Upload
others
View
2
Download
0
Embed Size (px)
Citation preview
1
Profa. Léia Bernardi Bagesteiro (CECS) E-mail: [email protected]
Instrumentação Biomédica
•! Sensores e Transdutores •! Posição, Deslocamento, Temperatura •! Exemplos
LabVIEW
Principais Transdutores Resistivos
Exemplos:
Fornecem uma resistência em resposta ao estímulo Extensômetros:
•! Deformação linear
Extensômetros:
•! Circuitos em ponte •! Compensação para efeitos de temperatura •! Conveniente para pequenas variações de temperatura
Fotoresistores:
•! Intensidade luminosa
2
Transdutor Potenciométrico
•! Fornecem uma resistência em resposta a posição do cursor
Transdutor Potenciométrico
•! Função de Transferência Teórica
Potenciômetros rotativos:
•! Respondem a posição angular do cursor
Potenciômetros lineares:
•! Respondem a posição linear do cursor
Tipos de Potenciômetros: Exemplos aplicações:
•! Goniômetro para medição de posição articular
3
TRANSDUTORES
•! Transdutores de Temperatura –!Termopares
–!Resistance-Temperature Detectors (RTD)
–!Termistores
Termopares - Princípio
Conexão (ou soldagem) de 2 fios
Operação normal, junção fria colocada em “banho frio” Termopares
•! Type K : Chromel-Alumel
•! Type J : Iron-Constantan
•! Type E : Chromel-Constantan
•! Type N : Nicros-Nisil
•! Type T : Copper-Constantan
•! É importante notar que termopares medem a diferença de temperatura entre dois pontos, e não a temperatura absoluta.
Termopares Termopares
4
Termopares – aplicações
•! Para medições de temperatura em intervalos grandes, até 1800 K.
Exemplo: Type K : Chromel-Alumel (-190!"#$%#1260!") Type J : Iron-Constantan (-190!"#$%#760!") Type E : Chromel-Constantan (-100!"#$%#1260!") •! Para medições em intervalos de temperatura entre 0-100ºC
com alta precisão (0.1ºC), mais indicado RTD e termitores.
Magnitude da E térmica
Onde: c e k = constantes dos materiais do termopar
T1 = temperatura da junção “quente”
T2 = temperatura da junção “fria” ou junção de “referência”
)()( 2
2
2
121 TTkTTcE !+!=
Exemplo Termopar (E2):
UTI Neonatal Tincubadora = 35°C T UTINeo = 23°C Termopar tipo K
Exemplo Termopar (E2):
Exemplo Termopar (E2): Exemplo Termopar (E2):
5
Termoresistivos:
RTD (Resistance Temperature Detectors)
Termistores (PTC e NTC)
RTD (Resistance Temperature Detectors)
Considerações importantes:
RTD (Resistance Temperature Detectors)
PT100 (Platina 100! a 0ºC) •! Função de Transferência Simplificada
RTD (Resistance Temperature Detectors)
Resistance temperature detector (RTD)
Resistance temperature detectors (RTDs), também chamados termômetros de resistência, são sensores de temperatura que apresentam mudança de resistência elétrica conhecida de acordo com a temperatura.
Temperatura Resistência Metal
Idealmente a resistência varia linearmente com a temperatura.
Resistance temperature detector (RTD)
Uma reta aproxima os pontos da curva que representa as temperaturas, T1 e T2, e T0 representa o ponto médio de temperatura.
6
Equação da reta:
R(T) = aproximação da resistência na temperatura T R(T0) = resistência em T0
!o = fração de mudança na resistência por grau de temperatura em T0
!T = T - T0
!
R(T) = R(To)[1+"
o#T] T
1< T < T
2
Resistance temperature detector (RTD) Sensor de temperatura (thin-film gold)
Sensor micro-fabricado
RTD - Exemplos de "
Equação da reta
R2 = resistência em T2
R1 = resistência em T1
)()(
1
12
12
0 TT
RR
TRo
!
!="
Resistance temperature detector (RTD)
RTD – aproximação quadrática
•! Maior precisão na representação da curva R-T em alguns intervalos de temperatura.
R(T) = aproximação quadrática da resistência em T
R(T0) = resistência na temperatura T0
!1 = fração linear de mudança de resistência com temperatura
!2 = fração quadrática de mudança de resistência com temperatura
!T = T - T0
21
2
21 ])(1)[()( TTTTTTRTRo
<<!+!+= ""Platinum
Copper
Tungsten Nickel
Platinum: >> repetitividade, sensibilidade, alto custo Nickel: << repetitividade, sensibilidade, menor custo
7
RTD – sensibilidade
•! Sensibilidade é dada pelo valor de !o –! Platinum – 0.004/ °C
–! Nickel – 0.005/ °C
•! Então, para 100! platinum RTD, uma variação de 0.4 ! ocorreria caso a temperatura tivesse variação de 1°C
RTD – tempo de resposta
•! Geralmente entre 0.5 to 5 segundos
•! O tempo de resposta é devido principalmente a condutividade térmica para trazer o sistema para o equilibrio térmico com o ambiente.
Termistor
•! Sensor de resistência Semicondutora
•! Diferente dos metais, termistores respondem negativamente a temperatura e seu coeficiente de resistência é da ordem de 10 vezes mais que a platina ou o cobre.
•! Temperatura resistência semicondutora
•! Símbolo
Termistor
•! Sensor de resistência Semicondutora
Termistor: resistência vs temperatura Termistor: resistência vs temperatura
Coeficiente ~ 5%/°C na temperatura corporal (37°C)
8
Termistor: resistência vs temperatura
COMPARATIVO Exemplo Termistor
(E5):
Fig.6.6a
Termistores (Thermally Sensitive Resistor) – PTC e NTC
Considerações importantes:
Termistores (Thermally Sensitive Resistor) – PTC e NTC
•! Não são lineares;
•! Sensibilidade elevada (típica 3% a 5% por ºC) com faixa de operação típica de -100ºC a +300ºC;
•! Disponibilidade variada de tamanhos (0,005’’ a 0,05’’ de diâmetro) e formas;
•! Faixa de tolerância de fabricação também varia (tipicamente de 5 a 20%)
Termistores (Thermally Sensitive Resistor) – PTC e NTC Termistores (Thermally Sensitive Resistor) – PTC e NTC
9
Termistores (Thermally Sensitive Resistor) – PTC e NTC
•! Função de Transferência para o NTC
Modelo de 2 ou 3 parâmetros
Termistores (Thermally Sensitive Resistor) – PTC e NTC
•! Linearidade – ganho – custo – faixa de operação
Termistores (Thermally Sensitive Resistor) – PTC e NTC Temperatura por Efeitos Mecânicos (não resistivo)
•! Efeitos Mecânicos:
Termômetros de expansão de líquidos em bulbo de vidro
Termômetros
Expansão de líquidos em bulbo de vidro
Termômetros Bimetálicos
Princípio: duas tiras de metal com coeficiente de dilatação térmica diferentes.
