Embed Size (px)
DESCRIPTION
Chapter 4 -- Modular Combinational Logic. Decoders. Decoder Realization. More complex decoders. Example 4.1 -- Realize f(Q,X,P) = m (0,1,4,6,7) = M (2,3,5). Example 4.1 (concluded). K-Channel multiplexing/demultiplexing. Figure 4.22. Four-to-one multiplexer design. - PowerPoint PPT Presentation
Citation preview
Chapter 4 -- Modular Combinational Logic
L S B
M S B
D eco d e rn - to -2 n
x 0
x 1
y 0
y 1
x n-1y 2n -1
Decoders
m 0
m 1
m 2
m 3
(a ) (b )
(c )
L S B A
M S B Bm 0
m 1
m 2
m 3
m 1
m 0
m 2
m 3
L S B A
M S B B
L S B A
M S B B
Decoder Realization
C AB
(a )
(b )
(c )
m 0 = C B A
m 1 = C B A
m 2 = C B A
m 3 = C B A
m 5 = C B A
m 4 = C B A
m 6 = C B A
m 7 = C B A
B
BA
A
m 0
m 1
m 2
m 3
m 4
m 5
m 6
m 7
C
D
ABL S B
M S B
k0
k1
k2
k3
m 0
m 4
m 8
m 1 2
2 -to -4
A
AA
A
A
AB
B
C
C
m 1
m 5
m 9
m 1 3
m 2
m 6
m 1 0
m 1 4
m 3
m 7
m 11
m 1 5
l0 l3l1
l2
2 -to -4
More complex decoders
P
X
Q
(a ) (b )
A
B
C f(Q , X , P )
0
1
2
3
4
5
6
7
P
X
Q
A
B
C f(Q , X , P )
0
1
2
3
4
5
6
7
Example 4.1 -- Realize f(Q,X,P) = m(0,1,4,6,7) = M(2,3,5)
(c ) (d )
f(Q , X , P )
A
B
C f(Q , X , P )
0
1
2
3
4
5
6
7
P
X
Q
A
B
C
0
1
2
3
4
5
6
7
P
X
Q
Example 4.1 (concluded)
A in
B in
K in
S W 1 S W 2
(a )
(b )
S in g lech an n e l
A o u t
B o u t
K o u t
B o u t
K o u t
A o u t
a
b
k
M u ltip le x e r D e m u ltip le x e r
A in
B in
K in
a
b
k
S in g lech an n e l
ÉÉ
K-Channel multiplexing/demultiplexing
Figure 4.22
(a )
Y4 -to -1
M u ltip le x e r
Y
B A
B
0011
A
0101
(b )
(c )
0 1 2 3
2 -to -4D e co d e r
D 0
D 1
D 2
D 3
Y
D 0D 1D 2D 3
D 0
D 1
D 2
D 3
B A
Y
(d )
D 0
D 1
D 2
D 3
B A
S elec t io n co d e
Four-to-one multiplexer design
(a )
(b )
V C C
C AB Yfx 1 x 3x 2
x 1 x 3x 2
01234567
00001111
00110011
01010101
10110100
D 0 = 1D 1 = 0D 2 = 1D 3 = 1D 4 = 0D 5 = 1D 6 = 0D 7 = 0
C B A
YW
7 4 1 5 1 A
f(x 1 , x 2, x 3)
i D 0D 1D 2D 3D 4D 5D 6D 7G
S e lec tio n co d e
Use a 74151A multiplexer to Realizef(x1,x2,x3) = m(0,2,3,5)
Figure 4.30
Half Adders
H A
(a )
(b )
(c )
x i y i
x i y i
c i s i
c i s i
0011
0101
0001
0110
y i
x i
s i
c i
Figure 4.35 (a) -- (c)
Full Adders
(d )(e )
(f)
(g )
x i y i c i-1
00001111
00110011
01010101
00010111
01101001
c i s i
F A
x i y i
c i s i
c i-1
s i
c i
c i-1
y i
x i
c i-1
y i
x i
s i
Figure 4.35 (d) -- (g)
Ripple Carry Adder
y n-1 c 1x 1 y 1 c 0 x 0 y 0
z 1 z0
c n-1
zn-1
(e n d ca rry )
F A H A
c n-2x n-1
F A
zn
Figure 4.36
Addition Time for a Basic Ripple-Carry Adder
Let tgate = the propogation delay through a typical logic gate
Half adder propagation delays tadd = 3 tgate
tcarry = 2 tgate
Full adder propagation delaystadd = 3 tgate
tcarry = 2 tgate
Ripple-Carry Adder (n-bits) tadd = (n - 1)2 tgate + 3 tgate = (2n + 1) tgate
SN7482 Two-Bit Pseudo Parallel Adder Module
1 4 1 3 1 2 11 1 0 9 8
7654321
A 2 B 2 S 2 G N D N C N CC 2
A 2B 2 S 2
S 1A 1 B 1 C 0
(a )A 1 B 1S 1 V C C N C N CC 0
C 2
Package Pin Configuration
SN7482 Pseudo Parallel Adder -- Truth Table
A 2 A 1 C 2 S 2 S 1
LLLLLLLLHHHHHHHH
LLLLHHHHLLLLHHHH
LLHHLLHHLLHHLLHH
LHLHLHLHLHLHLHLH
LLLLLLLHLLHHLHHH
LLHHLHHLHHLLHLLH
LHLHHLHLLHLHHLHL
LLLHLLHHLHHHHHHH
LHHLHHLLHLLHLLHH
HLHLLHLHHLHLLHLH
B 2 B 1 C 2 S 2 S 1
W h en C 0 = HW h en C 0 = L
O u tp u tsIn p u ts
(b )
SN7482 Pseudo Parallel Adder -- Logic DiagramC 0
A 1
B 1
A 2
B 2
C 1
C 2
S 2
S 1
(c )
SN7482 Two-Bit Adder -- Logic Equations
C1 = C0A1 + C0B1 + A1B1 (4.20)
1 = C0C1 + A1C1 + B1C1 + A1B1C0 = C1(C0 + A1 + B1) + A1B1C0 = (C0+A1)(C0+B1)(A1+B1) (C0 +A1+B1) +A1B1C0 = (C0+ A1B1)(A1+B1)(C0 +A1+B1) +A1B1C0 (4.21) = [C0(A1+B1)+ C0A1B1](A1+B1)+A1B1C0 = C0A1B1+C0A1B1+C0A1B1+A1B1C0 = C0 A1 B1
Similarly
C2 = C1A2 + C1B2 + A2B2 (4.22)
2 = C1 A2 B2
Add Time for SN7482 Adder Circuits
SN7482 propagation delays
t1 = 5 tgate
tC1 = 2 tgate
t2 = 6 tgate
tC2 = 4 tgate
SN7482-based ripple-carry adder (n-bits)
tadd = (2n + 2) tgate
SN7483 Four-Bit Adder Module
1 6 1 5 1 4 1 3 1 2 11 1 0
7654321
9
8
B 4 S 4 C 4 G N DC 0
V C C
A 1B 1 S 1
A 3 S 2 A 2B 2S 3
(a )
B 3A 4
S 4 C 4 C 0 A 1B 1
A 3 S 2 B 2S 3 B 3
S 1
A 2A 4
B 4
Package Pin Configuration
SN7483 Four-Bit Adder Module -- Logic Diagram
B 4
S 4
C 4
A 4
B 3
A 3
B 2
A 2
B 1
A 1
C 0
P 4
S 3
C 3
P 3
S 2
C 2
P 2
S 1
C 1
P 1
C 0
(b )
SN7483 Four-Bit Adder -- Logic Equations
Pi = (BiAi)(Ai + Bi) = (Ai + Bi)(Ai + Bi) = Ai Bi (4.24)
i = Pi Ci-1 = Ai Bi Ci-1 (4.25)
C1 = [C0(A1B1) + (A1 + B1)] = [C0(A1B1)](A1 + B1) = (C0+(A1B1))(A1 + B1) = C0A1 + C0B1 + A1B1 (4.26)
Similarly
Ci = Ci-1Ai + Ci-1Bi + AiBi
Add Times for SN7483 Adder Circuits
SN7483 propagation delays
t1 = 3 tgate
t2 = t3 = t4 = 4 tgate tC1 = tC2 = tC3 = tC4 = 3 tgate
SN7483-based Ripple-Carry Adder (n-bits)
tadd = (3m + 1) tgate
where m = n/4.
