STEADY CODES WITH HAMMING- DISTANCES 1 AND 2 DGT D = 1 C 2 D = 2 C 1 C Digital Circuits. Hamburg. Prof. Dr. F.
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1 C D = amburg C 2 STEADY CODES C WIT C D = 2 AMMING- DISTANCES AND 2 C 2 C DGT Digital Circuits
2 DECIMA NUMBER 8 WEIGT 4 2 P u P g amburg PARITYBIT AT BCD- CODE DGT Digital Circuits 2
3 amburg DEZIMA- i i i 3 2 i c c c c c c c 2 ZA (7,4,3)-CODE DGT Digital Circuits 3
4 amburg CODE WORDS OF TE CYCIC (7,4,3)- CODE DGT Digital Circuits 4
5 VD Introduction II Digital Circuits 5
6 E 2-to--MUX with enable MUX MUX MUX S G G G E EN Y EN EN I I Digital Circuits 6
7 entity MUX2TO is port ( I: in bit_vector ( downto ); S, E: in bit; Y: out bit); end MUX2 TO ; architecture MUX of MUX2TO is begin Y <= (I() and not E and not S) or (I() and not E and S); end MUX; architecture MUX2 of MUX2TO is begin with S select Y <= (I() and not E) when, end MUX2; (I() and not E) when ; architecture MUX3 of MUX2TO is begin Y <= (I() and not E) when S= else (I() and not E); end MUX3; Digital Circuits 7
8 Combinational logic. Boolean equations entity FUADD is port ( E, E, CIN: in bit; SUM, COUT: out bit); end VOADD; architecture BEAVIOUR of FUADD is begin SUM <= E or E or CIN; COUT <= (E and E) or (CIN and (E or E)); end BEAVIOUR; compact description no dont t care Digital Circuits 8
9 2. Truth tables entity FUADD is port ( E, E, CIN: in bit_vector( downto ); SUM, COUT: out bit); end FUADD; architecture BEAVIOUR of FUADD is signal TEMP: bit_vector(2 downto ); begin TEMP <= CIN E E; -- concatenation with TEMP select SUM <= when, when, when, when, when, when, when, when others; with TEMP select -- with = or COUT <= when, when others; end BEAVIOUR; Digital Circuits 9
10 architecture BEAVIOUR of FUADD is signal TEMP: bit_vector( downto ); -- local signals signal TEMP2: bit_vector(2 downto ); begin TEMP2 <= CIN E E; -- concatenation with TEMP2 select TEMP <= when, when, when, when others; COUT <= TEMP(); SUM <= TEMP(); end BEAVIOUR; Digital Circuits
11 For bit string literals dual, octal and headecimal notation is allowed. With underscore ( _ ) groups are possible. E b _ base 2, identification b or B o 7 4_3 base 8, identification o or O AFFE_9D base 6, identification or X ength of a vector at octal: integral multiple of 3 at headecimal: integral multiple of 4 E... TEMP <= b _ when o, b _ when o o 2 o 4, b _ when o 3 o 5 o 6, b _ when others; Digital Circuits
12 Use of don t care a) at the output E E(3) E(2) E() E() A(2) A() A() rest Digital Circuits 2
13 port ( E: in std_logic_vector(3 downto ); A: out std_logic_vector(2 downto )); with E select A <= -- when, when 3, when 4, -- when B, --- when others; b) at the input with E select A <= when --, Digital Circuits 3
14 don t care at input and output E E(3) E(2) E() E() A(2) A() A() rest A <= -- when E = else when E = 3 else when E(3 downto 2) = else -- when E(3) = and E( downto ) = else -- when E(3) = and E() = else --- ; Digital Circuits 4