10
TRANSDUTORES
•! Resistivo de posição
•! Deslocamento
•! Resistivo sensível a força
Transdutor Resistivo - posição
Distância
Sinal Elétrico
Transdutor Resistivo posição
ToV
RR
RV
21
2
+=
2R
1R
Transdutor Resistivo - posição
Exemplo Transdutor Resistivo (E6A):
Encontrar a resolução de um transdutor de resistência variável em que: RT = 1000! Nº voltas = 100
Exemplo Transdutor Resistivo (E6):
Fig.6.8b
11
Transdutor Resistivo – circuito em ponte TRANSDUTORES
•! Resistivo de posição
•! Deslocamento
•! Resistivo sensível a força
LVDT – Linear Variable Displacement Transducer
•! Princípio: modulação do sinal de excitação.
•! Consiste na variação de sinal entre primário e secundário dependendo do posicionamento no tubo (núcleo).
LVDT – Linear Variable Displacement Transducer
LVDT – Linear Variable Displacement Transducer
Eixo no centro
V1 = V2
Vo = 0
LVDT – Linear Variable Displacement Transducer
12
Eixo movendo
em direção a S1
V1 > V2
Vo aumenta
LVDT – Linear Variable Displacement Transducer
Eixo movendo
em direção a S2
V2 > V1
Vo diminui
LVDT – Linear Variable Displacement Transducer
LVDT – Linear Variable Displacement Transducer
LVDT
LVDT Linear Variable
Differential Transformer
http://www.pages.drexel.edu/~pyo22/mem351-2004/lecture04/pp062-073lvdt.pdf
An LVDT is used as a sensitive displacement sensor: for example, in a cardiac assist device or a basic research project to study displacement produced by a contracting muscle.
TRANSDUTORES
•! Resistivo de posição
•! Deslocamento
•! Resistivo sensível a força
FRS – Resistor Sensor de Força (Force Sensitive Resistors )
13
FSRs – o que são? •! Force Sensitive Resistors ou Pressure Sensors
•! Tipo de resistor no qual a resistência muda quando uma força ou pressão é aplicada
•! A resistência é inversamente proporcional a força aplicada
[ 1. Resistance (Ohms) vs. Force (g) for an Interlink FSR ]
O limiar, ou ”ponto limite de força", que modifica R encontra-se entre 1M e 50-100 K
FSRs – como funcionam:
•! Partícula do tamanho na escala de microns
•! Formulado para reduzir dependência a temperatura, e melhorar propriedades mecânicas
•! Força na superfície causa o contato das partículas no eletrodo de condução modificando a resistência
•! FSRs consistem de polímero condutivo piezoresistivo, que modifica a resistência de maneira conhecida de acordo com a aplicação de força na sua superfície
•! Usualmente disponível entre filmes sensitivos
•! Filme: 1) condutor elétrico e 2) não-condutor de partículas suspensas na matriz.
FSRs – como funcionam:
FSRs Características •! Fabricado em camada simples, arrays 2D e outras
diversas formas
•! Detecta pequenas forças. Reconhece a magnitude da força e também diferenças na maneira de tocar
•! 3 componentes principais da montagem do FSR: –! Substrato para conexão
–! FSR
–! Microcontrolador
•! Não é sensivel a vibração ou calor
FSRs Características •! Resposta na ordem de 0-2kg, com aplicações
comuns na interface humana.
force vs. conductance (1/resistance)
14
FSRs Características Simple FSRs and Arrays
Parameter
Value
Conditions
Size Range
Max = 20" x 30" (51 x 76 cm) Min = 0.2" x 0.2" (0.5 x 0.5
cm)
Any shape
Device Thickness
0.008" to 0.050" (0.20 to 1.25 mm)
Force Sensitivity Range
30g to 10kg
Pressure Sensitivity Range
0.45psi to 150psi (0.03 kg/cm2 to 10 kg kg/cm2)
30g to 10kg 1 cm2 actuator
Part to Part Force Repeatability
± 15% full scale
For typical part with consistent actuation
Single Part Force Repeatability
± 2% full scale
FSRs Características Force Resolution
Better than 0.5% full scale
Break Force
30 to 100g (1 to 3.5 oz) typical
Dependent on probe size/shape
Stand-Off Resistance
> 1M
Switch Characteristic
Essentially zero travel
Device Rise Time
1-2msec (mechanical)
Lifetime
>10 million actuations
Use Temperature
-30ºC to 170ºC
High temperature adhesives
Maximum Current
1 mA/cm2 of applied force
Sensitivity to Noise/Vibration
Not significantly affected
EMI/ESD
Passive device -- not damaged by EMI or ESD
Lead Attachment
Standard flex circuit techniques
See TechNote
!
FSRs Tipos: •! Sensor Básico – ponto simples (circular)
•! Array Simples – Dois ou mais PS3s em um substrato com uma linha de condução comum, e linhas separadas para cada sensor
•! Matriz – linhas ou colunas
•! Tira Contínua – até 15m.
FSR - Fornecedores – Fabricantes:
•! Interlink electronics, http://www.interlinkelec.com/
•! IEE (UK), http://www.steadlands.com/
•! Tekscan, http://www.tekscan.com/index.html
Referências Bibliográficas
* Instrumentação e Fundamentos de Medidas. V.1 (e V.2). Balbinot e Brusamarello. LTC. 2006 e 2007. * Instrumentation Reference Book. 3rd Ed. – W. Boyes (Ed.) Butterworth and Heinemann. 2003. * Measurement, Instrumentation and Sensors Handbook. J.G.Webster (Ed.) - CRC Press. 1999.
