f ab c d abc - wordpress.com...f 1 ab c d abc++ ab (c c) (d d) c d (a a) (b b) abc (d d)⋅+ ⋅+ +...
Post on 17-Jan-2020
44 Views
Preview:
TRANSCRIPT
F1 AB C D ABC+ +
AB (C C) (D D) C D (A A) (B B) ABC (D D)⋅ + ⋅ + + ⋅ + ⋅ + + ⋅ +
AB (CD CD CD C D) CD (AB AB AB A B)⋅ + + + + ⋅ + + + + +ABCD ABCD
ABCD ABCD ABCD ABC D ABCD AB CD ABCD+ + + + + + +
A B C D ABCD ABCD+ + A A A+ =
A B C D ABCD AB CD ABCD ABCD+ + + +
ABC D ABC D ABCD ABCD+ + +
f (x, y, z) (xy z) (y x z)+ +
xy xyz y z x z+ + +
xy (z z) xyz yz (x x) x z (y y)⋅ + + + ⋅ + + +
xyz xyz xyz xyz xyz xyz xy z+ + + + + +
xyz xyz xyz xy z+ + +
(P Q) (P R)+ +
(P Q R R) (P R Q Q)+ + ⋅ + + ⋅
(P Q R) (P Q R) (P Q R) (P Q R)+ + + + + + + + A BC (A B) (A C)+ = + +
(P Q R) (P Q R) (P Q R)+ + + + + + A A A⋅ =
TECHNICAL PUBLICATIONS - An up thrust for knowledgeTM
F (A, B, C, D) B C BD AC+ +
∴ F (w, x, y, z) w x y xyz w z+ +
∴ F (w, x, y, z) (w x) (w y z)+ + +
TECHNICAL PUBLICATIONS - An up thrust for knowledgeTM
00 01 11 10
00
01
11
10
ABCD
1 X
X
1 1
1 1
1111
X
wxyz
1 1
1
00 01 11 10
00
01
11
10
w z
w yxX
1 1
1
X X
x y z
w xy z
w + x
w + x
w x+
w + x
y + z
0
XX
X
X X X
y + z y z+ y + z
0
0 0 0 0
w + y + z
w + x
∴ A B DE A B CD A B E A C E ABCD ABDE ABC D+ + + + + +
F (A, B, C, D, E) A B D B C D A D E+ +
TECHNICAL PUBLICATIONS - An up thrust for knowledgeTM
x
w
x
w
w
yz
F
BCDE
1
1
1
11
00 01 11 10
00
01
11
10
A B D E
A B C D
A EB
1
1
A = 0
BCDE
1
1
1
11
00 01 11 10
00
01
11
10
A EC
A CB D1
A = 1
1
1
A B D E
A B C D
00 01 11 10
00
BCDE
01
11
10
1 1
1 1
For A = 0
00 01 11 10
00
BCDE
01
11
10
1
For A = 1
1
1
1
1
m1 m1
m3 m8
m6 m3
m7 m6
m8 m9
m9 m10
m10 m12
m12 m7
m14 m14
m15 m11
m11 m13
m13 m15
TECHNICAL PUBLICATIONS - An up thrust for knowledgeTM
(B D)
∴ F (A, B, C, D) BD A BC+ +
m0 m0
m1 m1
m2 m2
m3 m3
m10 m10
m11 m12
m12 m11
m13 m13
m14 m14
m15 m15
TECHNICAL PUBLICATIONS - An up thrust for knowledgeTM
Primeimplicants
m1
1, 3, 9, 11 (BD)
8, 9, 10, 11, 12, 13, 14, 15
6, 7, 14, 15 (BC)
m3 m6 m9 m10 m12 m14 m15m7 m8 dm11 dm13
F (A, B, C, D) A B AC AB+ +
m0 m0
m1 m1
m2 m2
m8 m8
m9 m9
m15 m17
m17 m24
m21 m21
m24 m25
m25 m15
m27 m27
m31 m31
TECHNICAL PUBLICATIONS - An up thrust for knowledgeTM
Primeimplicants
m0
0, 1, 2, 3 (AB)
2, 3, 10, 11 (BC)
10, 11, 14, 15 (AC)
12, 13, 14, 15 (AB)
m1 m2 m11 m12 m13 m14m3 m10 m15
F (A, B, C, D, E) A C D B C D AB C E ABCE BCDE AB D E+ + + + +
TECHNICAL PUBLICATIONS - An up thrust for knowledgeTM
Primeimplicants
m0
0, 1, 8, 9 (ACD)
8, 9, 24, 25 (BCD)
0, 2 (ABCE)