15 ogical/pyhysical Relations Digital Circuits 5
16 amburg SWITCING DEVICE SYMBOS DGT Digital Circuits 6
17 CASE INPUT OUTPUT e i j a ZA e i j a e i j a ZB e i j a e i j a PA e i j a e i j a PB e i j a amburg ASSIGNMENT OF OGIC STATES AND PYSICA EVES DGT Digital Circuits 7
18 a b a b y b a y y b a y b a y a b a b a b a y y y y b amburg POARITY INDICATOR AND INVERSION BUBBE DGT Digital Circuits 8
19 POSITIVE OGIC TRUT FUNCTION TABE FUNCTION TABE I I Q NEGATIVE OGIC TRUT TABE FUNCTION AND OR OR AND NAND NOR NOR NAND amburg COMBINATION AT POSITIVE AND NEGATIVE OGIC DGT Digital Circuits 9
20 POSITIVE OGIC TRUT FUNCTION TABE FUNCTION TABE I I Q NEGATIVE OGIC TRUT TABE FUNCTION AND OR OR AND NAND NOR NOR NAND amburg COMBINATION AT POSITIVE AND NEGATIVE OGIC DGT Digital Circuits 2
21 U CC R R R 2 4 I I 2 T 3 T T 2 Q OE T 4 R 3 amburg TRI-STATE - OUTPUT DST Digital Circuits 2
22 amburg OE Q OE 2 Q 2 D A T A TRI-STATE OUTPUT B U S APPICATION OE n Q n DST Digital Circuits 22
23 U CC R 2 U S * Q T 2 R Pull-up resistor I Q T 4 U Q R 3 amburg OPEN COECTOR - OUTPUT DST Digital Circuits 23
24 U CC amburg R U Q OPEN COECTOR FAN OUT I Q I I M N DST Digital Circuits 24
25 amburg SYMBOS FOR OPEN OUTPUTS DGT Digital Circuits 25
26 WIRED-AND WIRED-OR amburg SYMBOS FOR WIRED-AND AND WIRED-OR DGT Digital Circuits 26
27 VD Introduction III Digital Circuits 27
28 Data type std_logic_64 Other values as and Fied in a VD-library library ieee; use ieee.std_logic_64.all; -- integration of the library -- definition of the partial content -- packet std_logic_64 -- all etensions of the language Values of std_logic and std_logic_vector: U unknown; simulator, not initialized X unknown, strong; simulator, e.g. bus conflict and, strong, strong Z igh_z Tristate, weak open emitter, weak open collector W unknown, weak; simulator, e.g. bus conflict and - don t care Digital Circuits 28
29 E TRISTATE-DRIVER library ieee; use ieee.std_logic_64.all; entity TRI_DRV is port ( X: in std_logic; EN: in bit; Y: out std_logic); end TRI_DRV; architecture BEAVIOUR of TRI_DRV is begin Y <= X when EN = else Z ; end BEAVIOUR; Digital Circuits 29
30 Programmable ogic Devices Digital Circuits 3
31 PROGRAMMABE MEMORIES AND OGIC DEVICES amburg STORAGE OF A TABE (PROGRAM) STORAGE OF A OGICA FUNCTION NOT NOT VOATIE VOATIE VOATIE (NOT)-VOATIE NOT ERASABE ROM ERASABE RAM SRAM DRAM PD FPGA CA OVERWIEW OVER PROGRAM- MABE OGIC ROM EPROM PA CPD PROM EEPROM GA PA DGT Digital Circuits 3
32 RAM SRAM DRAM ROM PROM EPROM EEPROM FPGA CA PD PA GA PA CPD RANDOM ACCESS MEMORY STATIC RAM DYNAMIC RAM READ ONY MEMORY PROGRAMMABE ROM ERASABE PROM EECTRICAY ERASABE PROM FIED PROGRAMMABE GATE ARRAY OGIC CE ARRAY PROGRAMMABE OGIC DEVICE PROGRAMMABE ARRAY OGIC GENERIC ARRAY OGIC PROGRAMMABE OGIC ARRAY COMPEX PD amburg PROGRAMMABE DEVICES ABBREVIATIONS DGT Digital Circuits 32
