Black Box
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![Page 1: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/1.jpg)
Black Box
Op {X, Z}
ZX Y Bündel von Leitungen
![Page 2: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/2.jpg)
Signalklassifizierung
x(t)
t
x(k)
kTA
x(t)
t
x(k)
kTA
![Page 3: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/3.jpg)
Zustandstabelle
ESx(t)
t
x(t)
t
TO
TU
xbin
t
1
0
xbin
t
1
0
Zuordnung
![Page 4: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/4.jpg)
Blockschaltbild
f(x)x y
f(x)x y
f(x)x y
![Page 5: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/5.jpg)
BDD
f
V1
V2 V3
V4 V5 V6 V7
0 0 1 0 0 1 1 1
0
0
0
0
0 0 0
1
1
11
1
11
x0
x1
x2
Wurzelknotenroot-node
innere Knoteninternal nodes
Endknotenterminal nodes
(enthalten f-Werte)
![Page 6: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/6.jpg)
BDD
f
V1
V2 V3
V4 V5 V6 V7
0 1
0
0
0
0
00 0
1
1
11
1
11
x0
x1
x2
f
V1
V2 V3
V5 V6
0 1
0
0 0
00
1
1
1
1
1
![Page 7: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/7.jpg)
c f(x)0 0 1 1 01 0 0 1 0
0 1 1 0 b0 0 1 1 a
c g(x)0 0 1 0 01 1 1 1 0
0 1 1 0 b0 0 1 1 a
y2 h*(y)0 1 11 0 1
0 1 y1
Verhaltensmodell
a
b
cx
y2=g(x)
y1=f(x)
z=h*(y)=h(x)
![Page 8: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/8.jpg)
Abbildungsprodukt
c h(x)0 1 1 1 11 0 0 1 1
0 1 1 0 b0 0 1 1 a
a
b
c
z=h(x)
![Page 9: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/9.jpg)
Kontaktschaltungen
AK
f1
a
+
RK
f2
a
+
f3
+
f4
+
R
+ +
RKf2=a
r
![Page 10: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/10.jpg)
Gatterschaltungen
1a f2=a
+
a f2=a
Tp
Tn
p-leitend
n-leitend
Tp
Tn
high
low
low
high
low
high
![Page 11: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/11.jpg)
Kontaktschaltungen
f5
a
+
b
f6
a
+
b
![Page 12: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/12.jpg)
Gatterschaltungen
&af5=ab
b
1af6=ab
b
&afNANDb
fNAND
a
+
b
a b
+
n
n
pp
fNAND
a
b
![Page 13: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/13.jpg)
Analyse und Vereinfachung
+
b
a b
ca
f
+
a b
c
f
![Page 14: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/14.jpg)
XOR und XAND
=1ab ~f
=ab
f~
![Page 15: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/15.jpg)
Orthogonalität
001 101
000 100
011 111
010 110x2
x1
x0
![Page 16: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/16.jpg)
MUX8to1
a=1 a=1 a=1 a=1a=0 a=0 a=0 a=0
b=0 b=0b=1 b=1
c=1 c=0
MUX8-to-1
f(0,0,0)
f(1,1,1)
… f(c)
a b c
![Page 17: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/17.jpg)
Transformation
BF, KP, TVL
Disjunktive FormD(f)
Konjunktive FormK(f)
ÄquivalenzformE(f)
AntivalenzformA(f)
Orthogonalisierung
![Page 18: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/18.jpg)
Gatter- und Zweigschaltung
&ab 1
cf
+
b
ca
f
![Page 19: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/19.jpg)
Analyse des Verhaltens
=1ab baf ~
&b
1 f‘(x)&a
a
b
v1
v2
![Page 20: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/20.jpg)
Analyseprinzip
&
&
&
&
a
b
g1
g2
g3
f(x)
![Page 21: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/21.jpg)
Prinzip
?
?
?
?