1, 17 (BCDE)
m1 m2 m15 m17 m21 m24 m25m8 m9 m27
17, 21 (ABDE)
17, 25 (ACDE)
25, 27 (ABCE)
15, 31 (BCDE)
27, 31 (ABDE)
m31
M d( , , , , , ) ( , , )0 1 4 11 13 15 5 7 8∏ ∏+m d( , , , , , , ) ( , , )2 3 6 9 10 12 14 5 7 8+∑
m2 m2
m3 dm8
m6 m3
m9 m6
m10 m9
m12 m10
m14 m12
dm5 dm5
dm7 m14
dm8 dm7
TECHNICAL PUBLICATIONS - An up thrust for knowledgeTM
A B C
A C D
A B D
A C
C D
A D
( ) ( ) ( )1 0 0 0 1 1 0- - - - -+ +
∴ ABC AC AD+ +
m0 m0
m1 m1
m4 m4
TECHNICAL PUBLICATIONS - An up thrust for knowledgeTM
Prime implicants
ABC 8, 9
m2 m3 m6 m9 m10 m12 m14 dm5 dm7 dm8
ACD 8, 12
ABD 5,7
AC 2,3,6,7
CD 2,6,10,14
AD 8,10,12,14
X
ABCD
00 01 11 10
00
01
11
10
X 1
1 1
1
11
X 1
AC
ADABC
m5 m16
m16 m5
m17 m17
m21 m21
m25 m25
m29 m29
x x x1 2 4
x x x2 3 4
x x x2 4 5
x x x1 4 5
TECHNICAL PUBLICATIONS - An up thrust for knowledgeTM
x x x x x x x x x1 4 5 2 3 4 1 2 4+ +
TECHNICAL PUBLICATIONS - An up thrust for knowledgeTM
BCD
ACD
BCD
ABD
ABC
AB
ABD
1,9
4,6
6,7
9,11
7,15
11,15
8,9,10,11
m1 m4 m6 m7 m8 m9 m10 m11 m15Prime
implicants
TECHNICAL PUBLICATIONS - An up thrust for knowledgeTM
S0I3 I2 I1 I0
D1 D0 D1 D0
D1 D0
S S2 : 1MUX 2
2 : 1MUX 1
2 : 1MUX 3
Y
Y2
SS1
Y1 Y0
E
Y Y
a
a
D0 D1 D2 D3 D4 D5 D6 D7
0 1 2 3 4 5 6 7
8 9 10 11 12 13 14 15
1 a a a a a a0
TECHNICAL PUBLICATIONS - An up thrust for knowledgeTM
D31 7ID30 6ID29 5ID28 4ID27 3ID26 2ID25 1ID24 0I
E S2 S1 S0
8 : 1MUX 4 Y4
D23 7ID22 6ID21 5ID20 4ID19 3ID18 2ID17 1ID16 0I
8 : 1MUX 3
Y3
S2 S1 S0E
D15 7ID14 6ID13 5ID12 4ID11 3ID10 2ID9 1ID8 0I
E S2 S1 S0
8 : 1MUX 2 Y2
D7 7ID6 6ID5 5ID4 4ID3 3ID2 2ID1 1ID0 0I
8 : 1MUX 1
Y1
E
Y
S0 S1 S2
S4 S3
TECHNICAL PUBLICATIONS - An up thrust for knowledgeTM
a
D0D1D2D3D4D5D6D7
S S S2 1 0
B C D
8 : 1MUX Y
1
0
D0 D1 D2 D3 D4 D5 D6 D7
0 1 2 3 4 5 7
10 11 12 13 14 159
A
A
0A A A A A
6
8
0 0
For F1
D8 D9 D10 D11 D12 D13 D14 D15
0 1 2 3 4
10 11 12 13 14 159
A
A
0A A A A
8
5 6 7
A A A
For F2
D16 D17 D18 D19 D20 D21 D22 D23
0 1 2 3
10 11 12 13 159
A
A
A0 A 0 A
8
5 6 7
1 1 0
4
14
For F3
C m (3, 5, 6, 7)out =∑∑ m (1, 2, 4, 7)
D 1in =
TECHNICAL PUBLICATIONS - An up thrust for knowledgeTM
D24 D25 D26 D27 D28 D29 D30 D31
0 1 2 3
10 11 12 13 15
A
A
AA A A 1
5 6 7
0 A 0
4
148 9
For F4
1 : 8DEMUX
YYYYYYYY
01234567
S0 S1 S2
A B C
D = 1in
Cout
S
TECHNICAL PUBLICATIONS - An up thrust for knowledgeTM
1 : 8DEMUX
YYYYYYYY
01234567
S S S0 1 2
A B C
D = 1in
f1
f2
Y0Y1Y2Y3Y4Y5Y6Y7Y8Y9
Y10Y11Y12Y13Y14Y15
F1
F2
A
B
C
D
A
B
C
D4 : 16
Decoder
TECHNICAL PUBLICATIONS - An up thrust for knowledgeTM