33 BIN/Y A A 2 3 Nr. A A Y 2 Y Y Y 2 Y Y 2 3 amburg CIRCUIT AND TRUT TABE OF A ROM DGT Digital Circuits 33
34 amburg ROM 4*3 A A A 3 A A Y Y SYMBO 2 A Y 2 OF A ROM DGT Digital Circuits 34
35 DECIMA NUMBER D C B A a b c d e f g amburg SEGMENT- DISPAY f e a g b c d DGT Digital Circuits 35
36 ADDRESS CONTENT EXADECIMA DUA DUA EXADECIMA E D C B A h g f e d c b a F amburg PROGRAM TABE DGT Digital Circuits 36
37 PROM 32*8 ADDRESS EXADECIMA CONTENT EXADECIMA A B A A a b 2 3 C D 4 A A A A c d e A f 6 A g EN 7 A amburg SYMBO AND PROGRAM TABE DGT Digital Circuits 37
38 C B A Y Z Y: A amburg B EXAMPE C TO TE APPICATION OF Z: A PROGRAMMABE OGIC DEVICES B C DGT Digital Circuits 38
39 D C B A D C B A Y Y D C B A D C B A Y Y amburg REPRESENTATION OF TE CONNECTIONS DGT Digital Circuits 39
40 amburg PRINCIPE CIRCUIT OF OGIC DEVICES > > DGT Digital Circuits 4
41 C B A amburg AND-ARRAY AND OR-ARRAY DGT Digital Circuits 4
42 C B A amburg ARRAYS OF A PA Y Z DGT Digital Circuits 42
43 C B A amburg ARRAYS OF A PA Y Z DGT Digital Circuits 43
44 C B A amburg ARRAYS OF A PA Y Z DGT Digital Circuits 44
45 Digital Circuits DGT-2565 PA 6R D C EN EN > EN > EN > EN > > D C EN > D C EN > D C EN > (9) (8) (7) (6) (5) (4) (3) (2) () (9) (8) (7) (6) (5) (4) (3) (2) () P 3 P amburg
46 Digital Circuits DGT-258 PA 22V OE 7 OE EN > > MACRO- CE 9 EN MACRO- CE... OE > EN MACRO- CE OE OE > 3 EN MACRO- CE OE > 5 EN MACRO- CE () (23) (2) (3) (4) (5) (22) (2) (2) (9) AR amburg
47 MUX amburg D C 3 2 EN MUX G 3 MACROCE G S S DGT Digital Circuits 47
48 32*64 7 EN > amburg PA DGT Digital Circuits 48
49 JTAG- PORT JTAG CTR. IN-SYSTEM PROGRAMMING CONTROER 36 I/O 8 FB I/O I/O I/O I/O I/O I/O I/O/GCK I/O/GSR I/O/G R I/O B O C K S S W I T C M A T R I X MC -8 FB 2 MC -8 FB n MC -8 amburg XC95 CPD ARCITECTURE DGT Digital Circuits 49
50 amburg XC95 CPD FUNCTION BOCK Source: XIINX DGT Digital Circuits 5
51 Source: XIINX amburg XC958 CPD I/O-BOCK DGT Digital Circuits 5
52 Combinational ogic Devices Digital Circuits 52
53 A S E A B S E G B G A B A B S E G amburg COMPARATOR DGT Digital Circuits 53
54 A COMP amburg A A 2 P A 3 3 I I I 2 < = > P P P < = > Q Q Q Y Y Y 2 SYMBO OF TE TT-IC SN7485 B B B 2 Q B 3 3 DGT Digital Circuits 54
55 A3, B3 A2, B2 A, B A, B I 2 I I Y2 Y Y A3 A3 A3 A3 A3 A3 A3 A3 A3 A3 > B3 < B3 = B3 = B3 = B3 = B3 = B3 = B3 A3 = B3 A2 = B2 = = B3 B3 A2 A2 A2 A2 A2 A2 A2 A2 > B2 < B2 = B2 = B2 = B2 = B2 = B2 = B2 A A A A A A A > = B < B = B = B B = B = B A A A A A > B < B = B = = B B A3 A3 A3 = B3 = B3 = B3 A2 A2 A2 = B2 = B2 = B2 A = B A = B A A = = B B A A = B = B amburg FUNCTION TABE OF TE TT-IC SN7485 DGT Digital Circuits 55
56 A COMP A 4 COMP A A 2 P A 5 A 6 P A 3 3 A 7 3 < P < Q < P < Q A < B = P = Q = P = Q A = B > P > Q > P > Q A > B B B 4 B B 2 Q B 5 B 6 Q B 3 3 B 7 3 amburg SERIA-EXTENSION DGT Digital Circuits 56