Fully Parallel Three-Bit Adder c0 = x0y0 (4.30) s0 = x0 y0
c1 = x1y1c0’+x1y1c0+x1y1’c0+x1’y1c0
= x1y1+(x1y1)c0
= x1y1+(x1y1)(x0y0) (4.31)s1 = x1y1c0
= x1y1 x0y0
c2 = x2y2+(x2y2)c1
= x2y2+(x2y2)[x1y1+(x1y1)(x0y0)] = x2y2+(x2y2)(x1y1)+(x2y2)(x1y1)(x0y0) (4.32)s2 = x2y2c1
= x2y2[x1y1+(x1y1)(x0y0)]
Add Time for a Fully Parallel Adder
Assuming a three-level realization
tadd = 3 tgate
However, the fan in requirements become impractical as n increases.
Carry Look-Ahead Adders -- Basic Idea
Recall that ci = xiyi + xici-1 + yici-1
= xiyi + xiyici-1 + xiyici-1 + xiyici-1 + xi yici-1
= xiyi + xiyici-1 + xi yici-1
= xiyi + (xiyi + xi yi)ci-1
= xiyi + (xi yi)ci-1
Let gi = xiyi [carry generate] (4.33)
pi = xi yi [carry propagate] (4.34)
Then ci = gi + pi ci-1
si = pi ci-1 (4.38)
Carry Look-Ahead Adders -- Three-Bit Example
c0 = g0 (4.35)s0 = p0
c1 = g1 + p1c0
= g1 + p1g0 (4.36)s1 = p1 c0
c2 = g2 + p2c1
= g2 + p2(g1 + p1g0) = g2 + p2g1 + p2p1g0 (4.37)s2 = p2 c1
Carry Look-Ahead Adder Design
(a ) (b )
x i y i c i
g i p i s i
g 2 p 2 g 1 p 1 g 0
c 1 c 0
x 2 y 2
g 2 s 2
c 2 c 1 c 0
p 2 g 1 s1p 1 g 0 s 0
p 0
x 1 y 1 x 0 y 0 0
c 2
A d d er
C L A circu it
A d d er A d d er
(c)
Figure 4.39
Add Times for Carry Look-Ahead Adders
Adder modules
tg = tp = ts = tgate
CLA module
tc = 2 tgate
Overall
tadd = tgate + 2 tgate + tgate
= 4 tgate
Binary Subtraction Circuits
Recall that (R)2 = (P)2 - (Q)2
= (P)2 + (-Q)2
= (P)2 + [Q]2
= (P)2 + (Q)2 + 1
For an SN7483 adder
()2 = (A)2 + (B)2 + (C0)2 (4.39)
where = 4321, A = A4A3A2A1, and B = B4B3B2B1
If C0 = 0, A = P, and B = Q, then ()2 = (P)2 + (Q)2 .
If C0 = 1, A = P, and B = Q, then ()2 = (P)2 - (Q)2 .
Two’s Complement Adder/SubtracterQ = (q 3 q 2 q 1 q 0)2
P = (p 3 p 2 p 1 p 0) 2
4 A 3 A 2 A 1 B4 B 2 B3 BSG
C 0C 4
S e lec t
R = (r 4 r 3 r 2 r 1)2
R = P + Q
R = P + Q + 1
0
1
S elec t F u n c tio n
1 A
1 Y2 Y3 Y4 Y
A 4 A 3 A 2 A 1 B 4 B 3 B 2 B 1
S 4 S 3 S 2 S 1
M U X (7 4 1 5 7 )
A D D E R (7 4 8 3 )
Figure 4.41
Arithmetic Overflow Detection
an-1 bn-1 cn-2 cn-1 sn-1 V
0 0 0 0 0 00 0 1 0 1 10 1 0 0 1 00 1 1 1 0 01 0 0 0 1 01 0 1 1 0 01 1 0 1 0 11 1 1 1 1 0
Overflow Detection Circuits
(a )
(b )
F A
a n -1 b n -1 a n -2 b n -2
c n -2c n -1
s n -1 s n -2
V
c n -3F A
F A
a n -1 b n -1 a n -2 b n -2
c n -2
c n -1
s n -1 s n -2
V
c n -3F A
Figure 4.42
T o p lev e l
L ev e l 2
L ev e l3
L ev e l4
B 11S en so rA
B 12S en so rB
B 21A +B
B 22A ÐB
B 23M in (A ,
B )
B 24M ax (A ,
B )
B 2 31C o m p areA &B
B 2 32S e lect
M in
B 2 41C o m p a reA &B
B 2 42S e lectM ax
(a )
*
* = L ea fn o d e
BD a ta acq u is itio n
sy stem
B 1In p u t sen so r d a ta
B 2C o m p u te v a lu es
B 3S e lec t o u tp u t
* **
** **
*
(b )
S en so rs
F u n c tionse lect
B 3O u tp u tse lec t
BP ro cess co n tro lsy s tem
B 1 ÐIn p u t B 2 Ð
C o m p u ta tio n
O u tp u t
B 11C o n v e rtA
B 12C o n v e rtB
B 21B in a ryad d er
B 22B in arysu b trac tor
B 2 31C o m p are
B 2 32S e lect
A
s1
B
s2
B 23
M in im u m
B 2 41C o m p are
B 2 42S e lect
B 24M ax im u
m
L S B
M S B
D eco d e rn - to -2 n
x 0
x 1
y 0
y 1
x n-1y 2n -1
Decoders
m 0
m 1
m 2
m 3
(a ) (b )
(c )
L S B A
M S B Bm 0
m 1
m 2
m 3
m 1
m 0
m 2
m 3
L S B A