15
Estruturas e Funções do LabVIEW
!"#$$%&'&!()*+,%$&-#&.'-%$&!"#$%&'()&(*+,-(./0&+(
! !"#$%&'(1"&( 2-3#&4&5("5(&+&06)-(736"()&(68',36$9-(6-("'":3;-<(='(631";0-'( '9-( 68&3,-'( &( 2&4>6)-'( 6",-56,;465&#,&( &5( "56( -?&36$6-(,36#'?63&#,&(6-("'":3;-@(! A'43&0&(&5( B'?3&6)'>&&,( 2;+&C( 631";0-( ,;?-( ,68&+6@( 4-#0&3,&( "5(6336D( EF(-"(GF()&(#H5&3-'(4-5(?3&4;'9-(';5?+&'(?636("56(',3;#7()&(,&I,-(&(&'43&0&(&''6(',3;#7(&5("5(#-0-(631";0-(*JKLL(-"(6);4;-#6(6(',3;#7(&5("5(631";0-(&I;',&#,&M(
! NO()&("5(631";0-(B'?3&6)'>&&,(2;+&C((,;?-(,68&+6@(+O("5(&'?&4/2;4-(#H5&3-()&(+;#>6'(-"(4-+"#6'()&')&(-( ;#/4;-()&("5(631";0-( ,&I,-(#"5P3;4-(&(4-#0&3,&(-'()6)-'(?636("5(6336D(GF()&()6)-'<((
! A'43&0&( &5( "5( 631";0-( )&( 5&);)6'@( "5( &I?3&''( QL( 1"&( &'43&0&( )6)-'( &5( "5(631";0-()&(5&);)6'(B<+05C()&(,&I,-(-"(8;#:3;-(B,)5C<((
! NO()&("5(631";0-()&(5&);)6'@("5(AI?3&''(QL(1"&(+O()&("5(631";0-()&(5&);)6'(B<+05C(-"(B,)5C<((
!"#$$%&'&!()*+,%$&-#&.'-%$&!"#$%&'()&(*+,-(./0&+(
! !"#$%&'(1"&( 2-3#&4&5("5(&+&06)-(736"()&(68',36$9-(6-("'":3;-<(='(631";0-'( '9-( 68&3,-'( &( 2&4>6)-'( 6",-56,;465&#,&( &5( "56( -?&36$6-(,36#'?63&#,&(6-("'":3;-@(! A'43&0&(&5( B'?3&6)'>&&,( 2;+&C( 631";0-( ,;?-( ,68&+6@( 4-#0&3,&( "5(6336D( EF(-"(GF()&(#H5&3-'(4-5(?3&4;'9-(';5?+&'(?636("56(',3;#7()&(,&I,-(&(&'43&0&(&''6(',3;#7(&5("5(#-0-(631";0-(*JKLL(-"(6);4;-#6(6(',3;#7(&5("5(631";0-(&I;',&#,&M(
! NO()&("5(631";0-(B'?3&6)'>&&,(2;+&C((,;?-(,68&+6@(+O("5(&'?&4/2;4-(#H5&3-()&(+;#>6'(-"(4-+"#6'()&')&(-( ;#/4;-()&("5(631";0-( ,&I,-(#"5P3;4-(&(4-#0&3,&(-'()6)-'(?636("5(6336D(GF()&()6)-'<((
! A'43&0&( &5( "5( 631";0-( )&( 5&);)6'@( "5( &I?3&''( QL( 1"&( &'43&0&( )6)-'( &5( "5(631";0-()&(5&);)6'(B<+05C()&(,&I,-(-"(8;#:3;-(B,)5C<((
! NO()&("5(631";0-()&(5&);)6'@("5(AI?3&''(QL(1"&(+O()&("5(631";0-()&(5&);)6'(B<+05C(-"(B,)5C<((
!"#$$%&'&!()*+,%$&-#&.'-%$&!"#$%&'()&(*+,-(./0&+(
! !"#$%&'(1"&( 2-3#&4&5("5(&+&06)-(736"()&(68',36$9-(6-("'":3;-<(='(631";0-'( '9-( 68&3,-'( &( 2&4>6)-'( 6",-56,;465&#,&( &5( "56( -?&36$6-(,36#'?63&#,&(6-("'":3;-@(! A'43&0&(&5( B'?3&6)'>&&,( 2;+&C( 631";0-( ,;?-( ,68&+6@( 4-#0&3,&( "5(6336D( EF(-"(GF()&(#H5&3-'(4-5(?3&4;'9-(';5?+&'(?636("56(',3;#7()&(,&I,-(&(&'43&0&(&''6(',3;#7(&5("5(#-0-(631";0-(*JKLL(-"(6);4;-#6(6(',3;#7(&5("5(631";0-(&I;',&#,&M(
! NO()&("5(631";0-(B'?3&6)'>&&,(2;+&C((,;?-(,68&+6@(+O("5(&'?&4/2;4-(#H5&3-()&(+;#>6'(-"(4-+"#6'()&')&(-( ;#/4;-()&("5(631";0-( ,&I,-(#"5P3;4-(&(4-#0&3,&(-'()6)-'(?636("5(6336D(GF()&()6)-'<((
! A'43&0&( &5( "5( 631";0-( )&( 5&);)6'@( "5( &I?3&''( QL( 1"&( &'43&0&( )6)-'( &5( "5(631";0-()&(5&);)6'(B<+05C()&(,&I,-(-"(8;#:3;-(B,)5C<((
! NO()&("5(631";0-()&(5&);)6'@("5(AI?3&''(QL(1"&(+O()&("5(631";0-()&(5&);)6'(B<+05C(-"(B,)5C<((
!"#$%"&'$()*+,"&#$&-,$.."&/&-*01+2".&
!"#$%"&'$()*+,"&#$&-,$.."&/&-*01+2".&
!"#$$%&'&!()*+,%$&
!!"#$%"$ &'($)&"$*#$+,-./0%"$#$ 1.234#"$5+,+$+6,/,$ #$1#78+,$+,-./0%"9$:#,$#$#"7,#0#,9$7,/+,$*/,#;<,/%$=+:>?$*#$%.;,+"$1.234#"$!$5#"-./"#$7%?$%$8#:5@A$$
