數(shù)電課件數(shù)字邏輯

Chapter2

Numbersystemsandcodes

Codesindigitalsystem22.8BinaryCodesforDecimalNumber（十進(jìn)制數(shù)的二進(jìn)制編碼）BinaryCodes

Coding:istonameathingorastate.BinaryCode:isasetofn-bitbinarystringswhichareusedtorepresentdifferentthingsorstates.“編碼”是對(duì)一個(gè)事件或狀態(tài)“命名”.“二進(jìn)制編碼”就是用二進(jìn)制串對(duì)事件或狀態(tài)命名.CodeWord:isaparticularcombinationofnbit-values.“碼字”是指有確切含義的特定的n位組合.2.8BinaryCodesforDecimalNumber（十進(jìn)制數(shù)的二進(jìn)制編碼）

n-bitbinarycodescanrepresentatmost2n

thingsorstates.TorepresentNstates,atleast㏒2Nbitsareneeded.Ceilingfunction（上限函數(shù)）BinaryCodes4Torepresenttendigits(0~9),atleast

bitsareneeded.BinaryCodesforDecimalNumberSomeofthecommondecimalcodes:(Table2-9)BCD(8421)2421Excess-3（余3碼）Biquinary（二五混合碼）1-out-of-10（10中取1碼）2.8BinaryCodesforDecimalNumber（十進(jìn)制數(shù)的二進(jìn)制編碼）5BinaryCodesforDecimalNumberBCD(binary-codeddecimal)47.9610=()8421BCD

01000111.100101102.8BinaryCodesforDecimalNumber（十進(jìn)制數(shù)的二進(jìn)制編碼）---encodes0~9bytheir4-bitbinaryrepresentation---weighted(加權(quán)碼)---Ithas10validcodewordsand6invalidcodewords.

6BCD(binary-codeddecimal)

BCDaddition:similartoadding4-bitunsignedbinarynumbers.Ifaresultexceeds1001,itmustbecorrectedbyadding6.4+)590100+）010110019+)5141001+)01011110+)0110101009+)8171001+)100010001+)011010111BinaryCodesforDecimalNumber2.8BinaryCodesforDecimalNumber（十進(jìn)制數(shù)的二進(jìn)制編碼）72421(binary-codeddecimal)

BinaryCodesforDecimalNumber2.8BinaryCodesforDecimalNumber（十進(jìn)制數(shù)的二進(jìn)制編碼）plementin

自反碼:各位取反，正好是十進(jìn)制對(duì)9的自補(bǔ)碼。---weighted(加權(quán)碼)---Ithas10validcodesand6invalidcodes.8Excess-3(binary-codeddecimal)

BinaryCodesforDecimalNumber2.8BinaryCodesforDecimalNumber（十進(jìn)制數(shù)的二進(jìn)制編碼）---余3碼---Itsdigitisnotweighted;plementing;---8421code+“0011”.Examples:useBinarycodesfordecimalnumberA=19468421code:A=00011001010001102421code:A=0001111101001100Excess-3code:A=0100110001111001

Binarycodesfordecimaldigits

---十進(jìn)制數(shù)的二進(jìn)制編碼Binarycodesfordecimaldigits

---十進(jìn)制數(shù)的二進(jìn)制編碼11Biquinary(binary-codeddecimal)

BinaryCodesforDecimalNumber2.8BinaryCodesforDecimalNumber（十進(jìn)制數(shù)的二進(jìn)制編碼）---二五混合碼

---7-bits;twohotcode;5bitsisonehotcode---Error-detectingproperty!

121-out-of-10

(binary-codeddecimal)

BinaryCodesforDecimalNumber2.8BinaryCodesforDecimalNumber（十進(jìn)制數(shù)的二進(jìn)制編碼）---10中取1碼

---Onehotcode:Onlyonelineishot!Codesincontrolsystems數(shù)碼管工作原理15Otherdecimalcodes

2.8BinaryCodesforDecimalNumber（十進(jìn)制數(shù)的二進(jìn)制編碼）ASCIIcodes128Keyboardsigns,7-bitHowareyou!100100011011111110111010000011000011110010110010101000001111001110111111101010100001ASCIIcodes182810=()8421=()2421=()excess-3=()biquinary=()1-out-of-1000101000001011100101101101001001001000

