digital design slides
DESCRIPTION
Slides for DDTRANSCRIPT
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!
:
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. . . Boole, , . , Karnaugh, . . , , , . , , . , flip-flop, ROM & RAM. (Verilog, VHDL).
Mano Morris, Ciletti Michael, " ", 4 , (), , , 2010. J.F.Wakerly, " : & ", 3 ,
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vs
() .
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() () .
, .
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: CDplayer CDplayer CDplayer 10.000.000 CDplayer 20
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...
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20 ,,,
1947: transistor BellLabs JohnBardeenWalterBrattain(Nobel 1956 WilliamShockley)
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1,1 .
Jack KilbyTexas Instruments(Nobel ,2000)
transistor ( 1958)
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(SSI):>10
(MSI):>100
(LSI):>1000
(VLSI):>10000
2003:
IntelPentium4mprocessor (55 ) 512Mbit DRAM(>0.5 )
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Intel4004MicroProcessor
19711000transistors1MHzoperation
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Intel Pentium (IV) microprocessor
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1. (Supercomputers)
2. (Mainframes)
3. (Workstations)
4. (Microcomputers)
5. (Microcontrollers)
(Mainframes)
(Supercomputers) Workstation: Sun Ultra450
microcomputer
Personal Digital Assistant
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: () () ( ) () ()
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Bottom-up
Top-down
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wafer
die
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" ",
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: 2
0 1. 0 1 . 2, .
.
:0,1,2,3,4,5,6,7,8,9 (BInary digiT BIT):0,1
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A . :
0>1>
( bit) .
bits 2 ? bits 10 ?
n 2n
m log2m
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?
1/1/0000 ?
20bit ! ,, =>(5+4+12)=>21 ,,, =>(5+4+12 + 3)=>24
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()
=0=> =1=>
=0=> =1=>
, =f()=A!
?
A Z
AZ
-
2
Z
Z
A B
A
B
.
-
ZCA
B
, ,
1.
!
Z
A
B
-
?
: & &
{0,1,2,3,4,5,6,7,8,9}, = :+,,*,/ :{,[,(,/,*,,+ : 0 +, 1 *, +, * +,...
:x+x =2x f(x,y)=3x+5y
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A Boole
To1854(!!!)o Georgele : .
.. " " .
" " .
" , ".
?
-
Shannon
(1938), ClaudeShannon """" " " "", le .
Boole "switchingalgebra". . " " " " "1""0".
( ).
-
. {0,1} (')
=0=>'=1, =1=>'=0 :
(and/): ( )
(or/):+ :
0 0=0, 1+1=1 1 1=1, 0+0=0 0 1=1 0=0, 1+0=0+1=1
, :{,[,(,',,+
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+0=, 1= ( ) +1=1, 0=0 ( ) + =, = () (')'= () +'=1 '=0 ()
( )
-
+ = +, = ()
( +)+ = +( +), ( ) = ( ) () : ,
. w+x+y+z .
+ = ( +), ( +) ( +)= +( )() :
1. + ( )+( ). .
2. 2. x +.
: (W+Y) (X +) (V+Y) (W +) (X+Y) (V +) =[W+(Y )] [X+(Y )]
[V+(Y )]=(Y )+(V X W)
(1/2)( )
-
+ =, (X+) = ()
+ '= ( +) ( +')= () : Z' + ' Z'+ Z+ ' Z= Z'+ Z
=X
: , , 1 .
+' + = +' , ( +) ('+) ( +)=( +) ('+)
()
(2/2)( )
-
+ +...+ =, ... = ()
(1 +2 +...+n)'=1' 2' n' (1 2 n)'='1 +'2 +...+'n ( DeMorgan)
[F(1, 2, ..., n, +, )]'=F('1, '2, ..., 'n, ,+)( DeMorgan)
: F=(W' )+(X Y)+[W ('+Z')]. T F'=((W')'+X') ('+Y') [W'+( Z)]=
=(W+X') (X Y)' [W'+(X Z)]
F(1, 2, ..., n)=X1 F(1, 2, ..., n)+X1' F(0, 2, ..., n) F(1, 2, ..., n)=[X1 + F(0, 2, ..., n) [X1'+ F(1, 2, ..., n)](
Shannon)
: F(X,W,Z)=X+W Z. T F(0,W,Z)=W Z F(1,W,Z)=1. A F=X 1+X' W Z F=(X+W Z) (X'+1)
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?
