Digital Electronics: Principles, Devices and Applications

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224 Digital ElectronicsFigure 6.16Multiple Karnaugh map for a six-variable Boolean function.Solution• fA B C = ∑ 0 1 3 5 + ∑ 2 7 = ∏ 4 6 + ∏ 2 7.• From given Boolean functions in and notation, we can write sum-of-products and product-ofsumsBoolean expressions as follows:fA B C = ABC + ABC + ABC + ABC (6.58)fA B C = A + B + CA + B + C (6.59)
Boolean Algebra and Simplification Techniques 225Figure 6.17 Example 6.11.• The ‘don’t care’ input combinations for the sum-of-products Boolean expression are ABC ABC.• The ‘don’t care’ input combinations for the product-of-sums expression are A+B+CA+B+C.• The Karnaugh maps for the two cases are shown in Figs 6.17(a) and (b).• The minimized sum-of-products and product-of-sums Boolean functions are respectively given bythe equationsfA B C = C + A (6.60)fA B C = A + C (6.61)6.6.3 Karnaugh Maps for Multi-Output FunctionsKarnaugh maps can be used for finding minimized Boolean expressions for multi-output functions. Tobegin with, a Karnaugh map is drawn for each function following the guidelines described in the earlierpages. In the second step, two-function Karnaugh maps are drawn. In the third step, three-functionKarnaugh maps are drawn. The process continues until we have a single all-function Karnaugh map.As an illustration, for a logic system having four outputs, the first step would give four Karnaugh mapsfor individual functions. The second step would give six two-function Karnaugh maps (1−2, 1−3,1−4, 2−3, 2−4 and 3−4). The third step would yield four three−function Karnaugh maps (1−2−3,1−2−4, 1−3−4 and 2−3−4) and lastly we have one four-function Karnaugh map. A multifunctionKarnaugh map is basically an intersection of the Karnaugh maps of the functions involved. That is, a‘1’ appears in a square of a multifunction map only if a ‘1’ appears in the corresponding squares of themaps of all the relevant functions. To illustrate further, a two-function map involving functions 1 and2 would be an intersection of maps for functions 1 and 2. In the two-function map, squares will havea ‘1’ only when the corresponding squares in functions 1 and 2 also have a ‘1’. Figure 6.18 illustratesthe formation of a three-function Karnaugh map from three given individual functions.
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Digital ElectronicsDigital Electron
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Copyright © 2007John Wiley & Sons
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ContentsPrefacexxi1 Number Systems
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ContentsixReview Questions 67Proble
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Contentsxi6.3.8 Theorem 8 1966.3.9
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Contentsxiii9.11.3 Verilog 3399.11.
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Contentsxv12.2.5 Nonlinearity and D
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Contentsxvii13.10.3 80286 Microproc
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ContentsxixReview Questions 650Prob
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PrefaceDigital electronics is essen
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Prefacexxiiilogic analysers, freque
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Number Systems 3The value or magnit
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Number Systems 5The 1’s complemen
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Number Systems 7• The fractional
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Number Systems 9• The octal equiv
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Number Systems 11Solution• The gi
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Number Systems 13Hexadecimal system
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Number Systems 15Byte-1 Byte-2 Byte
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Number Systems 17Therefore, the exp
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2Binary CodesThe present chapter is
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Binary Codes 212.1.3 Higher-Density
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Binary Codes 23Fractional part = .7
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Binary Codes 252.3.2 Gray Code-Bina
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Binary Codes 27Solution(a) The bina
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Binary Codes 29Table 2.6(continued)
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Binary Codes 39fabDPegdc(a)afbegcDP
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Binary Codes 412.6.1 Parity CodeA p
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Binary Codes 43Table 2.9Generation
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Binary Codes 456. What is a parity
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48 Digital ElectronicsTable 3.1Bina
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50 Digital ElectronicsCase 1• Con
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52 Digital Electronics2. (AF1.B3) 1
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54 Digital ElectronicsCase 2• Let
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56 Digital ElectronicsExample 3.4Su
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58 Digital Electronics0110 1000 rep
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60 Digital ElectronicsTable 3.3Mult
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62 Digital ElectronicsTable 3.6algo
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64 Digital ElectronicsTable 3.8 Exa
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66 Digital Electronicsquotient is g
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68 Digital Electronics5. Prove that
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70 Digital ElectronicsIf the two vo
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72 Digital ElectronicsABCY=A+B+C(a)
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74 Digital ElectronicsABY=A.B(a)A00
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76 Digital ElectronicsXY=X(a)XY=XX0
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78 Digital ElectronicsAY1BCY(a)ABCD
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80 Digital ElectronicsABYABY=A+B(a)
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82 Digital ElectronicsABCDY=A.B.C.D
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84 Digital Electronics'1''1'ab c d
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86 Digital ElectronicsAY=A(a)ABY=A+
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88 Digital ElectronicsAYBEA00001111
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90 Digital ElectronicsABCD(AB+CD+EF
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92 Digital Electronics(a)(b)4V (vol
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94 Digital Electronics'1'I/PI/P(Vol
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96 Digital ElectronicsIOHIIHIIHIIH(