M S B B
L S B A
M S B B
Decoder Realization
C AB
(a )
(b )
(c )
m 0 = C B A
m 1 = C B A
m 2 = C B A
m 3 = C B A
m 5 = C B A
m 4 = C B A
m 6 = C B A
m 7 = C B A
B
BA
A
m 0
m 1
m 2
m 3
m 4
m 5
m 6
m 7
C
D
ABL S B
M S B
k0
k1
k2
k3
m 0
m 4
m 8
m 1 2
2 -to -4
A
AA
A
A
AB
B
C
C
m 1
m 5
m 9
m 1 3
m 2
m 6
m 1 0
m 1 4
m 3
m 7
m 11
m 1 5
l0 l3l1
l2
2 -to -4
More complex decoders
P
X
Q
(a ) (b )
A
B
C f(Q , X , P )
0
1
2
3
4
5
6
7
P
X
Q
A
B
C f(Q , X , P )
0
1
2
3
4
5
6
7
Example 4.1 -- Realize f(Q,X,P) = m(0,1,4,6,7) = M(2,3,5)
(c ) (d )
f(Q , X , P )
A
B
C f(Q , X , P )
0
1
2
3
4
5
6
7
P
X
Q
A
B
C
0
1
2
3
4
5
6
7
P
X
Q
Example 4.1 (concluded)
(a ) (b )
x 0
x 1
y 0
y 1
y 2
y 3
x 0
x 1
y 2
E
Ey 3
y 0
y 1
I0
I1
I2
y 2
y 3
y 0
y 1
E
x 0
x 1
O 0
O 1
O 2
O 3
O 4
O 5
O 6
O 7
E
x 0
x 1
y 2
y 3
y 0
y 1
y 2
y 3
y 0
y 1
E
x 0
x 1
O 8
O 9
O 1 0
O 11
O 1 2
O 1 3
O 1 4
O 1 5
E
x 0
x 1
y 2
y 3
y 0
y 1
I0
I1
y 2
y 3
y 0
y 1
E
x 0
x 1
O 0
O 1
O 2
O 3
O 4
O 5
O 6
O 7
E
x 0
x 1
y 2
y 3
y 0
y 1
E
x 0
x 1
y 2
y 3
y 0
y 1
I2
I3
1
(a ) (b )
1 6 1 5 1 4 1 3 1 2 1 1 1 0 9
(a )
G 1
A
B
C
(1 )
(2 )
(3 )
(4 )
(5 )
(6 )
G 2 AG 2 B
(1 5 )
(1 4 )
(1 3 )
(1 2 )
(1 1 )
(1 0 )
(9 )
(7 )
Y 0
Y 1
Y 2
Y 3
Y 4
Y 5
Y 6
Y 7
ABC
G 1G 2AG 2B
01234567
HHHHHHHHL
LLLLLLLLH´
LLLLHHHH
LLHHLLHH
LHLHLHLH
LHHHHHHHHH
HLHHHHHHHH
HHLHHHHHHH
HHHLHHHHHH
HHHHLHHHHH
HHHHHLHHHH
HHHHHHLHHH
HHHHH
HHLHH
E n ab le
S e lect
O u tp u ts
G 1G 2* ABC Y 0 Y 1 Y 2 Y 3 Y 4 Y 5 Y 6 Y 7
In p u ts
(c)
S e lect
E n ab le
B
V cc Y 0 Y 1 Y 2 Y 3 Y 4 Y 5
A CG 2B
G 2A G 1
7654321
Y 7O u tp ut
Y 6
8
G N D
Y 0 Y 1 Y 2 Y 3 Y 4 Y 5
Y 6
B CG 2A
G 2B G 1 Y 7
A
D atao u tp u ts
(b)
(d)
(e)
123
01234567
(1 )(2 )(3 )
(6 )(4 )(5 )
'1 3 8B IN /O C T
EN
A
B
C
G 1G 2
AG 2
B
&
(1 5 )(1 4
)
(1 3 )(1 2 )(1 1 )(1 0 )
(9 )(7 )
Y 0Y 1Y 2Y 3Y 4Y 5Y 6Y 7
G 2 * = G 2 A +G 2 B
7654321 8
(b )
1 29 1 0 1 1
O u tp u tsG N D
V C CIn p u ts O u tp u ts
(a )
0
1
2
3
4
5
6
7
8
9
1 0
1 1
1 2
1 3
1 4
1 5
G 1G 2
A
B
C
D
2 4 2 3 2 2 2 1 2 0 1 9 1 8 1 7 1 6 1 5 1 4 1 3
A B C D G 2 1 2
1 1
1 2 3 4 5 1 0
0
G 1 1 5 1 4 1 3
6 7 8 9
A B C DA B C D
O u tp u tsG 1 G 2 BCD A 0 1 2 3 4 5 6
In p u ts
(c)
LLLLLLLLLLLLLLLLHL
H
LLLLLLLLLLLLLLLLLHH
LLLLLLLLHHHHHHHH
LLLLHHHHLLLLHHHH´
LLHHLLHHLLHHLLHH´
LHLHLHLHLHLHLHLH´
LHHHHHHHHHHHHHHHHHH
HLHHHHHHHHHHHHHHHHH
HHLHHHHHHHHHHHHHHHH
HHHLHHHHHHHHHHHHHHH
HHHHLHHHHHHHHHHHHHH
HHHHHLHHHHHHHHHHHHH
HHHHHHLHHHHHHHHHHHH
HHHHHHHLHHHHHHHHHHH
HHHHHHHHLHHHHHHHHHH
HHHHHHHHHLHHHHHHHHH
HHHHHHHHHHLHHHHHHHH
HHHHHHHHHHHLHHHHHHH
HHHHHHHHHHHHLHHHHHH
HHHHHHHHHHHHHLHHHHH
HHHHHHHHHHHHHHLHHHH
HHHHHHHHHHHHHHHLHHH
7 8 9 1 0 1 1 1 2 1 3 1 4 1 5
A
B
C
D
G 1
G 2
0123456789
1 01 11 21 31 41 5
(d ) (e)
1
2
4
8
(2 3 )
(2 2 )
(2 1 )
(2 0 )
'154B IN /O C T
E N
A
B
C
D
G 1
G 2
&
(1 )(2 )(3 )(4 )(5 )(6 )(7 )(8 )(9 )
(1 0 )(1 1 )(1 3 )(1 4 )(1 5 )(1 6 )(1 7 )
01234567891 01 11 21 31 41 5
'154
(1 8 )
(1 9 )
0123456789
1 01 11 21 31 41 5
É
n -B it a d d re ss
S = se le c t d e v ic e
D e v ice a c ce ssco n tro l sig n a l
A 0
A 1
A n Ð 1
x 0
x 1
x n Ð 1
E
y 0
y 1
y 2 n Ð 1
S D e v ice 0
S D e v ice 1
S D e v ice 2 n Ð 1
É É
ABCD
G 1G 2
0123456789
1 01 11 21 31 41 5
4
56
8
7 4 2 0 /2
f2 = P M (6 , 9 )
f1 = å m (1 , 9 , 1 2 , 1 5 )