. ( ).
. :
.
. , .
-
O .
, .
6, 7404.
-
D .
4, 7408.
-
OR H .
4, 7432.
-
.
:
:F4(x,y,z)=x' z +y' x
G(X,W,Y,Z)=[' +] ( +W');
-
F(x,y,z)=x+y+z ? F(x,y,z)=x+y+z =(x+y)+z :
? ! . :
.
.
-
?
' '
' '
' '
'+' +' '
-
? ?
, 2 . . 0 1 22 .
=2 ?
0,1. unary/. .
-
:
F14 D. D(not AND). F8 OR. OR(not OR). F6 1 1 1 ( , 1 ). OR(eXclusiveOR) XOR.
F9 1 0 2 1 ( 1 ). (noteXclusiveOR) XNOR.
-
E :(1/2)
-
E :(2/2)
-
? (2)
-
AB
CY
BA CBA
A
B
C
DY
BACBA
DCBA
-
AB
CY
A
B
C
DY
-
CBAY =
ABC
Y
B C Y
X X 0 1
X 0 X 1
0 X X 1
1 1 1 0
DCBAY =C
AB
DY
A B C D Y
X X X 0 1
X X 0 X 1
X 0 X X 1
0 X X X 1
1 1 1 1 0
-
AB
CY
ABABCCAB
A
B
CY
BA +CBACBA ++++
-
A Y
YAA
BY
YA
B
A
BY
A
B
Y
A
BY
A
B
Y
-
BAY =AB
Y
A
B
Y
( ) ( )BABABA
BABBAA
ABBABAABBABAY
=+==+++=
=+==
-
YA
A
BY
A
BY
A
BY
YA
BA Y
A
B
Y
A
B
Y
-
BABA =+A
BY
B
Y
A A
B
A
BY
-
? . 6inverters 4OR,AND,
To : . =>.
: D,NOR . D,OR, ( transistor).
XOR,XNOR =>
-
, , .
1: .
2: .
3: .
, , .
-
!
F3 F4.
, .
4 3 F4.
To ?
:
-
F3 :F3(,,)= '+' +' '
:
' +' ' =' F3 = '+' =F4.
H ! , .
.
-
F(X,Y,Z)=X Y' Z+X' Y Z+Y Z==X Y' Z+Y Z ()= ( Y'+) ()= ( +) (1o )
F(X,Y,Z)=X Y'Z+X Y' Z+X Y Z'
F(X,Y,Z)=X Y' Z+X Y' Z+X Y Z'==X Y' Z+X Y Z' (A)= (Y' Z+Y Z') ()= ( ) ( XOR)
-
&
. .
.
, .
.
-
, , .
.
.
2 .
-
,,
:,',,'
AND :, ', ', ' '
OR :, +',+', +'+' (sumofproducts SOP)
SOP : + ' + ' + ' ' (productofsums POS)
. POS : ( +') (+') ( +'+') ,
( ) 1. .
: ' ', +'+' : ' ' , +'+'+
-
, . 2 .
F(X,Y) :' , , '
, . 2 .
F(X,Y) :'+, +, +' +
-
() . () () 1(0) .
M ( 1 0 ) .
.. 4=xy'z'.M 5=x'+y+z'
-
.
.
1 3 4 5
F3(x,y,z)=m1 +m3 +m4 +m5 =x'y'z +x'yz +xy'z'+xy'z =(1,3,4,5)
, . .
-
.
.
( 0) 0 2 6 7
F'3(x,y,z)='0 +'2 +'6 +'7=>F3(x,y,z)=0 2 6 7 =(x+y+z) (x+y'+z) (x'+y'+z) (x'+y'+z')=
(0,2,6,7)
, . .
-
0 1 .
.. F(A,B,C)= (1,4,6)=>F= (0,2,3,5,7)G(W,X,Y,Z)= (1,8,11,14,15)=>
G= (0,2,3,4,5,6,7,9,10,12,13)
F F' I m'i =Mi 'i =mi
m'0=(x'y'z')'=x+y+z=M0 A F(x,y,z)= (1,3,4) =>F=m1 +m3 +m4 =>
F'=(m1 +m3 +m4)'=M1 M3 M4 =(1,3,4)= (0,2,5,6,7)
-
} }
.
