, . 5-11. (5)
, 1 (3) 2 (4), AND, . , v, 1 , 1, 1 , 2 ,
AND .
Ext r--"'--.. ~ NC NC R/C C
NC v R 1nt . R/C Ext . C [xt ..
. 5-11. 74121.
5 2 7 4121 ( ). 5-12 ()-() . :
- 693xRC (5-7)
-
1v.S 2 1 74121
1 2
1 1 1 1 1 1 1 1 1
.l. 1 .L L .l. 1 1 .L L .l. .l. 1 .L L
i .L L i .L L
+SV
R
c 1L__
1_L
() -+SV
()
177
. 5-12. 74121 ) ) .
-
178 5
74122 74123
4121 4122 4123 (reset clear). 74123 74122. . 5-13
74122, . 5-14 5-15 .
NC c NC NC R,nt . R/C c
1 2 1 2 Cr Q GND Cr Clear
. 5-13. u 74122.
+5V
R 1 1 14 2 4 __ 13 8
c 11 74122
Resct 5 Tri 6 1l____ 3
. 5-14 74122.
-
119
+5V
R '
13 ~~_l_ c
11 74122 5
Tr1g 6 1'----- 1 L 2 7
. 5-15. 74122.
CMOS
CMOS 4047. , .
, . 5-16, :
= 2.48xRC sec (5-8)
CMOS 4098 7 4C221, 74123.
R
i VJ :\ 14 JL_
10 (3 4047 11 ,, 6 9 1 ~)
Cet R. t R/C AST AST -Trg -V;o':O ex com
. 5-16. 404 7 .
-
180 5 ----------------------
5-4
1
. 5-17 i 555, . , 1 ,
1.1xRC. , , ;-, .
12V
R=2
C =470 F
. 5-17.
2
(. 556),
, 555. . 5-18
555. (), -
---
-
181
1 . . u
12V
~-.-------+ 4.7 k -::-cf- _r-J----j
::_q. ':55 R
c 1
~ 1
....:::
. 5-18 555.
5-5
. 5-19. , _. 1 2 . t=O, 1 .
, , 1 , V: ( C,
Vc~c. ). , 1 , ,
Vc:c, -
-
182 5
. , , -V~ .
c, V .
. 5-19. .
, . 1 2 :
= 0.693 (R 81 C1 + R82 C2 ) , :
(5-9)
(5-10)
R1 R1,_'. , 1 =' .
5-6
RC 5-20. NAND NOR. 721/RC.
, , . , ,
a -
-
183
, 555 c't.
. 5-20. .
5-7
. 5-21 555. , C R1 R2 Vcc.
, 555 ("'4.5V), 2Vcc/3""3.3V. ,
, (7) R2. , ,
Vcc/3, 555 ( ) . ,
.
cc --tt------.----. R1
555 3
. 5-21. 555.
-
1 R4 5
. { 555 c( c V . /3 c 2V /3. F. y
tJ 0693 (R 1 f~ 2 )C (5-11) c'. r r) 2V ,)3 V /3, i .] { 555 , y
{
tCJ 693R2C (5-12) { 555 :
- toN 'toFF 0.693 (R 1 + 2R 2 )C {, r:
1 1443 - ------- -- ----
(R 1 + 2R 2 ) C
(5-13)
(5-14)
D=.Jr/T (duty cyc/e), :
(5-15)
. 5-21 R2 (
7 555), 50% . 5-22
CMOS 4047. (. ) , (13)
1 11 () 13 0.254/(RC) (Hz).
R
c
1 t----o ____L___ 11~ 13 LJlSlJlS
5-22 4047.
-
185
5-1 , 5 ms 5 k.
5 12 =50. ., ,,&.
5-2 , 2 ms 4.7 k.
8 . 12 . =65, 8, ccat 1 .
5-3 . .
5-4 555 1 sec.
5-5 , , 1 sec . , .
, , , .
5-6 , , . ==, =. , =1 =,
50 kHz. , = =1, 100 kHz .
5-7 , , . ==1, =. , , =1 =,
33 kHz. , = =1,
55kHz. .
-
186 5 --------------------------------------
5-8 1 rs. ( )
5-9 555, === ==1. =. .=1 =, 1, 1 sec.
5-1 555, , C . = =, 5 sec, C 1 ms. , =1 =, C 1 ms
5-11 404 7 , , C . =1 =, 5 sec, C 1 ms. , =, 8=1 C=1, 1 kHz.
5-12 555 , , C =1, = C , . .=, 8=1 C
.