7 4 1 5 4
2 3
2 2
2 1
2 0
1 8
1 9
2
7
1 0
1 4
1 7
7 4 0 8 /4
91 01 21 3
Z
Y
X
W
B C Din p u t
D e cim a lo u tp u ts
(a ) (b )
B C D c o d eD C B A D e cim a l d ig its
0 0 0 00 0 0 10 0 1 00 0 1 10 1 0 00 1 0 10 1 1 00 1 1 11 0 0 01 0 0 1
0123456789
D
C
B
A
0
1
2
3
4
5
6
7
8
9
B AD C
1
0 0 0 1 1 1 1 00 4 12 8
1 5 13 9
3 7 15 11
2 6 14 1 0
0 0
0 1
1 1
1 0
C
A
D
B
(a )
B AD C
0 0 0 1 1 1 1 00 4 1 2 8
1 5 1 3 9
3 7 1 5 11
2 6 1 4 1 0
0 0
0 1
1 1
1 0
C
A
D
B
(b )
B AD C
1
0 0 0 1 1 1 1 00 4 1 2 8
1 5 1 3 9
3 7 1 5 11
2 6 1 4 1 0
0 0
0 1
1 1
1 0
C
A
d
d
d d
d d
d
d
d d
d d
d
d
d d
d d
D
B
(c )
1 1
f
(a ) (b )
Ð +a
f
b
g
e
c
d
g
d
a
b
ec
C o m m o na n o d e
f
a
f
b
g
e
c
d
g
d
a
b
ec
C o m m o nca th o d e
+ Ð
C DA B
0 0 0 1 1 1 1 00 4 1 2 8
1 5 1 3 9
3 7 1 5 11
2 6 1 4 1 0
0 0
0 1
1 1
1 0
B
D
A
C
(a )
1 1
1 0
1
1
1 0
0 1
C DA B
0 0 0 1 1 1 1 00 4 1 2 8
1 5 1 3 9
3 7 1 5 11
2 6 1 4 1 0
0 0
0 1
1 1
1 0
B
D
A
C
(b )
1 1
1 0
1
d d
d d
d
d
d d
d d
d
d 1
1 1
1 0
A 0
0 4 1 2 8
1 5 1 3 9
3 7 1 5 11
2 6 1 4 1 0
X 2
X 0
X 3
X 1
(c )
1
10
0
d d
d d
d d
d
d
d d
d
d
A 1
0 4 1 2 8
1 5 1 3 9
3 7 1 5 11
2 6 1 4 1 0
x 2
x 0
x 3
x 1
0
11
0
d d
d d
d d
d
d
d d
d
d
4 -to -2E n co d e r
(a )
(b )
(d )
A 1 = X 2 + X 3
A 0 = X 1 + X 3
X 3 X 2 X 1 X 0 A 1 A 0
0000000011111111
0000111100001111
0011001100110011
0101010101010101
d00d1ddd1ddddddd
d01d0ddd1ddddddd
X 0
X 1
X 2
X 3
A 0
A 1
X 1
X 3
X 2
X 3
A 0
A 1
A 1
0 4 1 2 8
1 5 1 3 9
3 7 1 5 11
2 6 1 4 1 0
x 3
x 1
x 4
x 2
(c )
1
1
A 0
0 4 1 2 8
1 5 1 3 9
3 7 1 5 11
2 6 1 4 1 0
x 3
x 1
x 4
x 2
1
14 -to -3
E n c o d e r
(a )
(b )
X 4 X 3 X 2 X 1 A 2 A 1
0000000011111111
0000111100001111
0011001100110011
0101010101010101
0000000010000000
0010100000000000
x 1
x 2
x 3
x 4
A 0
A 1
A 2
0100100000000000
A 0
A 2
0 4 1 2 8
1 5 1 3 9
3 7 1 5 11
2 6 1 4 1 0
x 3
x 1
x 4
x 2
1
(d )
A 0
x 3x 2
x 1
x 4
A 1
A 2
x 2x 1
x 3x 4
x 3x 2
x 1
x 4
x 2x 1
x 3x 4
x 3x 2
x 1
x 4
A 0
0 0 0 1 1 1 1 00 4 1 2 8
1 5 1 3 9
3 7 1 5 11
2 6 1 4 1 0
0 0
0 1
1 1
1 0
x 2
x 0
x 3
x 1
(c )
1
1
1 1
1 1
1
1
1 1
A 1
0 4 1 2 8
1 5 1 3 9
3 7 1 5 11
2 6 1 4 1 0
x 2
x 0
x 3
x 1
11
1 1
1 1
1
1
1
1 11
4 -to -2P r io r ityen co d er
(a )
(b )
(d )
A 1 = X 2 + X 3
X 3 X 2 X 1 X 0 A 1 A 0
0000000011111111
0000111100001111
0011001100110011
0101010101010101
0000111111111111
0011000011111111
x 0
x 1
x 2
x 3
A 0
A 1
A 0 = X 3 + X 1 X 2
G SE O
G S E O
0111111111111111
1000000000000000
I n p u ts O u tp u ts
x 0
x 1
x 2
x 3A 0
G S
E O
A 1x 2
54 6 87 C
7654321
B
8
G N D
In p u ts O u tp u ts
V cc 3 1 9
In p u ts
N C 2O u tp u ts
AO u tp u t
D
1 6 1 5 1 4 1 3 1 2 1 1 1 0 9
D 3 2 1 9
A
5 6 7 8 C B
4
(c )
HL
HLH
HLHH
HLHHH
HLHHHH
HLHHHHH
LLHHHHHHH
HHHLLLLHHH
HHHLLHHLLH
HLHHHHHH
HLHHHHHHH
LHHHHHHHH
HLHLHLHLHL
1 2 3 4 5 6 7 8 9 D C B A
In p u ts O u tp u ts
(b )
(a )
4
5
6
7
8
9
A
B
C
D
1
2
3
54 6 E 17 A 2
7654321
A 1
8
G N D
(c )In p u ts O u tp u ts
V cc 3 1 0
1 6 1 5 1 4 1 3 1 2 1 1 1 0 9
In p u ts
E O 2O u tp u t
A 0G S
G S 3 2 1 0
A 0
5 6 7 E l A 2 A 1
4
E O
LLLLLLLLL
L
HLH
HLHH
HLHHH
HLHHHH
HHLLLLHHHH
HHLLHHLLHH
HHLHLHLHLH
HLHHHHH
HLHHHHHH
HLHHHHHHH
HHLLLLLLLL
E I 0 1 2 3 4 5 6 7 A 2 A 1 A 0 G S
In p u ts O u tp u ts
(b )
(a )
4
5