57 A 5 A 6 A 7 A 8 3 P COMP amburg B 4 < P < Q = P = Q A 4 > P > Q COMP B 5 B 6 B 7 B 8 A 3 Q COMP P 3 < P < Q = P = Q > P > Q A A A < = > B B B PARAE- EXTENSION A A 2 A 3 3 < P P < Q 3 Q = P = Q > P > Q B B B 2 B 3 3 Q DGT Digital Circuits 57
58 X/Y DEC/BCD.... a b 2 k l c 2 4 m BCD/Y d e n a /2 e f 5 b 2 /3 f g 6 c 4 g h 7 d 8 5/6 h i 8 8/9 i j 9 amburg SYMBOS FOR CODE-CONVERTERS DGT Digital Circuits 58
59 T A B C X/Y T K M INPUTS C B A M OUTPUTS K amburg SYMBO AND TRUT TABE OF A CODE-CONVERTER DGT Digital Circuits 59
60 T G G G 2 X/Y T D D D 2 INPUTS OUTPUTS G 2 G G D 2 D D amburg CONVERTER GRAY-CODE / DUA-CODE DGT Digital Circuits 6
61 D : D : G G G G G 2 G 2 D2 : G G G 2 amburg K - MAPS GRAY-CODE / DUA-CODE DGT Digital Circuits 6
62 amburg BIN/OCT A Y A Y A 2 EN 3 EN 2 EN 2 EN Y 2 Y 3 Y 4 Y 5 Y 6 SYMBO OF TE TT-IC SN Y 7 DGT Digital Circuits 62
63 FUNCTION TABE TT-IC SN7438 Y5 Y6 Y7 Y4 Y3 Y2 Y Y A A A2 EN3 EN EN2 OUTPUTS INPUTS DGT-247 amburg Digital Circuits
64 E S I I Y Y MUX X X X S G X X I X X I Y E EN Y amburg MUTIPEXER DGT Digital Circuits 64
65 S I Y I Y E amburg MUX - SCEMATIC DGT Digital Circuits 65
66 S S S 2 2 MUX G 7 amburg I I I 2 2 I 3 3 I 4 4 I 5 5 I 6 6 I 7 7 Y Y SYMBO OF TE TT-IC SN745 E EN DGT Digital Circuits 66
67 FUNCTION TABE TT-IC SN745 S S2 S OUTPUTS INPUTS E I I I 3 2 I I 6 7 I I 5 4 I Y Y DGT-223 amburg Digital Circuits
68 E A I Y Y DX X X A I E G Y Y A I Y Y E amburg DEMUTIPEXER DGT Digital Circuits 68
69 amburg DX A Y A A 2 I 2 G 7 Y Y 2 Y 3 Y 4 Y 5 Y 6 TT-IC SN7438 AS DEMUTI- PEXER Y 7 DGT Digital Circuits 69
70 FUNCTION TABE FOR SN7438 AS DEMUTIPEXER Y5 Y6 Y7 Y4 Y3 Y2 Y Y A A A2 OUTPUTS INPUTS I DGT-226 amburg Digital Circuits
71 Adder and Subtractor Circuits Digital Circuits 7
72 A S A B S C B C C A B S C amburg AF ADDER DGT Digital Circuits 72
73 A i C i- A i B i S i C i B i S i C i- CI C C i A B i i S i C i C i- amburg FU ADDER DGT Digital Circuits 73
74 S i : B i C i : B i A i A i C i- C i Digital Circuits 74
75 A A A 2 B B B 2 S S S 2 C 2 C CI C CI C TREE BIT ADDER DGT-22 amburg Digital Circuits 75
76 CPG amburg G CG G CG C C G 2 CG2 C C G 3 CG3 C2 C 2 P P P 2 CP CP CP2 CG CP G P CARRY- OOK-AEAD GENERATOR P 3 CP3 C i C I DGT Digital Circuits 76
77 A B S A B S A 2 B 2 S 2 A 3 B 3 S 3 S S S S CG CG CG CG CP CP CP CP C - C I C C I C C I C C I C CPG CG CG CG2 CG3 CP CP CP2 CP3 C C C2 CG CP C I amburg FOUR BIT ADDER WIT PARAE CARRY DGT Digital Circuits 77
78 amburg CG CG CG2 CG3 CP CP CP2 CP3 CPG C C C2 CG CP SYMBO OF TE TT-IC SN7482 C I DGT Digital Circuits 78
79 AU T C P C G M 3 C 4 C I P = Q P Q P Q P 2 Q 2 P 3 Q 3 AU SN748 Univ ersity of amburg DGT Digital Circuits 79
80 Finite State Machine Introduction Digital Circuits 8
81 X amburg COMBINATIONA OGIC X = X.. X Y X u - Y = f(x) COMBINATIONA OGIC AND STATE MACINE Y = Y Y.. STATE MACINE X Y Y v - Y(t n ) = f(x(t n ), X(t n - ),..., X(t )) DGT Digital Circuits 8