-
6 FLIP-FLOP
flip-flop, , . ,
, fli-flop . (LOW) 1 (HIGH). flip-flop
. , , flip-flop , 1 bit. , flip-flop , Q Q, . Q==O, flip-flop ,
bit a .
vcc
6-1. ( flip-flop) .
- ic flip-flop ~ 6- urJ cn cJJ () ve /) cj ~ , . . { ''CJ r. , iu
(OFF) r rvo uu h 13u ui
-
FLIP-FLOP 189 -----------------------------------
6-1
fl-flop 2 k 1 V , 12 V =50
. 6-1:
1. R =R1=R::> = 2 k.
2. VE (Vc2 "'1 V). , VE
-
190 6
6-1 FLIP-FLOP S-R
fl-flop , .
. 6-3 ()-(),
() ()
. 6-3. Flip-flop () , () NAND () NOR. (
).
, . 6-3() =1 8=0, 0=0 ( 0=1). , ,
() , . =1 8=1,
0=1 =1, 0=0 ( =1 ), 0=1
( =) 1 . , flip-flop
=1 = = 8=1.
-
FLIP-FLOP 191
-n--u--( ( r) I . 6-4. () Flip-flop S-R () ) .
, . () 1 fl-flop . 6-4 (). S, R, (Set) (Reset). S=R=O, fl-flop ,
NAND 1. ,
. S=1 R=O, NAND1 0=1 NAND2 Q =0. S=O R=1, , Q, Q, 1. , , S=R=1,
NAND 1. ,
flip-flop . , S=R=1, flip-flop , . flip-flop
flp-flop S-R . 6-4 (). flip-flop S-R :
Q -'Q R (6-3)
Q-S Q--S Q R=StO R (6-4)
Q Q" flip-flop S, R, 6.1, a . 6.2 flip-flop S-R .
, flip-flop rc ,
. , .
-
192 6
6 1 fl flo ) S-R
I
s R
1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
. 6.2 flip-flop S-R
s R
1 1 1 1
1 1
6.1 , flip-flop , 0+, R S , Q. flip-flop S-R i S=R=1 . . 6-5
74279 4 flip-flops S-R.
6 3: i: flip-flop S-R
Q Q+ s R
1 1 1 1 1 1
-
193
--
Vcc C' ~'' I R R
---
R S1 S 2 Q R S Q GND . 6-5. 74279 fl-flops S- R ( S, R).
6-2 FLIP-FLOP S-R
flp-flop S-R, 6-6(), fl-flo S-R .
, S, R Ck S, R (Set) (Reset), Ck
(clock).
ll k -() ()
. 6-6. () Flp-flop S-R () .
-
194 , 6
fl-flop S-R u :
u Cl< r1 1 c. Ck=O, ;;v NAND. NAND: : 1 . fl-flo
Ck , -i (Ck=1) flp-flop
S-R 6.1. , a fl-flop S-R flp-flop S-R , Ck= 1. S, R ,
f1p-f1op (Ck= 1 ). fl-flop 6.4. flip-flop S-R
. 6-6().
f. 6.4: flip-flop S-R .
s R Ck
1 1 1 1 1 1 1
1 1 1
6-3 FLIP-FLOP J-K
a : fl-flop S-R , Ck= 1 S=R= 1,
S= 1, R= 1. fl-flop S-R , . 6-7. flip-flop , flip-flop J-K, .
J,
Ck. Ck=1 J=K= 1, NAND, NAND1 , Q Q .
-
FLIP-FLOP 195
Pr
Cr
. 6-7. Flip-flop J-K Preset Clear.
a flip-flop S-R S=1, R=1 Ck=1. . 6-7, Pr (Preset) Cr (C/ear)
flip-flop. flip-flop 6.5. flip-flop, Pr Cr, a, 1.
.6.5: flip-flop J-K (Ck=O)
-
Pr Cr Q Q
1 1 1 1
1 1
flip-flop J-K 6.6. , Q Q+ flip-flop,
. , 6.6 Q=O, Q =1. J=K=O Ck ,
(Q,) . .
-
196 6
6 6 fl-flop J-K (Ck=1 Pr=1, Cr=1)
,. J t~AND NAND -
3 4 . + 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
, Q=O, Q =1, J=1, =, ( Ck=1) Q .. =J Q+=K.
NAND3 Ck=1. , NAND3 1
. , NAND4 1 ( ). NAND3 NAND, (Q) 1.
NAND2 1 ( Q ), . 4 6 6.6. J=K=1, Q=O Q =1, Ck=1 NAND3 NAND, 1.