!!"#$ %"$ 8/B8C:#0#:$ &'($ )&"$ *#$ +,-./0%"$ 5+,+$ 1+D#,$%5#,+3%4#"$ 7%?.2"$ 7%?%$ :#/;.,+$ #$ #"7,/;+$ *#$*/1#,#2;#"$;/5%"$*#$*+*%"A$$
!!"#$ :%EC:#0#:$ &'($ )&"$ *#$ +,-./0%"$ #$ 1.234#"$+0+23+*+"$5+,+$7%2;,%:+,$$%5#,+34#"$/2*/0/*.+/"$*#$+,-./0%"A$$
!"#$%&"'()#*%+,-**&'
!!"#$#%&'( )'( #"*+,-.&( /0122( 3.4( 3'"$#(5."4#$#67.8(
!9&+#:4';$'( +$,:,<#4( !/=( ';$"'( 3.:+;#&( '( >?@(AB(C2?>(';$"'(:,;D#&(
!A( C#EF2>G( H.&&+,( F2&( *+'( 'I'3+$#4( '&&#&(5+;6J'&(.+(3.;3#$';#4(&$",;K&(
!"#$%&"'()#*%+,-**&'
!!"#$#%&'( )'( #"*+,-.&( /0122( 3.4( 3'"$#(5."4#$#67.8(
!9&+#:4';$'( +$,:,<#4( !/=( ';$"'( 3.:+;#&( '( >?@(AB(C2?>(';$"'(:,;D#&(
!A( C#EF2>G( H.&&+,( F2&( *+'( 'I'3+$#4( '&&#&(5+;6J'&(.+(3.;3#$';#4(&$",;K&(
!"#$%&"'()#*%+,-**&'
!!"#$#%&'( )'( #"*+,-.&( /0122( 3.4( 3'"$#(5."4#$#67.8(
!9&+#:4';$'( +$,:,<#4( !/=( ';$"'( 3.:+;#&( '( >?@(AB(C2?>(';$"'(:,;D#&(
!A( C#EF2>G( H.&&+,( F2&( *+'( 'I'3+$#4( '&&#&(5+;6J'&(.+(3.;3#$';#4(&$",;K&(
!!"#$%& $'&()"%*+,-%%$&.#/%!" #$%&"&''&(")*"+,"-*".$".&.+/"0,12'34+/5"6+'1&7&"$//$/".&.+/"$"$/4'$8$"$1",1"&'9,38+:"
! .'"0*$& 12$'& .#/%!" #$%&" .36$'$07$/" 73#+/" .$" .&.+/" ;/7'30%5"0,1$'345" <++=$&0>" $" $/4'$8$" $//&" 306+'1&?@+" $1" ,1"&'9,38+5" ,73=3A&0.+" ,1" 4&130B+" ;#&7B>:" " C/7&" 6,0?@+" #+.$"304=,3'"8D'3+/"7$'130&3/".$".&.+/"/$"0$4$//D'3+:"
! 3""*4&$'&()"%*+,-%%$&($"#25!"2",1&"6,0?@+"9,$"6+'1&7&",1"&''&(".$".&.+/"$1",1&"/7'30%"9,$"#+.$"/$'"$/4'37&"$1",1"&'9,38+".$".&.+/:"
! 6'27*$%2*$%& ($"#25!" 6,0?@+" ,73=3A&.&" #&'&" 4'3&'" /7'30%/"=+0%+/"&"#&'73'".$"/7'30%/"4,'7+/"#'2E$F3/7$07$/:""
!!"#$%& $'&()"%*+,-%%$&.#/%!" #$%&"&''&(")*"+,"-*".$".&.+/"0,12'34+/5"6+'1&7&"$//$/".&.+/"$"$/4'$8$"$1",1"&'9,38+:"
! .'"0*$& 12$'& .#/%!" #$%&" .36$'$07$/" 73#+/" .$" .&.+/" ;/7'30%5"0,1$'345" <++=$&0>" $" $/4'$8$" $//&" 306+'1&?@+" $1" ,1"&'9,38+5" ,73=3A&0.+" ,1" 4&130B+" ;#&7B>:" " C/7&" 6,0?@+" #+.$"304=,3'"8D'3+/"7$'130&3/".$".&.+/"/$"0$4$//D'3+:"
! 3""*4&$'&()"%*+,-%%$&($"#25!"2",1&"6,0?@+"9,$"6+'1&7&",1"&''&(".$".&.+/"$1",1&"/7'30%"9,$"#+.$"/$'"$/4'37&"$1",1"&'9,38+".$".&.+/:"
! 6'27*$%2*$%& ($"#25!" 6,0?@+" ,73=3A&.&" #&'&" 4'3&'" /7'30%/"=+0%+/"&"#&'73'".$"/7'30%/"4,'7+/"#'2E$F3/7$07$/:""
!"#$%&'()&'*+,-./0&'
!"#$%&'()*+"',!"#$"%&'()"*)&+)"
*),"-./0"
!"#$%&'()&'*+,-./0&'
!"#$%&'()*+"',!"#$"%&'()"*)&+)"
*),"-./0"
16
!"#$%&'()*'"+,!"#$%&'(")'*+'("
,-"./0"1*&20"#-34"
!"#$%#%$&"!"#$%#%$&"''
!"#$%#%$&"!"#$%#%$&"''
!!"#$%&'()!*!+,-.*/0120340*
!!.-4506*/0120340*
!7)89!*!'-/0*
!:;<,0* *
!+=>*
!?-><@A0</*7=4-</*
!!;<B.*C0D</.0>*
!+006E-45*&=60/*
),D23/*C042>/=/*60*F>=D>-G-HI=**
!!"
!"#$%#%$&'()'$)*)#+,-.'/010'2!"#3'
#$%$"&"'(")"$*+",-".$//0","1$2$3"
" " 405$6'0")3"
" " 405$6'0",3"
" " 777"
" " 405$6'0"63"
8&5"#$%$3"
#%017"9:(;$6'%("<$:=&60*"!!"
!"#$%#%$&'()'$)*)#+,-.'/010'2!"#3'
#$%$"&"'(")"$*+",-".$//0","1$2$3"
" " 405$6'0")3"
" " 405$6'0",3"
" " 777"
" " 405$6'0"63"
8&5"#$%$3"
#%017"9:(;$6'%("<$:=&60*"
!!"