6
7
E l
A 0
A 1
A 2
1
2
3
HLHHHHHHHH
E O
0
G S
E O
O u tp u ts
A in
B in
K in
S W 1 S W 2
(a )
(b )
S in g lech a n n e l
A o u t
B o u t
K o u t
B o u t
K o u t
A o u t
a
b
k
M u ltip le x e r D e m u ltip le x e r
A in
B in
K in
a
b
k
S in g lech a n n e l
ÉÉ
K-Channel multiplexing/demultiplexing
Figure 4.22
(a )
Y4 -to -1
M u ltip le x e r
Y
B A
B
0011
A
0101
(b )
(c )
0 1 2 3
2 -to -4D e co d e r
D 0
D 1
D 2
D 3
Y
D 0D 1D 2D 3
D 0
D 1
D 2
D 3
B A
Y
(d )
D 0
D 1
D 2
D 3
B A
S elec t io n co d e
Four-to-one multiplexer design
Y
B A
I0
I1
I2
I3
D 0
D 1
D 2
D 3
Y
B A
I4
I5
I6
I7
D 0
D 1
D 2
D 3
Y
B A
I8
I9
I1 0
I11
D 0
D 1
D 2
D 3
Y
B A
I1 2
I1 3
I1 4
I1 5
D 0
D 1
D 2
D 3
Y
B A
D 0
D 1
D 2
D 3
In p u tlin e s
F irs tle v e l
O u tp u t lin e
S e co n dle v e l
S 3 S 2
S e le c tio n c o d e(h ig h er -o rd er b its)
Z
S 1 S 0
S elec tio n c o d e(lo w er-o rd e r b its)
V cc 5 6 A B
D a ta se le c tD a ta in p u ts
4 7 C
1 6 1 5 1 4 1 3 1 2 1 1 1 0 9
23 1 Y0 W
7654321
S tro b eG
8
G N D
(a )
D a ta in p u ts O u tp u ts
(d )
'1 5 1 A
0
1
2
3
4
5
6
7
G ABC
Y
W
'1 5 1 A
E N
0
2
0
1
2
3
4
5
6
7
G 07
(7 )
(1 1 )
(1 0 )
(9 )
(4 )
(3 )
(2 )
(1 )
(1 5 )
(1 4 )
(1 3 )
(1 2 )
(e )
(5 )
(6 )Y
W
G
A
B
C Ê
D 0
D 1
D 2
D 3
D 4
D 5
D 6
D 7
S tro b e
In p u ts O u tp u ts
S e lec t
C GAB´LLHHLLHH
´LHLHLHLH
HLLLLLLLL
LD 0D 1D 2D 3D 4D 5D 6D 7
Y WH
D 0D 1D 2D 3D 4D 5D 6D 7
´LLLLHHHH
(b )
D 4 D 5 D 6 D 7 A B
C
D 2 D 1 D 0 Y W S
D 3
O u tp u t YO u tp u t W
GS tro b een a b le
CA BA B C
D 0
D 1
D 2
D 3
D 4
D 5
D 6
D 7
(c )
A
B
C
(c )
´LLLLLLLLHHHHHHHH
´LLLLHHHHLLLLHHHH
´LLHHLLHHLLHHLLHH
´LHLHLHLHLHLHLHLH
HLLLLLLLLLLLLLLLL
D C B A
In p u ts
(b )
G W
HE 0E 1E 2E 3E 4E 5E 6E 7E 8E 9
E 1 0E 1 1E 1 2E 1 3E 1 4E 1 5
S e lec t S tro b e O u tp u t
G 1
D
C
B
A
S tr o b ee n a b le
O u tp u t
AA B C
W
E 0
E 1
E 2
E 3
E 4
E 5
E 6
E 7
E 8
E 9
E 1 0
E 1 1
E 1 2
E 1 3
E 1 4
E 1 5
DB C D
V C C
2 4 2 3 2 2 2 1 2 0 1 9 1 8
7654321 8
D a ta In p u ts
(a )
1 7 1 6 1 5 1 4 1 3
1 29 1 0 1 1
E 8 E 9 E 1 0 E 1 1 E 1 2 B
C
E 6 E 5 E 4 E 3 E 2 D
E 7
E 1 3 E 1 4 E 1 5 A
E 1 E 0 S W
D a ta se lec t
D a ta in p u tsG N D
8 9 1 0 1 1 1 2 1 3 1 4 1 5 A B C
7 6 5 4 3 2 1 0 WO u t-p u t
DD a tase lec t
S tro b eG
(d ) (e )
'1 5 0
W
'1 5 0
G
D C B A
E 0E 1E 2E 3E 4E 5E 6E 7E 8E 9
E 1 0E 1 1E 1 2E 1 3E 1 4E 1 5
01234567891 01 11 21 31 41 5
E 0
E 1E 2
E 3E 4
E 5
E 6E 7
E 8
E 9E 1 0
E 1 1E 1 2
E 1 3
E 1 4E 1 5
G
ABCD
E N
0
3
G 01 5
W
(9 )
(1 5 )(1 4 )(1 3 )(1 1 )
(8 )(7 )(6 )(5 )(4 )(3 )(2 )(1 )(2 3 )(2 2 )(2 1 )(2 0 )(1 9 )(1 8 )(1 7 )(1 6 )
(1 0 )
'153
1 G
1 C 01 C 11 C 21 C 3
2 G
2 C 02 C 12 C 22 C 3
(1 )(6 )(5 )(4 )(3 )
(1 5 )(1 0 )(1 1 )(1 2 )(1 3 )
(4 )
(7 )
(e )
(1 4 )
(2 )B
M U X
A
1 Y
2 Y
E N
0
1
2
3
0
1G 0
3
1 Y
2 Y
O u tp u tp a ir
A (L S B )B
P a ir 0
P a ir 1
P a ir 2
P a ir 3
S e lec tio n c o d eP o sitio n
1 C 0
2 C 0
1 C 1
2 C 1
1 C 2
2 C 2
1 C 3
2 C 3
(b )
0
1
2
3
S e le c tio n c o d e(B A )2
(a )
1 Y
2 Y
(c)
Y
B A
C 0
C 1
C 2
C 3
2
2
2
2
2
2
S tr o n g(e n a b le )
D a ta 1
D a ta 2
S e le ct
O u tp u t1 Y
S tr o b e(e n a b le )
1 G
B
A
O u tp u t2 Y
1 C 0
1 C 1
1 C 2
1 C 3
2 C 0
2 C 1
2 C 2
2 C 3
2 G (d )
1 C 02 C 0
1 C 12 C 1