NAND, (Ck=O) NAND4 1 NAND2 1. Q 1 .
, NAND1 (Ck= 1) NAND4 1 . NAND2 1.
, a . a
, flip-flop J-K.
-
FLIPH.OP 1 '--1 /
f iv 6 t
-
198 6
flp-flops (poste-edge negate-edge triggered). ". flip-flos .
f:
(Ck: _, I ). fl-flops .
;J J (Ck I --.> ) " , c , . flp-flop (leel-trggered). c'
, flip-flops (positie negatie Jeel triggered).
- Ck
- Cr
Ck
Pr Cr
J Pr 0
Ck
Cr 0
Pr Cr
. 6-8 flip-flop J-K , .
flip-f\ops , ! Pr Cr,
. 6-8. 6.9 flip-flops 7400 .
. , . 6-9 flip-flop 7 4 70 (AND Gated J-K flip-flop).
-
FLIP-FLOP
6.9 Flp-flops 7400
&
. .y y . 7470 4101 7475 7474 74102 7477
74109 74103 74100 74174 74106 74116 74175 74108 74256 74273
74112 74279 74376 74114 74375
74276
cc Pr Ck Kc 1 3
NC Cr J 1
199
. 6-9. Flip-flops J-K, , Pr Cr.
6-5 FLIP-FLOP - D
a flip-flops S-R flip-flops J-K flip-flops
. R ( ) S ( J), . 6-1 ( ), flip-flop J-K , (S, R J, ) , D,
-
JQO f\.'/\10 6
flp-flops u flip-flop D (data)
Q 0 Pr Q
Ck = Ck Ck Q Q Cr Cr
() ()
6-1 () Flip-flops D () .
6 7, flip-flop D (data) flip-flop
D . 6-10 (). . 6-11 flip-flop 7 4 7 4, D, 7400.
7474
. 6-11. flip-flop 7474 ( D)
flip-flop D . 6-12, D C:k, . , Q
flip-flop 1, LED , LED .
-~
-
FLIP-FLOP
,.-----.----,- s
Pr Ck
Cr 0
. 6-12. flip-flop D.
201
. 6-13 flip-flop D AND. . Ck . , ,
D, .
r-- __. . __ ~ D Q -----
r--.-- Ck Q
. 6-13. .
6-6 FLIP-FLOP MASTER-SLAVE
a flip-flop J-K, ,
flip-flop J-K flip-flop S-R. flip-flop J-K
master-slae . 6-14. flip-flop
. , Ck=1,
-
202 6
fl-flop J-K. flp-flop , fl-flop S-R, r Ck=O flip-flop J-K. Ck=O,
fl-flop S-R C-: = 1.
, flip-flop S-R ,
fl-flop S-R flip-flop J-K (master) , , flip-flop J-K
Ck=O. MASTER
SLAVE
Q
Q
. 6-14 Flip-flop J-K master-slae.
6.1 flip-flops J-K master-slae, . 6-15 7 4 73, flip-flops J-K
(master-slae) Cr (Ciear).
flip-flop master-slae flip-flops J-K.
6.10: Flip-flop J-K Master-Siae 7400 ( )
7472 7473 7476
J-K Flip-Fiop Preset Clear J-K Flip-Fiop Clear J-K Flip-Fiop
Preset Clear
-
FLIP-FLOP
. 6-15. flip-flop 7473.
.6.11 flip-flop J-K.
r r
J Q Q Q+ Q+ Q
1 1 1 1
1 1 1 1 1 1 1
1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
203
flip-flop , 0 . ,
6.11, 1 , , . Karnaugh
Q J 1
00 ~
01 1 ~
11 1 1 '--'
10 1
-
204 6
Karnaugh
0 JQ.KQ (6-5)
, flip-flop J-K,
( ) , (J, ). (6-5) J ( Q ), , Q
6-7 FLIP-FLOP -
flip-flop flip-flop J-K (master slae) J, (J=K). (r=J=K), (
toggle , . t: , ). flip-flop , . 6-16 6.12.
=
Pr Q Ck
Cr 0
. 6-16. flip-flop ( ).
. 6.12: ftip-ftop
-
Q+ Qt - Q Q
1 Q Q
, , flip-flop . =1 Ck,
.
-
t-:: 205
6-2
v r r1r r~ r, ucu . u , r . { , ( r
rr ), r, r
, ( ), .
, . 6-17, flp-flop ( ). , ( ~ I ) R 1. flip-flop. , ( Q =1 ),
0=1 ( Q =0). , 0=1, 0=0.
, flip-flop RC .
3