!"#$%#%$&'()'$)*)#+,-.'/010'2!"#3'
#$%$"&"'(")"$*+",-".$//0","1$2$3"
" " 405$6'0")3"
" " 405$6'0",3"
" " 777"
" " 405$6'0"63"
8&5"#$%$3"
#%017"9:(;$6'%("<$:=&60*"
!"#$%&'()*#%#+,-./-/.%#0+#.+1+-234"#!"##5/672"6%#0+#8%6+2.%#1%.+720%9#1".:8#"#
7;02<"#0+=+#+,-%.#0+6-."#0+#/8%#+,-./-/.%#0+6"826%0%#,/&02%<.%8%#>!"#$%""&?#
+@+7/-%#'#=+A+,#"#B/+#+,-C#6"#26-+.2".#0"#D""1#+#(#:#"#E6027+#B/+#=%.2%#0+#)#%-:#'*+FG#
H#-+.826%D#$#>2-+.%34"F#1",,2&2D2-%#.+<2,-.%.#"#6I8+."#
0+#.+1+-234"#0+,+J%0"?#K#%#1.28+2.%9#L#%#,+</60%#+#
%,,28#,/7+,,2=%8+6-+#%-:#%&'G##
H#-+.826%D#0+6"826%0"#,"-./#>7"6-%0".F?#%#
.+1.+,+6-%#"#6I8+."#0+#=+A+,#B/+#%#.+1+-234"#,+.C#
+@+7/-%0%G#
M%.%#2#0+#K#%-:#!NL#5%3%O#
# P"8%60"#LO#
# P"8%60"#QO#
# GGG#
# P"8%60"#6O#
R28#M%.%O#
!"#
!"#$%#%$&'()'$)*)#+,-.'!/012/34'5!"#$%6'
$%&'(%)*#+,*%-./0*1#2(/(3#
# # 4*5(%-*#63#
# # 4*5(%-*#73#
# # 888#
# # 4*5(%-*#%3#
9.5#$%&'(%)*3#
!"#
!"#$%#%$&'()'$)*)#+,-.'!/012/34'5!"#$%6'
$%&'(%)*#+,*%-./0*1#2(/(3#
# # 4*5(%-*#63#
# # 4*5(%-*#73#
# # 888#
# # 4*5(%-*#%3#
9.5#$%&'(%)*3#
!"#
!"#$%#%$&'()'$)*)#+,-.'!/012/34'5!"#$%6'
$%&'(%)*#+,*%-./0*1#2(/(3#
# # 4*5(%-*#63#
# # 4*5(%-*#73#
# # 888#
# # 4*5(%-*#%3#
9.5#$%&'(%)*3#
!"#
!"#$%&$''(#!#$%$&'()#*+#,-*.,+#/#0$1#+#2'$#$3(4#*+#.*($5.+5#6+#78+&+#92')65+:;#<$5,.*)#2')*6+#($5,.*)8#6$#&+*(5+8$#6+#!""##=+5#$%&'(#+'#)*+(#96$>$*6$*6+#6)#
3$8$?@+#6$3$A)6):;#
B)?)C#
# D+,)*6+#/C#
# D+,)*6+#EC#
# ;;;#
# D+,)*6+#*C#
F*2')*(+#G&+*6.?@+H#I#0$56)6$.5)C#
B)?)C#
# D+,)*6+#/C#
# D+,)*6+#EC#
# ;;;#
# D+,)*6+#*C#
F*2')*(+#G&+*6.?@+H#JKL#I#0$56)6$.5)#9=)83):C#
LM#
N5+=;#O8$%)*65$#P)87.*+(#!"#
!"#$%&$''(#!#$%$&'()#*+#,-*.,+#/#0$1#+#2'$#$3(4#*+#.*($5.+5#6+#78+&+#92')65+:;#<$5,.*)#2')*6+#($5,.*)8#6$#&+*(5+8$#6+#!""##=+5#$%&'(#+'#)*+(#96$>$*6$*6+#6)#
3$8$?@+#6$3$A)6):;#
B)?)C#
# D+,)*6+#/C#
# D+,)*6+#EC#
# ;;;#
# D+,)*6+#*C#
F*2')*(+#G&+*6.?@+H#I#0$56)6$.5)C#
B)?)C#
# D+,)*6+#/C#
# D+,)*6+#EC#
# ;;;#
# D+,)*6+#*C#
F*2')*(+#G&+*6.?@+H#JKL#I#0$56)6$.5)#9=)83):C#
LM#
N5+=;#O8$%)*65$#P)87.*+(#!"#
!"#$%&$''(#!#$%$&'()#*+#,-*.,+#/#0$1#+#2'$#$3(4#*+#.*($5.+5#6+#78+&+#92')65+:;#<$5,.*)#2')*6+#($5,.*)8#6$#&+*(5+8$#6+#!""##=+5#$%&'(#+'#)*+(#96$>$*6$*6+#6)#
3$8$?@+#6$3$A)6):;#
B)?)C#
# D+,)*6+#/C#
# D+,)*6+#EC#
# ;;;#
# D+,)*6+#*C#
F*2')*(+#G&+*6.?@+H#I#0$56)6$.5)C#
B)?)C#
# D+,)*6+#/C#
# D+,)*6+#EC#
# ;;;#
# D+,)*6+#*C#
F*2')*(+#G&+*6.?@+H#JKL#I#0$56)6$.5)#9=)83):C#
LM#
N5+=;#O8$%)*65$#P)87.*+(#
!"#
!"#$%&$''(#!#$%$&'()#*+#,-*.,+#/#0$1#+#2'$#$3(4#*+#.*($5.+5#6+#78+&+#92')65+:;#<$5,.*)#2')*6+#($5,.*)8#6$#&+*(5+8$#6+#!""##=+5#$%&'(#+'#)*+(#96$>$*6$*6+#6)#
3$8$?@+#6$3$A)6):;#
B)?)C#
# D+,)*6+#/C#
# D+,)*6+#EC#
# ;;;#
# D+,)*6+#*C#
F*2')*(+#G&+*6.?@+H#I#0$56)6$.5)C#
B)?)C#
# D+,)*6+#/C#
# D+,)*6+#EC#
# ;;;#
# D+,)*6+#*C#
F*2')*(+#G&+*6.?@+H#JKL#I#0$56)6$.5)#9=)83):C#
LM#
N5+=;#O8$%)*65$#P)87.*+(#
17
!"#$%&'(#)*+,-./%+#0-*12.&3#
!"#
$%&'()*+,#-)#
.,/-0*+,#&'1&'#-)#
'1&(2&2()#!"#$%&
'(()3#
4(,53#$%'6)/-('#7)%80/,&#
!"#$%#%$&'!"'(#$)*'!!"'"#$%&'"()')!!"'+,-.,"#,(*)+)/&012!3'%#4546&'+,-,'+,784+4,7&5'%&'()*+'*,-*'&'9"#$%#%$&'./!"*'
!"#$%#%$&'!"'(#$)*'!!"'"#$%&'"()')!!"'+,-.,"#,(*)+)/&012!3'%#4546&'+,-,'+,784+4,7&5'%&'()*+'*,-*'&'9"#$%#%$&'./!"*'
!"#$!!!"#"$%&'!(!)%'*+(!,-%.*/'0+'1'2!)%"!3(+!")%/4'5"6&"!7!"6&+'*'!"1!