00 00
01 01
00 1101 10 00 1101 10E E1 0
E E1 0 E E1 0
E E1 0E E3 2
E E3 2 E E3 2
E E3 2
X XX X0 0X X
1 11 00 00 1
10 10
11 11
1 11 00 00
X X1 0X XX X
For B0
B =0 0E
For B1
1
00
01
00 1101 10
XX 0X
00 00
10
11
00 0
X1 X
For B3
B = E + E= E + E
1 1 0 1 0
1 0
E E
B = E E + E E E3 3 2 3 1 0
00
01
00 1101 10
XX 0X
00 10
10
11
11 01
X0 XX
For B2
B = + E E E + E E2 2 1 2 1 0 3 1 0E E E
1
X
TECHNICAL PUBLICATIONS - An up thrust for knowledgeTM
BCD code
Excess -3 code
E3 E2 E1 E0
B0
B1
B2
B3
(G G G G ) G G (G G G G ) G G3 2 3 2 1 0 3 2 3 2 1 0+ + +
+ + + +(G G G G ) G G (G G G G ) G G3 2 3 2 1 0 3 2 3 2 1 0
(G 3 ⊕ G2) G G1 0 G 3 G2 G G1 0
(G 3 ⊕ G2 G G1 0 G 3 G2 G G1 0
⊕ G G1 0 (G G G G )1 0 1 0+
⊕ ⊕
⊕ G G1 0⊕ G G3 2⊕ ⊕
⊕ ⊕ ⊕
G G3 2 (G G G G ) G3 2 3 2 1+
⊕ G1
( ) ( )G G G G G G3 2 1 3 2 1⊕ + ⊕
G G G3 ⊕ ⊕2 1
TECHNICAL PUBLICATIONS - An up thrust for knowledgeTM
00
01
00 1101 10G G3 2 G G3 2
G G1 0 G G1 0
10 01
01 10
10
11
01 10
10 01
00
01
00 1101 10
1
0
0
1
1
0
0
1
10
11
1 1
1
0
0 1
0
0
For A For B
G G G G3 2 3 2+ G 3
⊕
TECHNICAL PUBLICATIONS - An up thrust for knowledgeTM
00
01
00 1101 10G G3 2 G G3 2
G G1 0 G G1 0
00 00
11 11
10
11
1 1
00 00
00
01
00 1101 10
0
0
0
0
0
0
0
0
10
11
1 1
1
1
1 1
1
1
For C For D
1 1
G3 G2 G1 G0
Gray code
Binary code
A
B
C
D
2n ≥
∴
Qn Qn+1
QD QC QB QA QD+ QC
+ QB+ QA
+ JD KD JC KC JB KB JA KA
TECHNICAL PUBLICATIONS - An up thrust for knowledgeTM
TECHNICAL PUBLICATIONS - An up thrust for knowledgeTM
0
0 0 1 0
X X X X
X X X X
0 0
Q QA B
Q QC D00 01 11 10
00
01
11
10
0
J = Q Q QD B C D
X
X X X X
0 0 X 1
X X X X
X X
Q QA B
Q QC D00 01 11 10
00
01
11
10
X
K = QD C
For JD For KD
0
X X X X
0 0 X 0
X X X X
1 0
Q QA B
Q QC D00 01 11 10
00
01
11
10
0
J = Q QC C D
For JC
X
0 0 1 0
X X X X
X X X X
X X
Q QA B
Q QC D00 01 11 10
00
01
11
10
X
K = Q QC C D
For KC
TECHNICAL PUBLICATIONS - An up thrust for knowledgeTM
0 1 X X
0 1 X X
X X X X
1 X X
Q QA B
Q QC D00 01 11 10
00
01
11
10
0
J = QB D
X X 1 0
X X 1X
X X X X
X 1 0
Q QA B
Q QC D00 01 11 10
00
01
11
10
X
K = Q + QB A D
For JB For KB
X X
1 X X 0
X X X X
X
1
1
Q QA B
Q QC D00 01 11 10
00
01
11
10
X
1
1
J = Q + QA A C
X 1 1 X
1 X XX
X X X X
Q QA B
Q QC D00 01 11 10
00
01
11
10
1 1 XX
K = 1A
For JA For KA
JA QA
KA QA
A
QAQC
CLK
JB QB
KB QB
B
QAQD
QD JC QC
KC QC
C
QCQD
JD QD
KD QD
D
QB
QDQC
QC
(LSB)QA QB QC Q (MSB)D
Output
1
TECHNICAL PUBLICATIONS - An up thrust for knowledgeTM
A0 D0
A1 D1
A2 D2
A3 D3
ROM4 16×
Addresslines
Binaryinput
Datalines
Gray codeoutput
top related