…1., 2. Stufe
f(x)x2
x1
xk
x2
0. Stufe(Negation)
![Page 22: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/22.jpg)
Beispiel
&
b 1 f&
c
a
c
&a
&
b & f&
c
a
c
&a
1
b& f
1
ca
c
a1
b1 f
1
ca
c
a
1
1 f1
c
ac
1
a
b
1
& f1
c
ac
1
a
b
&
& f&
c
a
ca
b
&
1 f&
c
a
ca
b
![Page 23: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/23.jpg)
Einfache Synthese
&
a1
ai
ai+1
an
f(x)&
a1
ai
ai+1
an
f(x)
&
&
&……
…
&
a1
an
f(x)&
&…
…
&
&
![Page 24: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/24.jpg)
Multiplexer
MUX2-to-1
1
0
f(a=1)
f(a=0)f(x)
a
MUX4-to-1
11
10
f1,1
f(x)
a
01
00
f1,0
f0,1
f0,0
b
MUX4-to-1
11
10 f(x)
a
01
00
b
1cd
d
1
=1cd
![Page 25: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/25.jpg)
Statische Nebenbedingungen
a b
&
b & fopt
&
da
c
![Page 26: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/26.jpg)
Praktische Erfahrung
x(t) y(t)
z
e a
s
s 1se/a
s
1s1
e/a
1s2
1sn
…e/a
e/a
![Page 27: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/27.jpg)
zeitliches Verhalten
s(0)e(0)/a(0)
s(1)e(1)/a(1)
s(1) … s(n)
Anfangs-zustand
![Page 28: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/28.jpg)
Moore und Mealy
e sδ
sλ
a
e sδ
sλ
a
![Page 29: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/29.jpg)
Automatenmodelle
s 1se/a
Ursache Wirkung
1 2
3 4
5
α/1
β /0
β /0
α/0
α/1β /1 α/1β/0
α/1
β /0
T4 – Zyklus(Länge 4)
für α
![Page 30: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/30.jpg)
Beispiel
z 1zx/y
z
z1z21z1
1z2x
21zz
y
Moore Automat
![Page 31: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/31.jpg)
Beispiel
01 11
1000
z1z2
x=0
x=0
x=1
x=1
010
1z1
z2
y=1 0
01
1,0 21 zz
0,1 21 zz
121 zz
![Page 32: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/32.jpg)
Automatengraph des FF
Q 0 1
F0
F1
F1
F0
![Page 33: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/33.jpg)
Struktur von FF-Schaltwerken
kombinatorischesFunktionenbündel
für 1z = f(x, z)
FF1
FFk
…
1z1
1zk
λkombi-
natorisches Bündel
x z
z1
zk
y
C = Takt an jeden FF
CCCC 1 CCC 2
![Page 34: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/34.jpg)
Master-Slave-Technik
MasterFF
SlaveFF
CCC 1 CCC 2
x Q
![Page 35: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/35.jpg)
FF-Schema
E1
E2
…&…
CLK
Q
Q
Ei1
Eik
…
S
J
K
R
T Q
CLKCC
JCLK
K
Q
S
R
![Page 36: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/36.jpg)
RS-FF
1
1
R
S
Q
Q
0
0
0
0
11
11
0 1
S
R
RS
![Page 37: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/37.jpg)
JK-FF
0 1
J
K
KJ
1
1
Q
Q
&
&
K (=R)
J (=S)
C
![Page 38: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/38.jpg)
JR-FF und SK-FF
0 1
R
RRJ
JR
0 1
S
S SK
SK
![Page 39: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/39.jpg)
D-FF und T-FF
0 1
D
D
D
D
0 1
T
T
TT
DC
Q
TC
Q
![Page 40: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/40.jpg)
RST-FF und L-FF
0 1
ST
RT
RTST
0 1
L
L 1 Q&
&L
R
![Page 41: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/41.jpg)
Synthese
t1
0
C(t)
t1
0
C
t1
0
Q(t)dynCC
![Page 42: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/42.jpg)
Entwurfsbeispiel 1
1
1
1
1
DD
C
Q
Zwischenfunktion
a
abb
z
z
1z bilden bei Taktflanke
![Page 43: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/43.jpg)
Entwurfsbeispiel 1
&
&
R
C
Sa
ba
b
Q z
2. Möglichkeit1. Möglichkeit
&
&
D
C
V
a
bab
Q zb
&
![Page 44: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/44.jpg)
Entwurfsbeispiel 1
&
&
T
Caba
b
Q z&
z
![Page 45: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/45.jpg)
Entwurfsbeispiel 2
Sz1z0
000
210
101
xx
xx
x
x-
11
unbekannterZustand
![Page 46: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/46.jpg)
Entwurfsbeispiel 2
&
&
R
C
Sx
z0
Qz1=y1
&
x
z1
z0
R1
S1 &
&
R
C
Sx
Qz0=y0
&
xz1
z0
R0
S0
z1
![Page 47: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/47.jpg)
Veranschaulichung des Verhaltens
z 1zx, yKante
Phase (x, z, 1z, y)
Ursache Wirkung
![Page 48: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/48.jpg)
Beispiel
=1 J
C
K
x Qz1=D2 D
C
V
QD
C
Qz2=J3
K3
D1 z3=y
V2
![Page 49: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/49.jpg)
Automatengraph
001 101
000 100
011 111
010 110
z1z2z3
x=0
![Page 50: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/50.jpg)
Speichertechnische RealisierungMemoryAdresse
(1z, y) y(t-1)
zx
Takt an jedes Register FF-Register
10 11
0100
z1z0x/y
1/1
1/0
1/1
0/0
0/0
0/1
![Page 51: Black Box](https://reader035.fdokument.com/reader035/viewer/2022062516/56812a8a550346895d8e2d37/html5/thumbnails/51.jpg)
Schaltung für Beispiel
&
&
R
C
Sx
z0 Qz1
&
x
z1
z0
R1
S1
&
& R
C
S
xQ
z0
&
x z1
z0R0
S0
z1
z0
&x
z1
&x
&
z1&
x&
yz1
z0