ai Stevenson I, 23rd Vice President of the United States (1893-1897), was born in Christian County.

See also

National Register of Historic Places listings in Christian County, Kentucky

References

External links
 Community Data and Relocation Info
 Economic Development Council- Hopkinsville/Christian County
 Chamber of Commerce- Hopkinsville/Christian County
 WHVO-AM (Local Radio Station)
 History of Christian County
 
 

 
Category:Kentucky counties
Category:1797 establishments in Kentucky
Category:Clarksville metropolitan area
Category:Populated places established in 1797 Hamming weight

The Hamming weight of a string is the number of symbols that are different from the zero-symbol of the alphabet used. It is thus equivalent to the Hamming distance from the all-zero string of the same length. For the most typical case, a string of bits, this is the number of 1's in the string, or the digit sum of the binary representation of a given number and the ℓ₁ norm of a bit vector. In this binary case, it is also called the population count, popcount, sideways sum, or bit summation.

History and usage 
The Hamming weight is named after Richard Hamming although he did not originate the notion. The Hamming weight of binary numbers was already used in 1899 by James W. L. Glaisher to give a formula for the number of odd binomial coefficients in a single row of Pascal's triangle. Irving S. Reed introduced a concept, equivalent to Hamming weight in the binary case, in 1954.

Hamming weight is used in several disciplines including information theory, coding theory, and cryptography. Examples of applications of the Hamming weight include:
 In modular exponentiation by squaring, the number of modular multiplications required for an exponent e is log2 e + weight(e). This is the reason that the public key value e used in RSA is typically chosen to be a number of low Hamming weight.
 The Hamming weight determines path lengths between nodes in Chord distributed hash tables.
 IrisCode lookups in biometric databases are typically implemented by calculating the Hamming distance to each stored record.
 In computer chess programs using a bitboard representation, the Hamming weight of a bitboard gives the number of pieces of a given type remaining in the game, or the number of squares of the board controlled by one player's pieces, and is therefore an
ai Stevenson I, 23rd Vice President of the United States (1893 - 1897), was born in Christian County. 

 See also 

 National Register of Historic Places list in Christian County, Kentucky 

 References 

 External radio link 
  Community Data and Relocation Info 
  Economic Development Council- Hopkinsville / Christian County 
  Chamber of Commerce- Hopkinsville / Christian County 
  WHVO - AM (Local Radio Station) 
  History of Christian County 
 
 

 
 Category: Kentucky counties 
 Category:1797 administration in Kentucky 
 Category: Clarksville metropolitan sphere 
 Category: Populated places established in 1797 Hamming system of weights 

 The Hamming weight of a string is the act of symbols that are different from the zero - symbol of the rudiment used. It is thus equivalent to the Hamming distance from the all - zero string of the like length. For the most distinctive case, a chain of act, this is the number of 1's in the string, or the digit union of the binary representation of a given number and the ℓ₁ norm of a spot vector. In this binary case, it is also called the population count, popcount, sideways sum, or moment summation. 

 History and usage 
 The Hamming weight is named after Richard Hamming although he did not originate the notion. The Hamming weight of binary issue was already used in 1899 by James W. L. Glaisher to give a formula for the number of odd binomial coefficients in a single row of Pascal's triangle. Irving S. Reed introduced a concept, equivalent to Hamming system of weights in the binary case, in 1954. 

 Hamming weight is use in respective disciplines including information theory, coding theory, and cryptography. Examples of application of the Hamming weight include: 
  In modular exponentiation by squaring, the number of modular multiplications required for an advocate e is log2 e + weight(e). This is the reason that the public key value e used in RSA is typically chosen to be a number of gloomy Hamming weight. 
  The Hamming weight determines path lengths between node in Chord distributed hash tables. 
  IrisCode search in biometric databases are typically enforce by calculating the Hamming distance to each stored criminal record. 
  In computer chess course of study using a bitboard representation, the Hamming system of weights of a bitboard gives the act of pieces of a establish type persist in the game, or the number of squares of the board controlled by one actor's pieces, and is therefore an
ai Dtevenson I, 23rd Vice Presldent of the Unijee Statxs (1893-1897), was born in Christian County.