-
Boole .
: ( Karnaugh /kmap):
5.
QuineMcClauskey :
Espresso:
, ,D&OR.
-
.
.
, 1 . 0.
""( / 2 4 8 16 )
-
A B Y0 0 0 1 1 0 1 1
Karnaugh 2-
-
A B Y0 0 0 1 1 0 1 1
0 101
Karnaugh 2-
-
A B Y0 0 0 1 1 0 1 1
0 10 1
Karnaugh 2-
-
0 10 1
B
-
0 10 1
B
0 10 1
B
-
0 10 1
B
0 10 1
B
0 10 1
A
-
0 10 1
B
0 10 1
B
0 10 1
A0 1
0 1
A
-
A B Y0 0 10 1 11 0 01 1 0
-
A B Y0 0 10 1 11 0 01 1 0
0 10 1 11
-
A B Y0 0 10 1 11 0 01 1 0
0 10 1 11
AY =
-
A B Y0 0 00 1 11 0 11 1 1
-
A B Y0 0 00 1 11 0 11 1 1
0 10 11 1 1
-
A B Y0 0 00 1 11 0 11 1 1
0 10 11 1 1
-
A B Y0 0 00 1 11 0 11 1 1
0 10 11 1 1
BAY +=
-
0 10 11 1
BABABAY =+=
-
(2)
4, .
x 0 1.
y 0 1.
m0 m1m2 m3
xy xy
xy xy
yx0
1
0 1
1
yx0
1
0 1
1
1 1
yx0
1
0 1
xy =(3)=m3 x+y =(1,2,3)=m1+m2 +m3
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00 01 11 10 Gray 1 bit
00 01 11 1001
C
Karnaugh 3-
-
00 01 11 100 1 11
C
CBACBAY +=000 001
-
00 01 11 100 1 11
C
CBACBAY +=000 001
BAY =
-
00 01 11 100 1 1 1 11
C
-
00 01 11 100 1 1 1 11
C
AY =
-
00 01 11 100 1 1 1 11
C
AY =
00 01 11 100 1 11 1 1
C
-
00 01 11 100 1 1 1 11
C
AY = CY =
00 01 11 100 1 11 1 1
C
-
00 01 11 100 1 1 1 11
C
AY = CY =
00 01 11 100 1 11 1 1
C
00 01 11 100 1 1 1 11 1 1
C
-
00 01 11 100 1 1 1 11
C
AY = CY =
00 01 11 100 1 11 1 1
C
00 01 11 100 1 1 1 11 1 1
C
BAY +=
-
00 01 11 100 1 11 1 1
C
CABCBACBACBAY +++=000 100 010 110
-
00 01 11 100 1 11 1 1
C
CABCBACBACBAY +++=000 100 010 110
-
00 01 11 100 1 11 1 1
C
CABCBACBACBAY +++=
0
11 11 1
01 1100 10
000 100 010 110
-
00 01 11 100 1 11 1 1
C
CABCBACBACBAY +++=
CY =01
1 11 1
01 1100 10
000 100 010 110
-
(3) 8, .
Gray.
Gray
yz
.
.
-
(3)
F(x,y,z)=(2,3,4,5) F(x,y,z)=xy+xy
F(x,y,z)=(3,4,6,7) F(x,y,z)=yz+xz
-
(3)
F(x,y,z)=(0,2,4,5,6) F(x,y,z)=z+xy
F(A,B,C)=AC+AB+ABC+BC
F(A,B,C)=(1,2,3,5,7)=C+AB
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Karnaugh 4-
00 01 11 1000011110
BCD
-
00 01 11 1000 101 111 1 1 1 110 1
BCD
-
00 01 11 1000 101 111 1 1 1 110 1
BCD
00 01 11 1000 101 111 1 1 1 110 1
BCD
-
00 01 11 1000 101 111 1 1 1 110 1
BCD
CDABY +=
00 01 11 1000 101 111 1 1 1 110 1
BCD
-
00 01 11 1000 1 1011110 1 1
BCD
1 1
1 1
-
00 01 11 1000 1 1011110 1 1
BCD
1 1
1 1DBY =
-
BY =
00 01 11 1000 1 1 1 1011110 1 1 1 1
BCD
DBY +=
00 01 11 1000 1 1 1 101 1 111 1 110 1 1 1 1
BCD
-
00 01 11 1000 1 101 1 111 1 1 110 1 1
BCD
CABCDDCY ++=
-
(4)
2n n k n , k
.