"#$%&'&()*+,&-+./&0/,&1234,56+7&8++*/)1+&9!"#$!8!9!(%!%&'($)*)+2!(%!(!",-.!
!"#$!!!"#"$%&'!(!)%'*+(!,-%.*/'0+'1'2!)%"!3(+!")%/4'5"6&"!7!"6&+'*'!"1!
"#$%&'&()*+,&-+./&0/,&1234,56+7&8++*/)1+&9!"#$!8!9!(%!%&'($)*)+2!(%!(!",-.!
!"#$
%&'()*+)$,+)+$($-.+/)+0+$-&$12(3(4$&$3(*&3'+)$(4$564$&$*($
,+.*&2$7)(*'+2$-./.'+)$89:89$8%;9<$
=)(7>$?2&@+*-)&$A+21.*('$
!"#$%&'(%&%'"'(%)*+#',&"*$%#'+'+-+./$%&0'1#$+&%&'%'."*2)34"'2"'5"$4"'2+'
+*$&%2%'6!""#$%&70'8+(")9'.#).%&'+:''(")'6%*"+(,$-$./(0"&7;'
!"#$%#%$&'#()*'"+,-./0(&'1!"#$"%&"23'*',%&4$*'"+'&""+5+67&'&'%5&')+680%6&'4+'9(65+'9*#*:$;9(0*'!',%&/4*'*'<='>'&0(*/&4*?'+@+0%#&'&'"+,-./0(&'4+'+A+/#*"'4+'
0&4&',%&4$*?'/&'"+,-./0(&'+5',%+'9*$&5'5*/#&4*""#$%#&%#'%#(%#)'
B&'A+$"C*'D&E<=!F'G'+@("#+5'4*("'#()*"'4+'
H+,-./0(&'1/&"'A+$"I+"'&/#+$(*$+"'&)+/&"'
+"#&A&'4(")*/8A+6'&'"+,-./0(&'4*'#()*'
!'(&)"*+!"#$"%&"+!',$&'$,"2'
!"#$%#%$&'#()*'"+,-./0(&'1!"#$"%&"23'*',%&4$*'"+'&""+5+67&'&'%5&')+680%6&'4+'9(65+'9*#*:$;9(0*'!',%&/4*'*'<='>'&0(*/&4*?'+@+0%#&'&'"+,-./0(&'4+'+A+/#*"'4+'
0&4&',%&4$*?'/&'"+,-./0(&'+5',%+'9*$&5'5*/#&4*""#$%#&%#'%#(%#)'
B&'A+$"C*'D&E<=!F'G'+@("#+5'4*("'#()*"'4+'
H+,-./0(&'1/&"'A+$"I+"'&/#+$(*$+"'&)+/&"'
+"#&A&'4(")*/8A+6'&'"+,-./0(&'4*'#()*'
!'(&)"*+!"#$"%&"+!',$&'$,"2'
!"#$%#%$&'#()*'"+,-./0(&'1!"#$"%&"23'*',%&4$*'"+'&""+5+67&'&'%5&')+680%6&'4+'9(65+'9*#*:$;9(0*'!',%&/4*'*'<='>'&0(*/&4*?'+@+0%#&'&'"+,-./0(&'4+'+A+/#*"'4+'
0&4&',%&4$*?'/&'"+,-./0(&'+5',%+'9*$&5'5*/#&4*""#$%#&%#'%#(%#)'
B&'A+$"C*'D&E<=!F'G'+@("#+5'4*("'#()*"'4+'
H+,-./0(&'1/&"'A+$"I+"'&/#+$(*$+"'&)+/&"'
+"#&A&'4(")*/8A+6'&'"+,-./0(&'4*'#()*'
!'(&)"*+!"#$"%&"+!',$&'$,"2'
!!"#
$%#&'()*+#,-%).'+#
/-('-#01#()2(/'2%-#
)013-(/%#
4-%,5#6+*7')2-*#8'+9()%.#
!!"#$%&'(#)*+,-./%+#0-*12.&3#
!!"#
$%&'()#*+,'-%)#
./%)&%+#(#(0-12%+#,0#,1-+,0#340#2(#
0(567'8&%9#:3:;<=#<4>:?#@AA$#(#
<4>:?#B:CD:;E:#(#?4B.F@:#
B<GDE<DG:H#
18
!"#$
!%#$
!"#$
!%#$
!"#$
!%#$
Exercícios: Explicar o funcionamento das rotinas abaixo.
A
B
!"#$%&'(
!!"#$%&$&%'!()!('(*#!+&)!',%&-'!('(*#!
!!.#! ('(*#! -*()/! #)%! ()! $0-*#! (01)%)2$)#!
3(01)%)2$)!()!!""!#$4!+&)!#5!-*()/!#)%!()!&/!
6207*!$0-*8!
!!92:;*,*!'!&/'!$%"&'%!2*!<!*&!&/!"(')"*!2*!
='#7';!
!!.#!);)/)2$*#!$)/!()!#)%!$*(*#!#5!7*2$%*;)#!
*&!#5!02(07'(*%)#!
!!>'0#!*&!/)2*#!7*/*!?:%0*#! 10*#! @&2$*#!)/!
&/!7'A*!!
!"#$%&'(
!!"#$%&$&%'!()!('(*#!+&)!',%&-'!('(*#!
!!.#! ('(*#! -*()/! #)%! ()! $0-*#! (01)%)2$)#!
3(01)%)2$)!()!!""!#$4!+&)!#5!-*()/!#)%!()!&/!
6207*!$0-*8!
!!92:;*,*!'!&/'!$%"&'%!2*!<!*&!&/!"(')"*!2*!
='#7';!
!!.#!);)/)2$*#!$)/!()!#)%!$*(*#!#5!7*2$%*;)#!
*&!#5!02(07'(*%)#!
!!>'0#!*&!/)2*#!7*/*!?:%0*#! 10*#! @&2$*#!)/!
&/!7'A*!!