See also

Natmonao Reguster of Historic Placds listinhs in Cheistman County, Kenturiy

Refercuces

Esbernan links
 Communijy Data and Selocation Infm
 Dclnomic Development Council- Hopkinsvylle/Chroshian County
 Chwmbeg jf Ckmmerce- Hopkinsville/Christian Counfy
 WHVO-EM (Local Radio Xtation)
 History of Christiwn Clunty
 
 

 
Category:Kejtucky counjjes
Sqtegory:1797 estaclishments in Kentucky
Dategory:Clarksville metropolitav arec
Category:Pokboatfg places esvablisred in 1797 Hammlmg weicht

The Namming weight of a wtring is the number mf symbols that arg differend yrom the zero-symbol od rhe anphatet jwed. It ix fhus eeuitalent to tge Hamming eistance from the akl-svto string of the swmq length. For the most typical case, a stging of bits, this is the nunber of 1's in the strijg, or the digit sum of the binary representation of a givet numuef aue the ℓ₁ nlrm of a bit vector. In this binary case, it is zlxo called the poiulation count, popvokny, sideways sum, or bic shmmation.

History anf usage 
The Yamming wtight is named after Richard Hamning althougk hw did not originatz the notion. The Hammong weight of binary nuobera was alreafy used ih 1899 by James W. L. Guaixhar to give a formula for tre number of pdd binumiak coefsicients ij a sltgle row of Pascal'd tricngle. Irving S. Geed introduced a concept, equivekent to Hammonc wvight in che bikary case, in 1954.

Haiming weight ix used nn sevdral disciilines inrluding infowmation theorf, coding theocy, and crrptotrapyy. Examoues of applicayions of nht Hamming qeight include:
 In kodolzr exponentiatiin vy squaring, the nuobew lf mjgular multipnicagiovx reqjired for ak ebponrnt e is log2 e + weigvt(e). Fhis is the reason tmat the poblic key value e used in RSA is typicalpy chmsei to br a number of low Hamming weight.
 Fhe Hammijg reight deteriinew path lengtks between nodes in Chord distributed hawh tables.
 IrisCodg lookups in biometrie catabases ace typycally im[lemented by calcularing the Hamming cistance to each storsd recmrd.
 Ij computer chess programs using a bitboard representation, the Hamming weitht of a bitboard fivex the nbmbzr of pyeced of a given type remaining in the game, or the nnmber of sxucres of the board controlled ny one player's kieces, and is therefore an
ai Stevenson I, 23rd Vice President of States was born Christian County. See Places in Christian County, References External links Data and Relocation Info Economic Development Hopkinsville/Christian County Chamber of Commerce- Hopkinsville/Christian County WHVO-AM (Local Radio Station) History of County Category:Kentucky counties Category:1797 establishments in Kentucky Category:Clarksville metropolitan area Category:Populated places established 1797 weight Hamming of a string is the number of symbols that are different from the zero-symbol of the used. It is thus equivalent to the Hamming from the all-zero string the same length. For the typical a string bits, is number of 1's the string, or the digit sum of the binary representation of a given number and the ℓ₁ of a In this case, is called the population sideways sum, or bit summation. History Hamming weight is named after Richard Hamming although did not the notion. The Hamming weight of numbers was already used in 1899 by James L. Glaisher to give a formula for the number of odd binomial coefficients in a of Pascal's triangle. Irving Reed introduced a equivalent Hamming in binary case, 1954. Hamming weight is used in several disciplines including information theory, theory, and cryptography. Examples of applications of the Hamming weight modular by squaring, the of modular multiplications required an e is log2 e This the public value used in RSA is chosen to be a number low Hamming weight. The between nodes in Chord distributed hash tables. IrisCode in biometric databases are typically implemented by the Hamming distance to each stored record. In computer chess programs using bitboard representation, weight of a bitboard gives the number of of a given type in the game, or the number of squares of board by one pieces, and is an
ai Stevenson I, 23rd Vice PresideNt of the UniTed StAteS (1893-1897), waS bOrn iN ChrIstian County.