().
16, . Gray.
-
(4)
F(w,x,y,z)=(0,1,2,4,5,6,8,9,12,13,14)F(w,x,y,z)=y +wz +xz
F(A,B,C,D)=ABC +BCD +ABCD +ABCF(A,B,C,D)=BD +BC +ACD
11
-
.
..F(w,x,y,z)=(1,3,7,11,15) d(w,x,y,z)=(0,2,5)
10
wx0001
000111101 1 0
yz
0 0
0 0
1 0
1 0
11
10
10
wx0001
000111101 1 0
yz
0 0
0 0
1 0
1 0
11
10
F = yz + wx = (0,1,2,3,7,11,15) F = yz + wz = (1,3,5,7,11,15)
.
-
(5)
-
(5)
F(,,C,D,E)=(0,2,4,6,9,13,21,23,25,29,31)
F(A,B,C,D,E)=ABE +BDE+ACE
-
(Prime Implicants)
( prime .
O ( implicant.
implicant PI):
):
prime
1
1
AB00
01
00011110
1 1
1
CD
1
1 1
1
1 1
11
10
F(A,B,C,D)=(0,2,3,5,7,8,9,10,11,13,15)
A
D
C
B
.PI:BD,BD
1
1
AB00
01
00011110
1 1
1
CD
1
1 1
1
1 1
11
10A
C
D
B
PI:CD,BC,AD,AB
m3:CD,BCm9:AD,ABm11:CD,BC,AD,AB
F=(BD+BD)+(CD+AD)or(CD+AB)or(BC+
AD)or(BC+AB)
-
Karnaugh
1: B
1 " " .
1.
2: 1 "",
3: 2 "" 1.
-
NAND & NOR
-
NAND: F=AB+CD+ED.
-
(1)
-
F=(CD+E)(A+B)
(2)
-
NOR
.
-
NOR
F=( +E)(C +D)
-
XOR
(XOR)x y=xy +xy OYTE(XNOR)(x y) =xy +xy
..
:x 0=x x 1=xx x=0 x x =1x y =(x y) x y=(x y)
XOR :A B=B A
A (B C)=(A B) C=A B C XOR 2.
-
XOR XOR : 1
1.
-
XOR XORn 2n/2
.
-
.
bit
.
-
(Karnaugh ) ( ) ,D R.
: NAND,NOR,XOR,XNOR.
.
-
Karnaugh
G(,,C,D)=(0,1,2,4,5,8,9,10)
Karnaugh & :
G=(A+C)'+B'(C'+D')=
(A+C)'+B'(CD)'=
(A+C)'+(B+CD)'=((A+C)(B+CD))'
:
-
:Z(A,B,C,D)=D' Y(A,B,C,D)=CD+C'D'
X(A,B,C,D)=B'C+B'D+BC'D' W(A,B,C,D)=A+BC+B D
I : =(C D)' X=B'(C+D)+B(C+D)'=B (C+D) W=A+B(C+D)
X (C+D)
-
.
, : . , .
, .
, , .
. 0>1 1>0.
-
! arnaugh :
F(x,y,z)=xy'+yz, F(1,y,1)=y'+y=1, y.
y a y b .
x=1,z=1 y1>0.
A (static1 hazard).
m5 m7. 1,
-
:
m5 m7 1.
-
. :
: . .
: . . .
-
: /
/ / / /
-
-A (Half Adder)1. : .
2. /:2 2.
3. /: x,y ()C(),S () .
4. :
x y C S0 0 0 00 1 0 11 0 0 11 1 1 0
-
-x y C S0 0 0 00 1 0 11 0 0 11 1 1 0
()S=xy + xy
C = xy
()S=x yC = xy
-
A (Full Adder)1. : .
2. /:3 2.
3. /: x,y (),z C(),S () .