Payattentiontothedifferencebetweenbinarycodesandbinarynumbers:2810=(00101000)8421=(11100)2BinaryCodesforDecimalNumber2.8BinaryCodesforDecimalNumber（十進(jìn)制數(shù)的二進(jìn)制編碼）Codesforlowpowerdesign

Whenbinarycodedatachanged,transitionstatesmaybehappened

：0111—10000111—0011—0001—0000---10000111—1111---1011---1010---1000

Transitionstatesmaycauselargepowerconsumptionanddataerror202.9Graycode（葛萊碼）——

一種可靠性編碼Characteristic:Onlyonebitchangesbetweeneachpairofsuccessivecodewords.012345670000010100111001011101110000010110101101111011003-bitbinarycodeandGraycodeBinaryCodeGrayCodeDecimalNumber21Characteristic:Onlyonebitchangesbetweeneachpairofsuccessivecodewords.Mechanicalencodingdisk2.9Graycode（葛萊碼）——

一種可靠性編碼22HowtoconstructaGraycode?2.9Graycode（葛萊碼）——

一種可靠性編碼Method:FrombinarynumbertoGraycodeThewidthissame;TheMSBissame;Compareeachbitwithitsleftone:Samebecodeto0;Differbecodeto1.Examples:

binarynumber:1001001001100011Graycodes:1101101101010010Graycodes24

Examples(Graycode):

1-bit012-bit000111103-bit0000010110101101111011004-bit0000000100110010011001110101010011001101…HowtoconstructaGraycode?2.9Graycode（葛萊碼）——

一種可靠性編碼25Binary

BnBn-1···Bi+1Bi···B1B0 Gray

GnGn-1···Gi+1Gi···G1G0

Gn=Bn，Gi=Bi+1⊕Bi

Example.

(0101)2

(0111)GrayBinary-to-GrayCode26

Gray

GnGn-1···Gi···G1G0

Binary

BnBn-1···Bi+1Bi···B1B0

Bn=Gn,Bi=Bi+1⊕GiExample. (01 0 1)Gray

(01 1 0)2Gray-to-BinaryCode27Example. (100010101001)Excess-3=（ ）Gray

（1000

1010

1001）

Excess-3

（576）10

（1001000000）2

（1101100000）Gray

28Example. (10000111.11)2=( )BCD (10000111.11)2(135.75）10

(000100110101.01110101)BCDExample.

（21）10=()Gray=()Excess-3

（21）10=（10101）2=（11111）Gray

（21）10=（01010100）Excess-3

Parallelwayusen-linetotransmitann-bitscodewords;transmitann-bitscodewordsinonetimeperiod;Codestransmitwayindigitalcircuit29ComputerPrinter10110010t0t1Serialway

useonelinetotransmitann-bitscodewords;transmitann-bitscodewordsinntimeperiod;CodestransmitwayindigitalcircuitComputer10110010t0t1t2t3t4t5t6t7ModemSummaryofChap.2ConversionofnumbersystemsRepresentationofnegativenumbers

s-m、two’scomplement、one’scomplementAdditionoftwo’scomplementcomplementbits+1(subtraction)、overflowBinarycodesofdecimalnumbers

BCDcode、2421code、excess-3codeGraycode32Homework2.332.35Supplementary:

WritetheGraycodesforthefollowingbinarycodes.

（1）1001（2）1101000111Chap2Homework（P74～78）2.1(a)(d)(e)(i)(j)2.2(e)(f),2.3(e)2.5(e)(i)(j)2.6(a)(b)(h)Supplementary: 1.2510=?2,

105.20710=?2(errorε<0.05

)2.7(b)(d),2.8(b)(d)2.11,2.12,2.252.33,2.35Supplementary:WritetheGraycodesforthefollowingbinarycodes.（1）1001（2）110100011134Chapter3DigitalCircuitsTheelectricalaspectsofdigitalcircuits

（數(shù)字電路中的電氣知識(shí)）353.1LogicSignalsandGates（邏輯信號(hào)與門電路）BasiclogicgatesORgateTruthtable（真值表）000010100111ABZZ=A·BANDgateNOTgateZ=A+BZ=A’000011101111ABZAZ011