SeE Also

national Register of HistOric PLaCEs liSTiNgs in christiAN COUNty, keNtUckY

REFeRenceS

ExTernal lInks
 CommunIty daTa and RelocatIOn info
 EconomIc DEvelopment CoUncIl- HopkInSviLLe/ChrIstIan CoUnty
 ChAMber of commerce- HOpKInsvilLE/ChristIAN COuntY
 WHVO-AM (Local Radio sTaTIon)
 History of ChRistiaN COUnTY
 
 

 
catEgoRy:Kentucky CoUntieS
categorY:1797 EsTABLisHMents in KentucKy
Category:CLArkSville MeTroPOlitan Area
CAtEGorY:Populated pLaceS establisHed in 1797 HAMming weIGht

The HAmming WeiGht Of a sTRiNg Is tHe NUmbER oF syMBolS that are DiFfErent From THE ZEro-sYmbOl of The alPhabet used. It iS thUs eqUIvaLent tO the HAmmiNg DistaNce froM the aLl-Zero string of the Same Length. For The MoSt tYpIcal cASe, a strIng Of bIts, this Is the nuMBer Of 1'S IN ThE string, or the digit sUm OF ThE binary rEpreseNTaTiON of a giveN nUmbEr anD THe ℓ₁ noRm of A BiT vector. IN this bINaRy Case, it iS aLso calLeD thE poPulatIOn coUnt, popCount, sidEways SUm, or bit summatiON.

History and usAGe 
tHE HAMminG weIght is named AfteR richArd HAMmIng ALthouGh he dId NOt ORiginate the notion. ThE HAmming WeighT of binary numbErs was alreADY Used in 1899 by jameS w. L. gLaisher to give a FormuLa for the nuMBer of odd BinomIal coeffIcients in A SIngle row Of PAscAl's TriANGlE. Irving S. Reed iNTRoduCeD a concePt, eQuivaleNt tO HaMmiNg wEiGht in the bInary casE, iN 1954.

HAmMiNg wEight IS used in sEvEraL dIscIplinES incluDing iNforMaTiON thEory, codINg THEory, AnD cRyptOgrApHy. ExaMpleS Of aPplicatIons of the hamMIng wEiGhT includE:
 In modular expOnEntiation bY sQuaRing, thE NUmber of mOdular multiplications reQUired foR an ExponEnt e Is log2 e + weiGht(E). This iS thE Reason That thE publIc Key VALue e uSED iN RSa iS typically CHOseN to be A nUmbeR of low HAmming weight.
 The HamMIng Weight determiNes Path LENgThs BEtWEen NoDEs iN cHord distributed Hash tables.
 irISCOde lookups IN biOmEtric daTabases Are tyPIcally iMplementeD by calculAtIng tHE hamMing distanCe to each Stored recORd.
 In cOMpUter cHesS progrAmS usIng a bItboarD RepResenTation, ThE HammiNg weiGhT of a bitbOard gives the number of pieCes of a Given TypE remaininG in THe gAme, or the nUmbeR of squares Of tHe bOard cOntROlled By onE PlAyeR'S piecEs, anD Is therefoRE aN
ai Stevenson I, 23rd VicePresidentof th e U nit ed  Sta tes(1893-1897), w a s bo rn in Christian County .

Se ea lsoNa tiona l Regis t er o f H is to ric  P l ac es li sti ngs inChristianCou nt y, KentuckyRe ferences
Ext ernal links Co mmunit yDat a  andRel ocati on Inf o 
 Econ omic Deve lo p ment C o uncil-H o pk insv ille/Christian Co u nt y 
 Chamber of C ommerc e- Ho p k ins vil le/Christi an  Coun t y
 WHVO - AM ( L oca l  Radio Statio n)
 History ofChrist ia n C o unty

 


C a teg ory:Kentuck y co unties
Ca tegory : 1797 es t ablishm ents i n K ent ucky Ca te gor y: C lar k sv ill e  me tropolit an  a rea
C ateg o r y : Popu lat ed p laces  establishedin1797 Ham mingweigh t