!!Estrutura que agrupa dados
!"#$%&'()(!*+%'*"&$(&(,+-./0-*'&$(
( 1&"&/.*+&(#2(/"#$%&'(!"#$%&'(-0(30"&%0(('')*+,+
!"#$%&'( !*"*4#&(*$(*56&%*$(-&+%'*(-*(/"#$%&'(
!"#$%&'()(!*+%'*"&$(&(,+-./0-*'&$(
( 1&"&/.*+&(#2(/"#$%&'(!"#$%&'(-0(30"&%0(('')*+,+
!"#$%&'( !*"*4#&(*$(*56&%*$(-&+%'*(-*(/"#$%&'(
!"#$%&'()(!*+%'*"&$(&(,+-./0-*'&$(
( 1&"&/.*+&(#2(/"#$%&'(!"#$%&'(-0(30"&%0(('')*+,+
!"#$%&'( !*"*4#&(*$(*56&%*$(-&+%'*(-*(/"#$%&'(
!"#$%&'()&(!*+$%,+%&$(
-.((/&"&01*+&(,(2#+34*(!!"#$%&'(!)*$%+*%"#
+,(5,"&%,(!"#$%&'(
(6.((!*"*7#&(*(%15*()&(),)*()&+%'*()*(!"#$%&'(8,91*(0'1,)*(
((((:'',;(8,91*()&(0*+$%,+%&(0'1,)*((
((((:'',;(0*+$%,+%&(
!"#$#%&'()*+$,-"./*0&/&*0&--&/*(&()-*&*1,234-*
!-.*5$,-"./-*0&/&*
0&--&/*67/#)-*(&()-*
0)/*&0.'&-*,8*"./8#'&$*
*
9.-)$6.*)*0/)2$.8&*()*
$#8#".*(.*:;*"./8#'&#-*
*
*
1#80$#<#5&=*.*8,#")=*&-*
$#>&[email protected]**
!"#$#%&'()*+$,-"./*0&/&*0&--&/*(&()-*&*1,234-*
!-.*5$,-"./-*0&/&*
0&--&/*67/#)-*(&()-*
0)/*&0.'&-*,8*"./8#'&$*
*
9.-)$6.*)*0/)2$.8&*()*
$#8#".*(.*:;*"./8#'&#-*
*
*
1#80$#<#5&=*.*8,#")=*&-*
$#>&[email protected]**
!"#$#%&'()*+$,-"./*0&/&*0&--&/*(&()-*&*1,234-*
!-.*5$,-"./-*0&/&*
0&--&/*67/#)-*(&()-*
0)/*&0.'&-*,8*"./8#'&$*
*
9.-)$6.*)*0/)2$.8&*()*
$#8#".*(.*:;*"./8#'&#-*
*
*
1#80$#<#5&=*.*8,#")=*&-*
$#>&[email protected]**
!"#$%&'()(*#+,-.(/#+0"&(
!"#$%&'
!"#$%&''
!(')*+&'
!"#$%&'%()*)%!+&,-."%,-$./.0*'"+'0%"12&3'
&4.12&'
12$34(0&5&(&67$%7'(#8(9"#$%&'(7+797:"(;:':(#$:'(&$%:(<#+,-.3(
!"#$%&'()(*#+,-.(/#+0"&(
!"#$%&'
!"#$%&''
!(')*+&'
!"#$%&'%()*)%!+&,-."%,-$./.0*'"+'0%"12&3'
&4.12&'
12$34(0&5&(&67$%7'(#8(9"#$%&'(7+797:"(;:':(#$:'(&$%:(<#+,-.3(
!"#$%&'()(*#+,-.(/#+0"&(
!"#$%&'
!"#$%&''
!(')*+&'
!"#$%&'%()*)%!+&,-."%,-$./.0*'"+'0%"12&3'
&4.12&'
12$34(0&5&(&67$%7'(#8(9"#$%&'(7+797:"(;:':(#$:'(&$%:(<#+,-.3(
!"#$%&'()(*#+,-.(/+0#+1"&(
!"#$"%&'( !"#$"%&'()*(+,-'(
!"#$%&'(2'341.(+.(543+&"(*'.+%4"(
!"#$%&'()(*#+,-.(/+0#+1"&(
!"#$"%&'( !"#$"%&'()*(+,-'(
!"#$%&'(2'341.(+.(543+&"(*'.+%4"(
!"#$%&'()(*#+,-.(/+0#+1"&(
!"#$"%&'( !"#$"%&'()*(+,-'(
!"#$%&'(2'341.(+.(543+&"(*'.+%4"(
!"#$%&'()(*#+,-.(/+0#+1"&(
!"#$"%&'( !"#$"%&'()*(+,-'(
!"#$%&'(2'341.(+.(543+&"(*'.+%4"(
19
! !"#$%&'()#*%('*&%'+,*$('(-&.+./*&.(&0-+&#,%('+12/&+%3&/0%'+4&
! 5/%2/&.#'(#%/&,/& 6+./&.#'(#%/&/0&(*70('./&.(&0-&6+1/& $/'&/0&8"#6(&(&*(6(9#/,(&:..&!"#$%&;()#*%('<&
! =& %('-#,+6& .#'(#%/& +'-+>(,+& .+./*& ./& $#,+6& .+& #%('+1+/<&?+./*&+@+'(9(,./&,/&%('-#,+6&(*70('./&!&#,A9#/&.+&@'BC#-+&#%('+1+/<&
! D-&*"#$%&'()#*%('&+.+@%+&70+670('&%#@/&6#)+./&,+&(,%'+.+<&
! D-&(,%'+.+&.(&E&'(*06%+'#+&(-&0-+&*+A.+&.(&F&,+&@'#-(#'+&#%('+1+/G&HE&,+&*()0,.+&#%('+12/&(&HF&,+&%('9(#'+<&&
! I-& /0%'+*& @+6+J'+*G& *"#$%& '()#*%('*& *2/& 0*+./*& @+'+& '(%('&J+6/'(*&.(&0-+&#%('+1+/&@+'+&+&@'BC#-+<&
! !2/& K%(#*& (-& -0#%+*& +@6#9+1L(*& 70(& 0*+-& -(-B'#+& /0&'(+6#-(,%+1+/&(,%'(&(*%+./*<&
! =&$((.M+9N&,/.(&3&/0%'+&'(@'(*(,%+1+/&./&-(*-/&9/,9(#%/<&
! :-M/*&@'/)'+-+*&+&*()0#'&@'/.0>(-&/&-(*-/&'(*06%+./<&&
&
!"#$%&;()#*%('&!! Transfere dados de uma iteração até
outra (memória ou realimentação). !"#$%&'()#*%(+&