82 X Z + Z Y amburg BOCKS OF A STATE-MACINE DGT Digital Circuits 82
83 Z X NEXT STATE DECODER Z + STATE MEMORY OUTPUT OGIC Y amburg MEAY-MACINE DGT Digital Circuits 83
84 amburg X ( t n ) X ( t n+ ) Z ( t n ) Z ( t n+ ) Z + ( t n ) Z + ( t n+ ) TIME RESPONSE OF TE MEAY- MACINE Y ( t n ) Y ( t n+ ) t t n t n+ DGT Digital Circuits 84
85 NEXT Z COMBINATIONA OGIC Z + STATE REGISTER X Y amburg MEAY MACINE WIT COMBINATIONA OGIC MEAY-MACINE WIT COMBINED OGIC DGT Digital Circuits 85
86 X SYNCRONI- ZATION Z NEXT STATE DECODER Z + PRESENT STATE REGISTER OUTPUT FORMING OGIC Y CK amburg MEAY-MACINE WIT INPUT SYNCRONIZATION DGT Digital Circuits 86
87 X Z NEXT STATE DECODER Z + PRESENT STATE REGISTER OUTPUT FORMING OGIC Y SYNCRONI- ZATION Y * CK amburg MEAY-MACINE WIT OUTPUT SYNCRONIZATION DGT Digital Circuits 87
88 Z NEXT PRESENT OUTPUT STATE STATE FORMING Y X DECODER Z + REGISTER Z OGIC amburg MOORE-MACINE DGT Digital Circuits 88
89 amburg X ( t n ) X ( t n+ ) Z ( t n ) Z ( t n+ ) Z + ( t n ) Z + ( t n+ ) TIME RESPONSE OF TE MOORE- MACINE Y ( t n ) Y ( t n+ ) t t n t n+ DGT Digital Circuits 89
90 CK X X X2 + Z + Z Z Z Y Y Y2 t amburg PUSE DIAGRAM DGT Digital Circuits 9
91 amburg STATE DIAGRAM DGT Digital Circuits 9
92 amburg POSSIBE STATES DGT Digital Circuits 92
93 Z E / A Z B Z C Z A Ek / Az Z D amburg TRANSITION BEAVIOUR DGT-255 OF A MEAY-MACINE Digital Circuits 93
94 Z A E Z B A B Z C A C Z A A A Ek Z D A D amburg TRANSITION BEAVIOUR DGT-256 OF A MOORE-MACINE Digital Circuits 94
95 NEXT STATE TABE: OUTPUT TABE (MEAY): X X X X u- X X X X u- Z Z + Z Y z z z Z Z Z z Z 2 z z z i z j z k Z w- Z w- NEXT STATE AND OUTPUT TABE: y 3 y y y y y y i y j y k OUTPUT TABE (MOORE): X X X X u- Z Y Z Z Z. Z + / Y z /y 3 z /y z /y Z Z.. y y 3.. amburg NEXT STATE TABE AND OUTPUT TABE DGT Digital Circuits 95
96 z z z + z + y y amburg STATE TABE DGT Digital Circuits 96
97 - Accepts the input of and 2 in its slot - Change push button CB starts the process of money changing - As a corresponding response, ten c or twenty c coins will be dispensed - 2 is the largest amount of money which can be accepted all other coins will be returned without waiting for the push button CB Inputs Present state of MCM Outputs EU - one coin is entered EU2 - one 2 coin is entered CB - CB button is pressed NI - no input at all ES - one coin is stored ES2 - one 2 coin or two coins are stored ND - no debt, no coin stored C dispense of ten c coins 2C - dispense of twenty c coins EO return of one coin EO2 return of one 2 coin NO - no reaction, no output Money Changer Machine MCM Digital Circuits 97
98 amburg STATE DIAGRAM DGT Digital Circuits 98
99 INPUT STATE NEXT STATE OUTPUT NI NI NI EU EU EU EU EU2 2 EU2 2 EU2 2 EU CB CK CB CK CB CK amburg STATE TABE DGT Digital Circuits 99
100 INPUT E E STATE Z Z OUTPUT A2 A A amburg CODING AND STATE DIAGRAM DGT Digital Circuits
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