4. : x00001111
y00110011
z01010101
S01101001
C00010111
-
-
S = xyz+xyz+xyz+xyz C=xy +yz +xz
-
-E S = (x y) z
C=xy +yz +xz =xy +z(x+y)=xy +z(x'y +xy'+xy)=xy +zxy +z(x'y +xy')=xy +z(x y)
M 2 OR.
-
(1/4)
-
(2/4)
-
(3/4)
4 . 4 . MSI, LSI( ).
S3
S3
-
(4/4)
, .
: . , 1 .
, .
( )
-
: 9 29=512.
S3
-
= +()= + +1
= 1
-
/
-
(): : .
2 .
2 n nbits.
. . .
: "". .
-
(Carry Look-Ahead)
Pi=AiBiGi=AiBi
Si=PiCiCi+1=Gi+PiCi
C0 = C1= G0+ P0C0C2= G1+ P1C1=G1+ P1(G0+ P0C0) = G1+ P1G0+ P1P0C0C3= G2+ P2C2= = G2+ P2G1+ P2P1G0+ P2P1P0C0
Ci+1=Gi +PiCi , :
!
-
C1= G0+ P0C0C2= G1+ P1G0+ P1P0C0C3= G2+ P2G1+ P2P1G0+ P2P1P0C0
-
Pi=AiBiGi=AiBi
Si=PiCi
-
(Comparator)
:
(,=).
n bits 22n.
.
=3210 =3210 .
= (Ai,Bi) , 3=3 2=2 1=1 0=0.
(=) =x3x2x1x0 xi =iBi+Aii
-
.
.
Ai =1 Bi = 0 >, i = 0 i = 1 )= 33 + x3A2B2 +x3x2A1B1 +x3x2x1A0B0
(
-
(=) =x3x2x1x0 xi =iBi+Aii(>)=33+x3A2B2+x3x2A1B1+x3x2x1A0B0
(
-
/ 2x2 bit
-
/ 4x3 bit
-
(Decoder)
: n 2n
( n ).
: 38
1 2n .
-
. .( ).
-
(Demultiplexer)
2n
n .
-
/
2 3 8
1 4 16
-
2n .
n m n2n m H.
2n/2, F. F.
-
.S(x,y,z) =(1,2,4,7)C(x,y,z) =(3,5,6,7)
-
(Encoder)
: 2n n
.
:
1 . (:)
0 0 D01. (: )
-
3
-
.
: 4
-
4
x =D2+D3y=D3+D1D2V=D0+D1+D2+D3
1 .
-
(Multiplexer)
.
.
2n1 n2n 2n . .
-
41
-
() .
-
2n 1 n+1 :
1. n .
2. .
-
F(x,y,z)=(1,2,6,7)
-
Boole
n :
1. 2n11 n1 .
1. .
2. n 1 ( ).
3. , .
-
F(A,B,C,D)=(1,3,4,11,12,13,14,15)
-
. . ?
!
, !
PC ? USB ?
T , .
-
In En Out
0 0 Z1 0 Z0 1 01 1 1
-
vs : . , .
: . .
. . .
2 : . .
-
vs
()
, .
.
. .
(feedback) .
.
-
/ -
:
(2) : :
.
(latches)
-
/ - 2
flip-flops
-
!
Vcc
Gnd
s Y Q Gnd0 1 0
Vcc
1 0 1 Gnd0 0 1
! "" 1. !!!
-
S-R latch
s sr
Q' Q
R
S
Q
Q'
E Q=a Q'=~a.
S=R=0.
-
S-R latch -2R
S
Q
Q'
O Q=1 Q'=0 ( ) Q=0 Q'=1 ( ) .
R=0
S=1
Q=1
Q'=0
R=0
S=0
Q=1
Q'=0
M S=1 R=0 . S=R=0 !
-
S-R latch -3R=1
S=0
Q=0
Q'=1
R=0
S=0
Q=0
Q'=1
M S=0 R=1 ( / ) latch. S=R=0 !
() => .
-
S-R latch -4R=1
S=1
Q=0
Q'=0
R=0
S=0
Q=X
Q'=X
M S=1 R=1, Q=Q'=0. "".
o S=R=0 !!!
S, R.
S, R, .
-
S-R latch D~R
~S
Q'
Q
H S-R latch NOR.
~S=~R=1.