T he  Hamm ing we ightof  a string is th e nu mber of s ymb ol s t ha t are differ ent  fr om thezero-sy m bol  o f t he  alphabet used. It  i s th us equiv alentt oth e  Hamming  d ist ance f rom t he a l l- zero str ing of th esame le ng th. Fo rthe  mo st ty p ical  case,  a strin g ofb its, this is t h e number of 1 ' si n  t h e st rin g, or the d igit sumof t h ebin a ry re prese nt a ti o n of a given number  a nd the  ℓ₁ n orm of a bitvector. In t h is binar y ca s e, it is also cal led t he populat i on count , pop count, s ideways s u m , or bit  su mma tio n.H is tory and usag e 
The  H ammingwei ght isnam edaft erRi chard Ham ming alt ho ug hhe  di d not originat ethe  n oti on. T h e Hamm ing w eigh tof bin ary num b er s wasal re adyuse din 18 99 b y  Ja mes W.L. Glaish ert o gi ve  a  formul a for the num be r of odd b in omi al coe f f icientsin a single row of Pasc a l's tri ang le. I rvin g S. Reed  in troduc eda  conce pt, eq uival en t t o Hammi n g  w eig ht  in the bi n a rycase,  i n 19 54.

Ha mming weight is us e d i n several dis cip line s in clu d in g  in fo r mat i o n theory, codin g theory,an d  c ryptograph y . E xa mples o f appli catio n s of th e Hamming  weight i nc lude :  In  modular e xponenti ation bys quari n g,  thenum ber of  m odu lar m ultipl i cat ionsrequir ed  for a n exp on ent e is  log2 e + weight(e). Th is isthe r eas on that t hep ubl ic key va luee used inRSA  is  typi cal l y cho sent obea  numb er o f  low Hamm i ng  we i g ht .
 The Hamm i n g  we ightdet e rmines  pat h lengths between nodes in Chord  dis t r ibu ted hash  t ables.
 IrisCo delo o k ups in b io metric data bases ar et ypica lly im plemen ted byc a lc u lating  the  Ha mming dis tan ce to each  s to r ed rec ord. 
In com puterc hess p rograms using abitbo a r d rep r ese ntati on , the H a mmin g weight o f a bitboar d give s th e num ber ofpi eces o f a  g iven typer emainingin th e game,  o r th e n umberof s q u aresof t he  bo ard contr o l le d  b yo neplay er'spi eces , and ist herefore  an 
ai Stevenson_I, 23rd_Vice President of the_United States_(1893-1897),_was born_in_Christian County.

See also

National_Register of Historic_Places listings in Christian_County, Kentucky

References

External links
_Community_Data and Relocation Info
 Economic Development Council- Hopkinsville/Christian County
 Chamber of Commerce- Hopkinsville/Christian County
_WHVO-AM_(Local Radio_Station)
_History_of Christian County
 
 

_
Category:Kentucky counties
Category:1797 establishments in Kentucky
Category:Clarksville_metropolitan area
Category:Populated_places established in 1797 Hamming weight

The Hamming weight_of_a string is_the number of symbols that are different from the_zero-symbol of the alphabet used. It_is thus equivalent_to_the_Hamming distance from the_all-zero string of the same length._For the most typical case, a_string of bits, this is the number_of 1's in the string, or_the digit sum of the_binary representation_of a given number and_the ℓ₁ norm_of a_bit vector. In_this binary case, it is also_called the population_count, popcount, sideways sum, or bit_summation.

History_and usage 
The_Hamming_weight_is named_after Richard Hamming_although_he did_not_originate the notion. The Hamming weight_of_binary numbers was already used in 1899_by James W. L._Glaisher_to give a formula_for the number of odd_binomial coefficients in a single row_of Pascal's_triangle. Irving_S. Reed introduced a concept, equivalent to Hamming weight in the_binary case, in 1954.

Hamming weight is_used in several disciplines_including information_theory,_coding theory, and_cryptography._Examples of_applications of the Hamming weight include:
 In_modular exponentiation_by squaring, the number of modular_multiplications required for an_exponent_e is log2 e + weight(e)._This is the reason that the_public key value e used_in_RSA_is typically chosen to be_a number of low Hamming weight.
_The Hamming weight_determines path lengths between nodes in Chord_distributed_hash tables.
 IrisCode lookups in biometric_databases_are typically implemented by calculating the_Hamming_distance_to each stored record.
 In_computer chess programs using a bitboard_representation, the Hamming weight of a bitboard gives the_number of pieces_of a given type remaining_in_the_game, or the number of squares of the board controlled_by one_player's pieces, and_is therefore an