1 C 22 C 2
1 C 32 C 3
1 AS e le ct 1 B 2 A1 CO u tp u t
2 B
7654321
2 YO u tp u t
8
G N D
In p u ts In p u ts
V cc S tro b e 4 Z A 4 BO u tp u t
4 Y 3 A 3 B
1 6 1 5 1 4 1 3 1 2 1 1 1 0 9
In p u tsIn p u tsO u tp u t
3 Y
G 4 A 4 B 4 Y 3 A 3 B
3 Y
1 A 1 B 1 Y 2 A 2 B 2 Y
S
(a )
In p u ts O u tp u t
D a taS tro b eG
S e le c tS
HLLLL
´LLHH
´LH
´´
LH
LLHLH
A B Y
(b )
'157
1 A1 B2 A2 B3 A3 B4 A4 B
(2 )(3 )(5 )(6 )
(1 1 )(1 0 )(1 4 )(1 3 )
(4 )
(7 )
(9 )
(1 2 )
1 Y
2 Y
3 Y
4 Y
(d )
(1 5 )
(1 )A /B
E N
M U X
G 1
1
1
G
S tr o b e GS e le c t S
(c )
1 Y
2 Y
3 Y
4 Y
1 A
1 B
2 A
2 B
3 A
3 B
4 A
4 B
1 AS e le ct 1 B 2 A1 CO u tp u t
2 B
7654321
2 YO u tp u t
8
G N D
In p u ts In p u ts
V cc S tro b e 4 Z A 4 BO u tp u t
4 Y 3 A 3 B
1 6 1 5 1 4 1 3 1 2 1 1 1 0 9
In p u tsIn p u tsO u tp u t
3 Y
G 4 A 4 B 4 Y 3 A 3 B
3 Y
1 A 1 B 1 Y 2 A 2 B 2 Y
S
(a )
In p u ts O u tp u t
D a taS tro b eG
S e le c tS
HLLLL
´LLHH
´LH
´´
LH
LLHLH
A B Y
(b )
'157
1 A1 B2 A2 B3 A3 B4 A4 B
(2 )(3 )(5 )(6 )
(1 1 )(1 0 )(1 4 )(1 3 )
(4 )
(7 )
(9 )
(1 2 )
1 Y
2 Y
3 Y
4 Y
(d )
(1 5 )
(1 )A /B
E N
M U X
G 1
1
1
G
S tr o b e GS e le c t S
(c )
1 Y
2 Y
3 Y
4 Y
1 A
1 B
2 A
2 B
3 A
3 B
4 A
4 B
(b )
4
S o u r c e XD 7 Ð D 0
S o u r c e WD 7 Ð D 0
0
D 7 Ð D 4 D 3 Ð D 0
4 A Ð 1 A 4 B Ð 1 B
4 Y Ð 1 Y
G
S
S e lec t0 = X1 = W
D 7 Ð D 0D estin a tio n
7 4 1 5 7
S o u r c e MD 3 Ð D 0
S o u r c e ND 3 Ð D 0
D 0D 1D 2D 3
4 Y 3 Y 2 Y 1 Y
S 0 S 1
S 0 S 1 S o u rc e0011
0101
MNOP
4 A Ð 1 A 4 B Ð 1 BG
S7 4 1 5 7
S o u r c e OD 3 Ð D 0
S o u r c e PD 3 Ð D 0
4 Y 3 Y 2 Y 1 Y
444
(a )
4
4 A Ð 1 A 4 B Ð 1 BG
S7 4 1 5 7
4 A Ð 1 A 4 B Ð 1 BG
S7 4 1 5 7
444
0
88 D 3 Ð D 0
D 7 Ð D 4
8
44
4 Y Ð 1 Y
D 7 Ð D 4 D 3 Ð D 0
D estin a tio n
(a )
(b )
V C C
C AB Yfx 1 x 3x 2
x 1 x 3x 2
01234567
00001111
00110011
01010101
10110100
D 0 = 1D 1 = 0D 2 = 1D 3 = 1D 4 = 0D 5 = 1D 6 = 0D 7 = 0
C B A
YW
7 4 1 5 1 A
f(x 1 , x 2, x 3)
i D 0D 1D 2D 3D 4D 5D 6D 7G
S e lec tio n co d e
Use a 74151A multiplexer to Realizef(x1,x2,x3) = m(0,2,3,5)
Figure 4.30
(c )
(d )
0011
0101
M U X In p u ts
S e le c tio n c o d e
D 0D 1D 2
D 3
AB
Yf(a , b , c ) f(a , b , c )
01aa
D 0 = 0D 1 = 1D 2 = aD 3 = a
b c
01aa
b c
(a )
(b )
0011
0101
M U X In p u ts
S e le c tio n c o d e
D 0D 1D 2
D 3
AB
Yf(a , b , c ) f(a , b , c )
c0c1
D 0 = cD 1 = 0D 2 = cD 3 = 1
a b
c0c1
a b
(a ) (b )
C B A Y
i fX 1 X 2 X 3 X 4
0000000011111111
0000111100001111
0011001100110011
0101010101010101
1111100001000111
D 0 = 1
D 1 = 1
D 2 = X 4
D 3 = 0
D 4 = X 4
D 5 = 0
D 6 = X 4
D 7 = 1 S e lec tio n co d e
YW
D 0
D 1
D 2
D 3
D 4
D 5
D 6
D 7G
C B A
V CC
f(x 1 , x 2 , x 3 , x 4 )
x 1 x 2 x 3
7 4 1 5 1 A
x 4
0
1
2
3
4
5
6
7
1
1
X 4
0
X 4
0
X 4
1
f
Y 0
Y 1
Y 2
Y 3
Y n Ð 1
Y 0
Y 1
m 0 m 1 m 2 m 3
AB
DE
(a )(b )
In p u t
E n a b le
S e lec tio nco d e
2 -to -4D e c o d e r
1 2 É
1 -to -nD e m u lt ip le x e r
S
In p u tÉ O u tp u ts
S e lec tio nco d e
1 6 lin e s
5 l in e s
S in g le d a tach a n n e l (Q )
2 32 22 12 0
1 9
1 8
1 0Y
G 1
G 2
D C AB
E 0E 1E 2E 3E 4E 5E 6E 7
E 8E 9E 1 0E 11E 1 2
E 1 3E 1 4E 1 5G
C 3C 2C 1C 0
x 0
x 1
x 2
x 3
x 4
x 5
x 6
x 7
x 8
x 9
x 1 0
x 11
x 1 2
x 1 3
x 1 4
x 1 5
0123456789
1 01 11 21 31 41 5