~S=0 ~R=1. ~S=1 ~R=0. H ~S=~R=0 .
-
SQR
Q'
SQ
RQ'
S R Q Q0 0 Q Q ()
0 1 0 1 Reset (Q=0)1 0 1 0 Set (Q=1)1 1 0 0
S R Q Q
0 0 1 1
0 1 1 0 Set (Q=1)
1 0 0 1 Reset (Q=0)
1 1 Q Q ()
-
S-R latch
NAND C. S R latch
C S R Q (next state)
0 X X Q (t-1)
1 0 0 Q (t-1)
1 0 1 0 ()
1 1 0 1 ()
1 1 1
-
D latch :
Q'
Q
D
C(clk)
C D Q (next state)
0 X Q (t-1)
1 0 0 ()
1 1 1 ()
S, R 1. D, C 1.
-
D latch -2
D latch (transparent).
N : To D latch C
-
Q'
Q0
0
1
1
1
:
Q'
Q
0->1
0->1
1
1->0
1->0
:
Q'
Q
1
1
0
0
1
!!!
-
: D
C. O .
Setup time ( ). D C .
Hold time ( ). D C .
-
Flip-flops A latches (level-triggered) flip-flops (edge triggered) !
.
,
.
-
Latches vs Flip-flops
-
flip-flops ?
()
O flip-flops
: latch latches .
-
D flip-flop ?
QD
C DC
Q
Q'Q'
D
C
Q D
C
QD
CLK
Q' Q'MASTER SLAVE
D latches(master and slave)
M
-
DC
Q D
C
QD
CLK
Q' Q'MASTER SLAVE
CLK = LOW => Master , Slave . Master. Slave CLK = IGH => Master
. Slave aster .
Master 1, Slave 0 CLK .
D flip-flop
-
D CLK Q Q'
0 0 11 1 0X 0 Q(t-1) Q'(t-1)X 1 Q(t-1) Q'(t-1)
D
C
Q D
C
QD
CLK
Q' Q'MASTER SLAVE
QM
-
D flip-flop
D
C
Q D
C
QD
CLK
Q' Q'MASTER SLAVE
QM
D CLK Q Q'
0 0 11 1 0X 0 Q(t-1) Q'(t-1)X 1 Q(t-1) Q'(t-1)
-
D-FF
3 S-R 4
2 CLK D, .
CLK = 0, S = R = 1 .
-
D-FF - 2
D = 0 CLK R = 0, S = 1 Q=0 Q'=1.
A D .
D = 1 CLK S = 0, R = 1 Q=1 Q'=0.
A D S 0 R 1 .
-
FF
FF D CLK
.
: (Preset / Direct Set). H Q 1 (Q' 0).
/ (Reset / Clear). Q 0 (Q' 1).
-
1 :
, FF, .
-
D-FF Reset ( )
Reset = 0, Q'=1. E S=1 Q=0. Reset = 1, D FF .
-
D-FF Clear Preset
~Clear=0 ~Preset=1 => ~Q=1, S=1 Q=0.
~Preset=0 ~Clear=1, => Q=1, R=1 ~Q=0.
~Clear = ~Preset =0, Q=~Q=1. A.
~Clear = ~Preset =1, D FF.
-
D-FF Reset Preset
SN 74 (ALS) 74Dual Positive Edge D Flip Flops with Asynchronous Preset and Clear
-
2 :
, , FF, . FF .
-
D Flip Flop Reset Preset
D Flip Flop D .
~Clear
D
~Preset
D~Preset
D
~Clear
~Clear
-
DQ'
Q
D-FFCLK
PRE'
CLR'
D
Q'
Q
D-FFCLK
PRE'
CLR'
-
A flip - flop
D flip flop .
. flip flop : aster / Slave S-R Flip Flop To Master / Slave J-K Flip Flop To J-K Flip Flop To T Flip Flop To Scan Flip Flop
, .
.
-
aster / Slave S-R Flip Flop
O Master / Slave D FF D latches, S-R latches Master / Slave S-R FF.
C S R Q (next state)
0 X X Q (t-1)1 0 0 Q (t-1)1 0 1 0 ()
1 1 0 1 ()1 1 1
-
aster / Slave S-R Flip Flop - 2
S
RC
Q
Q
S
RC
Q
Q
S
R
C
Q
Q'
O 1, Slave . 0 Slave Master Slave.