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98 Digital ElectronicsThe output of
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100 Digital ElectronicsE1LLHE2LHXOp
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102 Digital Electronics1A1B2A2B3A3B
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104 Digital Electronics4.13.2 AND G
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106 Digital ElectronicsFigure 4.53(
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108 Digital ElectronicsTable 4.1(co
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110 Digital Electronics(c) a three-
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114 Digital Electronics6. It is pro
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116 Digital Electronicsother and th
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118 Digital Electronics5.1.2.3 ECL
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120 Digital Electronics• LOW-leve
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122 Digital Electronics• Enable t
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124 Digital ElectronicsExample 5.2R
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126 Digital Electronics+VCC+VCCR 3I
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128 Digital Electronics4K 1301.6KVC
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130 Digital Electronicsbe in cut-of
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132 Digital ElectronicsVCC4K1.6KInp
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134 Digital Electronicslow-power TT
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136 Digital Electronics5.3.5.1 Char
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138 Digital ElectronicsVCCR 137KR 2
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140 Digital Electronicsfeatures of
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142 Digital ElectronicsFigure 5.24H
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144 Digital Electronics+VCC+VCCR1IO
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146 Digital ElectronicsFigure 5.30
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148 Digital Electronics5.4.1.2 MECL
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150 Digital ElectronicsFigure 5.33E
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152 Digital Electronicsfunctions as
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154 Digital ElectronicsVDDAQ1BQ 2Y=
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156 Digital ElectronicsVDDAQ 1BQ2Q5
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158 Digital ElectronicsFigure 5.42T
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160 Digital Electronics+VDDQ7Q8Q5Q6
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162 Digital ElectronicsFigure 5.46C
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166 Digital Electronicslogic status
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168 Digital Electronics5.5.2.4 74AC
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170 Digital Electronics+VDDA+VDDA -
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276 Digital ElectronicsTable 8.2 Im
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280 Digital Electronics8.1.4 Cascad
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282 Digital ElectronicsD 0 D 1 D 2
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284 Digital ElectronicsExample 8.4W
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286 Digital ElectronicsAB2-to-40123
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288 Digital ElectronicsABC2 2012345
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290 Digital Electronics0CBA12 22F3-
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292 Digital Electronics(a) Since bo
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294 Digital ElectronicsTable 8.12(c
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296 Digital ElectronicsD 0I 0I 1S 0
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298 Digital ElectronicsFurther Read
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300 Digital Electronicslogic functi
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302 Digital Electronics3. In the ca
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304 Digital ElectronicsD C B AProgr
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306 Digital Electronicsa GAL device
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308 Digital Electronicslarge memory
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310 Digital ElectronicsA B C D EHar
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312 Digital ElectronicsSolution(a)
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314 Digital ElectronicsInputs(n)(k)
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316 Digital ElectronicsABCiSCoFigur
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318 Digital ElectronicsAA 1 0B1B000
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320 Digital ElectronicsA1A0B1B0O/P-
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322 Digital ElectronicsProgrammable
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324 Digital ElectronicsCDAB00 01 11
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326 Digital ElectronicsABCDP Q R SF
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328 Digital ElectronicsFigures 9.23
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330 Digital ElectronicsInputsGlobal
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332 Digital ElectronicsDQO/P4-input
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334 Digital Electronicsthat have ev
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336 Digital ElectronicsLogic CellSR
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338 Digital ElectronicsDesign Entry
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340 Digital Electronicsbraces to de
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342 Digital ElectronicsCLK120VccI02
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344 Digital ElectronicsCLK120VccI02
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346 Digital ElectronicsARDCLKQQ4to1
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348 Digital ElectronicsCentral Swit
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350 Digital ElectronicsTable 9.6Sal
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352 Digital ElectronicsQSA1A2A3A4A5
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354 Digital Electronics3. Determine
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10Flip-Flops and Related DevicesHav
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Flip-Flops and Related Devices 359V
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Flip-Flops and Related Devices 361+
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11Counters and RegistersCounters an
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Counters and Registers 413ripple co
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Counters and Registers 415Table 11.