1234567891 01 11 31 41 51 61 7
D e c o d e r / d e m u lt ip le x e rM u lt ip le x e r
7 4 1 5 47 4 1 5 0x 0x 1x 2x 3x 4x 5x 6x 7x 8x 9
x 1 0
x 11x 1 2x 1 3
x 1 4x 1 5
D C AB
1 51 41 31 1
876543212 32 22 12 01 91 81 71 69
1 4 1 3 1 2 11 1 0 9 8
7654321
A 2 B 2 S 2 G N D N C N CC 2
A 2B 2 S 2
S 1A 1 B 1 C 0
(a )
A 2 A 1 C 2 S 2 S 1
C 0
A 1
B 1
A 2
B 2
C 1
C 2
LLLLLLLLHHHHHHHH
LLLLHHHHLLLLHHHH
LLHHLLHHLLHHLLHH
LHLHLHLHLHLHLHLH
LLLLLLLHLLHHLHHH
LLHHLHHLHHLLHLLH
LHLHHLHLLHLHHLHL
LLLHLLHHLHHHHHHH
LHHLHHLLHLLHLLHH
HLHLLHLHHLHLLHLH
S 2
S 1
A 1 B 1S 1 V C C N C N CC 0
C 2
B 2 B 1 C 2 S 2 S 1
W h en C 0 = HW h en C 0 = L
O u tp u tsIn pu ts
(b )
(c )
1 6 1 5 1 4 1 3 1 2 1 1 1 0
7654321
9
8
B 4 S 4 C 4 G N DC 0
V C C
A 1B 1 S 1
A 3 S 2 A 2B 2S 3
(a)
B 3A 4
S 4 C 4 C 0 A 1B 1
A 3 S 2 B 2S 3 B 3
S 1
A 2A 4
B 4
B 4
S 4
C 4
A 4
B 3
A 3
B 2
A 2
B 1
A 1
C 0
P 4
S 3
C 3
P 3
S 2
C 2
P 2
S 1
C 1
P 1
C 0
(b )
(a ) (b )
(c )
x i y i ci
g i p i si
g 2 p 2 g 1 p 1 g 0
c 1 c 0
x 2 y2
g 2s2
c 2 c 1 c 0
p 2 g 1s1
p 1 g 0s0
p 0
x 1 y1 x 0 y0 0
c 2
A d d er
C L A c ircu it
A d d er A d der
V cc
1 6 1 5 1 4 1 3 1 2 1 1 1 0
7654321
9
8
G N D
In p u ts O u tp u ts
P 2 G 2 C n C n + x C n + y G C n + z
G 1 P 1 G 0 P 0 G 3 P 3
(a )
(b )
(e)
(c )
(f)
In p u ts O u tp u t
G 0 P 0 C n C n + x
L
L
H
HH
LA ll o th er
co m b in a tion s
P 2
C n C n + z
L
L
L
L
LL
LL
´L
L
L
LL
H
HHHL
L
L
L
H
P
In pu ts O u tp u t
P 2 G 2 C n C n + x C n + y G
P 1 G 0 P 0 G 3 P 3 P
G 1 C n + z
In p u ts O u tp u t
A ll o th er co m b in a tio n s
P 1P 3G 3 G 2 G 1 G 0
LLLLH
G
P 0
L
In p u ts O u tp u t
A ll o th er co m b in a tio n s
P 1G 0G 1 C n + y
P 2
In p u ts O u tp u t
A ll o th er co m b in a tio n s
P 1 P 0G 2 G 1 G 0
HHHHL
LL
´L
L
P 2
In pu ts O u tp u t
A ll o th ercom b in a tio n s
P 1 P 0
H
PP 3
L L L L
(d )
C n
P o r X
G o r Y
P 3 or X 3G 3 or Y 3
P 2 or X 2G 2 or Y 2
P 1 or X 1G 1 or Y 1
P 0 or X 0G 0 or Y 0
C n or C n
(g )
C n+ zorC n+ z
C n+ yorC n+ y
C n+ xorC n+ x
Q = (q 3 q 2 q 1 q 0 )2
P = (p 3 p 2 p 1 p 0 )2
4 A 3 A 2 A 1 B4 B 2 B3 BSG
C 0C 4
S elec t
R = (S 4 S 3 S 2 S 1 )2
R = P + Q
R = P + Q + 1
0
1
S elec t Fu n c tion
1 A
1 Y2 Y3 Y4 Y
A 4 A 3 A 2 A 1 B 4 B 3 B 2 B 1
S 4 S 3 S 2 S 1
M U X (7 4 1 5 7 )
A D D E R (7 4 8 3 )
(a )
(b )
F A
a nÐ 1 b nÐ 1 a n Ð 2 b n Ð 2
c nÐ 2cn Ð 1
sn Ð 1 sn Ð 2
V
cn Ð 3F A É
F A
a n Ð 1 b n Ð 1 a n Ð 2 bn Ð 2
c n Ð 2
c n Ð 1
sn Ð 1 sn Ð 2
V
c nÐ 3F A É
0 4 1 2 8
1 5 1 3 9
3 7 1 5 1 1
2 6 1 4 1 0
1
1 1 1
1 1
A
B
2
M agn itu d ecom p ara to r
f1 , A < B
f2 , A = B
f3 , A > B
i A 1 A 0
0123456789
1 01 11 21 31 41 5
0000000011111111
0000111100001111
0011001100110011
0101010101010101
0111001100010000
1000010000100001
0000100011001110
f1 , A < B
B 1
A 1
A 0
B 0
0 4 1 2 8
1 5 1 3 9
3 7 1 5 1 1
2 6 1 4 1 0
f2 , A = B
B 1
A 1
A 0
B 0
0 4 1 2 8
1 5 1 3 9
3 7 1 5 1 1
2 6 1 4 1 0
1
f3 , A > B
B 1
A 1
A 0
B 0
1
1
1
1
11
1 1
1
2
B 1 B 0 f1 f2 f3
(a )
(b )
(c )
A 1
B 1
A 0
B 0
f1
f3
f2
V cc
1 6 1 5 1 4 1 3 1 2 11 1 0
7654321
9
8
G N D
D a ta in p u ts
A 3 B 2 A 2 B 1A 1 B 0
B 3
A 0
(a )
A < BIn
A = BIn
A > BIn
A < BO u t
A = BO u t
A > BO u t
C asca d e in p u ts C asca d e ou tp u ts
A < BIn
A = BIn
A > BIn
A < BO u t