C.C S R Q (next state)0 X X Q (t-1)1 0 0 Q (t-1)1 0 1 0 ()
1 1 0 1 ()1 1 1
-
. 2 S-R latches S=R=1 aster latch.
aster / Slave J-K Flip Flop
S
RC
Q
Q
S
RC
Q
Q
C
Q
Q'K
J
J 1, S 1, Q' 1, Q 0 !
1, R 1, Q 1, Q' 0 !
-
aster / Slave J-K Flip Flop - 2
S
RC
Q
Q
S
RC
Q
Q
C
1
0K
J S
RC
Q
Q
S
RC
Q
Q
C
1
01
1
S
RC
Q
Q
S
RC
Q
Q
C
1
01
1 0
1
S
RC
Q
Q
S
RC
Q
Q
C
0
11
1 0
1
J = K = 1 .
Q=0 ~Q=1.
-
aster / Slave J-K Flip Flop 3C J K Q (next state)0 X X Q (t-1)1 0 0 Q (t-1)1 0 1 0 ()
1 1 0 1 ()1 1 1 ~Q(t-1)
-
J-K Flip Flop
D FF
Q
CLK
D
Q
JK
C
Q
~Q
-
J-K Flip Flop - 2
SN 74 (ALS) 109Dual Positive Edge J-~K Flip Flops with Asynchronous Preset and Clear
-
T(oggle) Flip Flop
To FF !!!
: FF !!!
FF D J-K FF.
D
CLK
Q
QT
JCLKTK
1 Q
~Q
-
T(oggle) Flip Flop
=> (enable) .
FF D J-K FF.
D
CLK
Q
QT
EN
JCLKTK
EN Q
~Q
-
Scan Flip Flop () FF.
FF .
( ) / FF.
scan FF / .
-
Scan D FF
D
CLK
Q
QCLKTI
TED
DFF ~ (est Enable).
= 0 D FF. = 1, D, (Test Input). O FF (scan chain).
-
Scan Chain
D
CLK
Q
QCLKTI
TED D
CLK
Q
Q
TE
TI
D
CLK
Q
Q
TE
TI
D
CLK
Q
Q
TE
TI
D
CLK
Q
Q
TE
TI
D
CLK
Q
Q
TE
TI
TO
TECLK
TI
O . FF = 1, , . =0 . =1 .
-
Level vs edge triggered . Reset Preset. Setup Hold. To D FF .
FFs J-K . FFs Scan.
J K Q(t+1)0 0 Q(t)0 1 01 0 11 1 ~Q(t)
D Q(t+1)0 01 1
EN Q(t+1)0 Q(t)1 ~Q(t)
-
DQ'
Q
FFCLK
K
J
Q'
Q
FFCLK
CLK D Qn+1 1 1 Load 1 (Set) 0 0 Load 0 (Reset)
D
Q'
Q
FFCLKT
CLK T Qn+1 0 Qn / 1 Qn (Toggle)
CLK J K Qn+1 0 0 Qn () 1 0 1 Load 1 (Set) 0 1 0 Load 0 (Reset) 1 1 Qn Toggle
FF
-
DQ'
Q
FFCLKK
J
Q'
Q
FFCLK
Qn Qn+1 D0 0 00 1 11 0 01 1 1
D
Q'
Q
FFCLKT
FF
Qn Qn+1 T
0 0 00 1 1
1 0 11 1 0
Qn Qn+1 J K0 0 0 X0 1 1 X1 0 X 11 1 X 0
vs ? ... ... ? transistor ( 1958) Intel Pentium (IV) microprocessor : 2 A ? () 2 ?A BooleShannon Karnaugh 2-Karnaugh 2-Karnaugh 2- (2) Karnaugh 3- (3) (3) (3) Karnaugh 4- (4) (4) (5) (5) (Prime Implicants) Karnaugh NAND & NOR NAND (1) NOR NOR XOR XOR XOR ! : -A (Half Adder)- A (Full Adder)-- (1/4) (2/4) (3/4) (4/4) / (Carry Look-Ahead) (Comparator) (Decoder) (Demultiplexer)/ (Encoder) 3 4 (Multiplexer) Boole