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Q 00Counters and Registers 4171JQ 0
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Counters and Registers 421'1'JPrQ A
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Counters and Registers 42311.5 Sync
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Counters and Registers 427Presettab
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Counters and Registers 429Clk(D)Q 0
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Counters and Registers 431Input AAO
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Counters and Registers 433ClockA-Ou
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Counters and Registers 435PLP3 P2 P
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Counters and Registers 437+V CCGNDU
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Counters and Registers 441The circu
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Counters and Registers 445CX (C) 1B
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Counters and Registers 447Figure 11
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Counters and Registers 449to the dr
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Figure 11.43 Logic diagram of IC 74
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Counters and Registers 45911.13 Shi
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Counters and Registers 461Clock-Inp
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Counters and Registers 4631JFClockC
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Counters and Registers 465R0(1)R0(2
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Counters and Registers 467(9)CLK C1
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Counters and Registers 4711OutputCJ
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12Data Conversion Circuits - D/Aand
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Data Conversion Circuits - D/A and
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{Data Conversion Circuits - D/A and
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(Data Conversion Circuits - D/A and
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526 Digital ElectronicsAddress BusM
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528 Digital Electronicsyear 1973. I
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530 Digital Electronicsto the addre
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532 Digital ElectronicsDemultiplexe
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534 Digital Electronicscounter and
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536 Digital ElectronicsOperationReg
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538 Digital Electronics13.6.1.2 Pow
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540 Digital Electronics13.7 Program
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542 Digital ElectronicsX1X2RESET OU
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544 Digital ElectronicsTable 13.3Si
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{{546 Digital ElectronicsSystem Dat
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{548 Digital ElectronicsBus Interfa
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550 Digital ElectronicsData Registe
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552 Digital ElectronicsBarrelShifte
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554 Digital ElectronicsSequencer an
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556 Digital Electronics64-bit inter
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558 Digital Electronicsfrom the Pen
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560 Digital ElectronicsPentium bran
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562 Digital Electronicsfor microcom
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564 Digital Electronics4. Briefly d
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566 Digital ElectronicsROMEEPROMRAM
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568 Digital ElectronicsFromSensorsT
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570 Digital ElectronicsThe digital-
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572 Digital Electronicsare embedded
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574 Digital Electronicscomprises on
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576 Digital Electronics14.3.2 Mappi
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578 Digital ElectronicsRegister-1Re
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580 Digital ElectronicsYet another
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582 Digital ElectronicsT2/P1.0T2EX/
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584 Digital Electronics14.5.1.8 68H
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586 Digital ElectronicsPA7/PAI/OC1P
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588 Digital ElectronicsPeripheral-r
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*590 Digital ElectronicsPP3/PW3PP4P
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592 Digital Electronicssignal-proce
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594 Digital ElectronicsV CCMicrocon
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596 Digital ElectronicsV CCI/O PinI
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598 Digital Electronicsdp1234567abc
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600 Digital ElectronicsV CC3V CC2Mi
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602 Digital ElectronicsReview Quest
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15Computer FundamentalsThis chapter
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Computer Fundamentals 607Secondary
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Computer Fundamentals 60915.3.3 Cla
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Computer Fundamentals 611CPURegiste
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Computer Fundamentals 613SelectData
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Computer Fundamentals 615DataInputI
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Computer Fundamentals 6171t RCAddre
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Computer Fundamentals 619as in the
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Computer Fundamentals 6211MUX1RAS1C
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Computer Fundamentals 623CLKCentral
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Computer Fundamentals 6251AddressIn
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Computer Fundamentals 627Row-0+V CC
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Computer Fundamentals 629erasabilit
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Computer Fundamentals 631code conve
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Computer Fundamentals 633AB 3Addres
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Computer Fundamentals 635and RAM-2
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Computer Fundamentals 637A 0 A 1 A
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Computer Fundamentals 63912 34 5678
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Computer Fundamentals 64115.8.2.1 I
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Computer Fundamentals 64315.9.1 Inp
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Computer Fundamentals 645The plasma
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Computer Fundamentals 647the disk s
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Computer Fundamentals 649The read o
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Computer Fundamentals 6512. A certa
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654 Digital ElectronicsFault detect
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656 Digital Electronics16.1.2.1 Ope
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658 Digital ElectronicsI 1456I 2121
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660 Digital ElectronicsClk-11Clk1D1
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662 Digital Electronicsthe clock si
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664 Digital ElectronicsSolution•
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666 Digital Electronics16.6.1 Advan
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670 Digital ElectronicsTriggerFigur
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672 Digital ElectronicsSignalSADC M
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674 Digital Electronics16.12.1.2 Ve
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678 Digital ElectronicsProbe BodyOs
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680 Digital ElectronicsTime BaseOsc
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682 Digital ElectronicsThe resoluti
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684 Digital ElectronicsI/PSamplerLP
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686 Digital ElectronicsReferenceOsc
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688 Digital ElectronicsFrequencyCon
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690 Digital Electronicssynthesizer
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692 Digital Electronicsto indicate
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694 Digital Electronics16.17.2.4 Cl
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696 Digital Electronicshaving a sam
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698 Digital Electronicsthe monitor
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700 Digital Electronicsetc., are th
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704 Digital Electronics(c) accuracy
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Index1’s complement 5, 610’s co
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Index 709A/D converter terminology
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Index 711Binary-to-hex conversion 1
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Index 713CoolRunner 347-8Counter ty
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Index 715Encoder 280-3EPROM 612, 62
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Index 717Hybrid computer 608Hystere
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Index 719Logic gates (Continued)NAN
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Index 721Multivibrator 357-71astabl
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Index 723Power supply decoupling 14
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Index 725Serial-in serial-out shift
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Index 727UP/DOWN counters 425-6US A
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