A = BO u t
A > BO u t
A 3 B 2 A 2 B 1A 1 A 0
B 3 B 0
D atain p u t
(b )
A > B A < B A = B
C om p a rin gin p u ts
C asca d in gin p u ts O u tp u ts
A 3 , B 3 A 2 , B 2 A 1 , B 1 A 0 , B 0 ´
A 2 > B 2A 2 < B 2A 2 = B 2A 2 = B 2A 2 = B 2A 2 = B 2A 2 = B 2A 2 = B 2A 2 = B 2A 2 = B 2A 2 = B 2A 2 = B 2
A 3 > B 3A 3 < B 3A 3 = B 3A 3 = B 3A 3 = B 3A 3 = B 3A 3 = B 3A 3 = B 3A 3 = B 3A 3 = B 3A 3 = B 3A 3 = B 3A 3 = B 3A 3 = B 3
´´
A 1 > B 1A 1 < B 1A 1 = B 1A 1 = B 1A 1 = B 1A 1 = B 1A 1 = B 1A 1 = B 1A 1 = B 1A 1 = B 1
´
´
A 0 > B 0A 0 < B 0A 0 = B 0A 0 = B 0A 0 = B 0A 0 = B 0A 0 = B 0A 0 = B 0
HLLHL
LHLHL
LLHLL
HLHLHLHLHLLLLH
LHLHLHLHLHLLLH
LLLLLLLLLLHHLL
A > B A < B A = B
B 1A 1
B 0A 0
(c)
A 3B 3
B 2A 2
A < B
A = B
A > B
A < B
A = B
A > B
4
C ascad ein p u ts
D ata
A < B
A = BA > B
A
f2 f1f3
0 1 0
7 4 8 5
C ascad ed in p u ts
A < B
A = BA > B
C ircu itou tp u ts
c 2 c 1c 3
B 1
B 0
B 2
B 3
A 1
A 0
A 2
A 3
(a )
(b )
f2 f1f3
c 2 c 1c 3
B 5
B 4
B 6
B 7
A 5
A 4
A 6
A 7
7 4 8 5
f2 f1f3
c 2 c 1c 3
B 9
B 8
B 1 0
B 1 1
A 9
A 8
A 1 0
A 1 1
7 4 8 5
f2
f1
f3
c 2 c 1c 3
B 1 3
B 1 2
B 1 4
B 1 5
A 1 3
A 1 2
A 1 4
A 1 5
7 4 8 5
C ascad ed in p u ts
C ascad ed in p u ts
A < BA = BA > B
f2
f1
f3
c 2
c 1
c 3
7 4 8 5
4BD ata
A L UC -G E N
C i
a i b i
fi
C iÐ 1
S 2S 1S 0
C n Ð 1
b n Ð 1an Ð 1
C n Ð 2
fn Ð 1 f1 f0
a 1 b 1 a 0 b 0
C 0C 1 C Ð 1
(a )
(b )
A LUA L U
A L U S 2
S 1S 0
LU A U
M U X
x y
f
s
y
a i b i
C iÐ 1
C i
S 2
S 1
S 0
c o ut
c in
fL U i fA U i
f
x y
fi
x 1 x 0
s
y
x 1 x 0
(a) (b)
(c)
(d)
MUX
x y
x 1x 0 x2 x 3
s1
s0
S 1 S 0
f
S 1
S 0
x y
x AND y
x OR y
NOT x
x XOR y
F LU
0000000011111111
0000111100001111
0011001100110011
0101010101010101
x y
s1
s0
0001011111000110
y
f
xys1 s0
0
00 01 11 100 4 12 8
1 5 13 9
3 7 15 11
2 6 14 10
00
01
11
10
0 0 1
0 1 1 1
1 1 0 0
0 1 1 0
b i
S 1 S 0
0
0 0 01 11 1 00 2 6 4
1 3 7 5
0
1
1 1 0
1 0 1 0
yib iS 1 S 0
00001111
00110011
01010101
01100011
A d d
S u b trac t
In c rem en t
D ecrem en t
b i
y i
S 1
S 0
(a )
(b )
(c )
S 0
S 1
0
0 10 2
1 3
0
1
1
1 0
S 1 S 0
0011
0101
0110
A d dS u b trac tIn c rem en tD ec rem en t
(a )
(b ) (c )
C Ð 1
C Ð 1
S 1 S 0
a i b i
S 1S 0
fL Ui
fA Ui
fi
C iÐ 1
S 2
Y -G E N
F A
L U
A U
M U X
C i
S to rag ereg ister
M od u le: SR
FA 4M o d u led es ign
s0
s1
s2
s3
a0
a1
a2
a3
b 0
b 1
b 2
b 3
gn d
N ,C .
ad d 1M od u le :
FA 1
ad d 0M od u le :
FA 1
ad d 2M od u le :
FA 1
ad d 3M od u le :
FA 1
ab
FA 1M od u led esig n
c in
co ut
a3
a2
X 1
a1
R 1
X 2
A 2
A 1
A 3
s
D isp layd riv er
A d d er
M od u le: FA 4
K eyp adin p u t
x1
a2
ab
c in
c o ut
a3
X 1
a1
R 1
X 2
A 2
A 1
A 3
s
M o d u le: F A 1
H iera rch ica lcon n ec tors
a
b
c in
c o ut
s
(a )
(b )
x 1
(a )
(b )
A (3 :0 )
B (3 :0 )
A (3 :0 )
B (3 :0 )P in B (3 :0 )
FA 4
A (0 )A (1 )A (2 )A (3 )
B (0 )B (1 )B (2 )B (3 )
S (0 )S (1 )S (2 )S (3 )
S (3 :0 )
FA 4
P in A (3 :0 )
P in S (3 :0 )S (3 :0 )
A 0A 1A 2A 3
B 0B 1B 2B 3
S 0S 1S 2S 3
T im e
057
1012
0 0 0 00 11 00 11 00 11 00 11 0
0 0 0 00 1 0 10 1 0 10 0 0 10 0 0 1
0 0 0 00 0 0 01 0 1 11 0 1 10 11 1
(a )
(b )
0 1 1 0
0 1 0 1 0 0 0 1
1 0 11
a (3 :0 )
b (3 :0 )
s (3 :0 )
0 5 1 0 15
0 0 0 0
0 0 0 0
0 0 0 0 0 1 1 1
T im e
a(3 :0 ) b (3 :0 ) s(3 :0 )
