Digital Design Slides

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

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

vs

() .

.

() () .

, .

?

: CDplayer CDplayer CDplayer 10.000.000 CDplayer 20

?

20 ,,,

1947: transistor BellLabs JohnBardeenWalterBrattain(Nobel 1956 WilliamShockley)

1,1 .

Jack KilbyTexas Instruments(Nobel ,2000)

transistor ( 1958)

(SSI):>10

(MSI):>100

(LSI):>1000

(VLSI):>10000

2003:

IntelPentium4mprocessor (55 ) 512Mbit DRAM(>0.5 )

Intel4004MicroProcessor

19711000transistors1MHzoperation

Intel Pentium (IV) microprocessor

1. (Supercomputers)

2. (Mainframes)

3. (Workstations)

4. (Microcomputers)

5. (Microcontrollers)

(Mainframes)

(Supercomputers) Workstation: Sun Ultra450

microcomputer

Personal Digital Assistant

: () () ( ) () ()

Bottom-up

Top-down

wafer

die

: 2

0 1. 0 1 . 2, .

.

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

A . :

0>1>

( bit) .

bits 2 ? bits 10 ?

n 2n

m log2m

?

1/1/0000 ?

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

()

=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

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

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

+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)

?

. ( ).

. :

.

. , .

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)

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

BAY +=

0 10 11 1

BABABAY =+=

(2)

4, .

x 0 1.

y 0 1.

m0 m1m2 m3

xy xy

xy xy

yx0

1

0 1

1

yx0

1

0 1

1

1 1

yx0

1

0 1

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

00 01 11 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 +++=

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

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)

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.

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.

(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. (: )

.

: 4

4

x =D2+D3y=D3+D1D2V=D0+D1+D2+D3

1 .

(Multiplexer)

.

.

2n1 n2n 2n . .

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

Documents

Digital Design Slides