!"#$%&'()#*%(+&
Valor atual
Próximo Valor
!"#$%&'(#)"*!""#$%*+",*&''(%)
! -$%&'%'&.$* *'"* /* +,-./* 0")/,*(#)/1.&* /* .+','2.&* #""#$%3* 4$%"* 5*+"#6/+()"*+","*.'%"7(#)/1.89"3*
" :* 0"#%"* )/* (#)/1.8."* 5*+6.,.)"*)/*%;#/23*
" :* 2.8"* *'"<* 0"&* )/=.'2%* 0"$$'(*.'%"7(#)/1.89"*6.>(2(%.).3*
" :* 2.8"*+,-./<*0"&*)/=.'2%*0"$$'(*.'%"7(#)/1.89"*)/$.>(2(%.).3*
*
! -1/,02"$?*
" @.>(2(%/* .'%"7(#)/1.89"* 0.&.*+"2/%.&* A.2"&/$* #"* 2.8"* /*+"#$%&'(&* "* .&&.B3* C")"$* "$*A.2"&/$* $9"* +"2"+.)"$*/,*.&&.B*."*$.(&*)"*2""03*
" D/$.>(2(%/* .'%"7(#)/1.89"* $/*A"+E*/$%(A/&* (#%/&/$$.)"*.0/#.$*#"*A.2"&*=(#.23*
F("*=(+.*,.($*/$0/$$"*
G'%"7(#)/1.89"*6.>(2(%.).*
G'%"7(#)/1.89"*)/$.>(2(%.).*F("*0/&,.#/+/*+",*.*,/$,.*
/$0/$$'&.*
H",/#%/*',*A.2"&*
I;2%(,.*(%/&.89"J*5*
0.$$.).*0.&.*="&.*
)"*.''()
!"#$%&'(#)"*!""#$%*+",*&''(%)
! -$%&'%'&.$* *'"* /* +,-./* 0")/,*(#)/1.&* /* .+','2.&* #""#$%3* 4$%"* 5*+"#6/+()"*+","*.'%"7(#)/1.89"3*
" :* 0"#%"* )/* (#)/1.8."* 5*+6.,.)"*)/*%;#/23*
" :* 2.8"* *'"<* 0"&* )/=.'2%* 0"$$'(*.'%"7(#)/1.89"*6.>(2(%.).3*
" :* 2.8"*+,-./<*0"&*)/=.'2%*0"$$'(*.'%"7(#)/1.89"*)/$.>(2(%.).3*
*
! -1/,02"$?*
" @.>(2(%/* .'%"7(#)/1.89"* 0.&.*+"2/%.&* A.2"&/$* #"* 2.8"* /*+"#$%&'(&* "* .&&.B3* C")"$* "$*A.2"&/$* $9"* +"2"+.)"$*/,*.&&.B*."*$.(&*)"*2""03*
" D/$.>(2(%/* .'%"7(#)/1.89"* $/*A"+E*/$%(A/&* (#%/&/$$.)"*.0/#.$*#"*A.2"&*=(#.23*
F("*=(+.*,.($*/$0/$$"*
G'%"7(#)/1.89"*6.>(2(%.).*
G'%"7(#)/1.89"*)/$.>(2(%.).*F("*0/&,.#/+/*+",*.*,/$,.*
/$0/$$'&.*
H",/#%/*',*A.2"&*
I;2%(,.*(%/&.89"J*5*
0.$$.).*0.&.*="&.*
)"*.''()
!"#$%&'(#)"*!""#$%*+",*&''(%)
! -$%&'%'&.$* *'"* /* +,-./* 0")/,*(#)/1.&* /* .+','2.&* #""#$%3* 4$%"* 5*+"#6/+()"*+","*.'%"7(#)/1.89"3*
" :* 0"#%"* )/* (#)/1.8."* 5*+6.,.)"*)/*%;#/23*
" :* 2.8"* *'"<* 0"&* )/=.'2%* 0"$$'(*.'%"7(#)/1.89"*6.>(2(%.).3*
" :* 2.8"*+,-./<*0"&*)/=.'2%*0"$$'(*.'%"7(#)/1.89"*)/$.>(2(%.).3*
*
! -1/,02"$?*
" @.>(2(%/* .'%"7(#)/1.89"* 0.&.*+"2/%.&* A.2"&/$* #"* 2.8"* /*+"#$%&'(&* "* .&&.B3* C")"$* "$*A.2"&/$* $9"* +"2"+.)"$*/,*.&&.B*."*$.(&*)"*2""03*
" D/$.>(2(%/* .'%"7(#)/1.89"* $/*A"+E*/$%(A/&* (#%/&/$$.)"*.0/#.$*#"*A.2"&*=(#.23*
F("*=(+.*,.($*/$0/$$"*
G'%"7(#)/1.89"*6.>(2(%.).*
G'%"7(#)/1.89"*)/$.>(2(%.).*F("*0/&,.#/+/*+",*.*,/$,.*
/$0/$$'&.*
H",/#%/*',*A.2"&*
I;2%(,.*(%/&.89"J*5*
0.$$.).*0.&.*="&.*
)"*.''()
!"#$%&'()*(!""#$%
! +,-,.#'%,()*(#""#$(,*(&'()"'*+(//(,'-."((//(!""#$0(,#)"/00(,(&*1+)."%2#*.)).(,($""$12,(3$"$('(3$#%,-(4"'%2$-5(
(
! 6""$12,()*(.'%2"'-,(')(#%&#.$2'"5((
(
! 7'.8(&,9,( #%1,"#"()*(':;,2'(%'(#""#$($%2,1(&,()1<=-'(%'(&#$>"$*$(&,(:-'.'1?((
(
(
(
(
!"#$%&'()*(!""#$%
! +,-,.#'%,()*(#""#$(,*(&'()"'*+(//(,'-."((//(!""#$0(,#)"/00(,(&*1+)."%2#*.)).(,($""$12,(3$"$('(3$#%,-(4"'%2$-5(
(
! 6""$12,()*(.'%2"'-,(')(#%&#.$2'"5((
(
! 7'.8(&,9,( #%1,"#"()*(':;,2'(%'(#""#$($%2,1(&,()1<=-'(%'(&#$>"$*$(&,(:-'.'1?((
(
(
(
(
!"#$%&'()*(!""#$%
! +,-,.#'%,()*(#""#$(,*(&'()"'*+(//(,'-."((//(!""#$0(,#)"/00(,(&*1+)."%2#*.)).(,($""$12,(3$"$('(3$#%,-(4"'%2$-5(
(
! 6""$12,()*(.'%2"'-,(')(#%&#.$2'"5((
(
! 7'.8(&,9,( #%1,"#"()*(':;,2'(%'(#""#$($%2,1(&,()1<=-'(%'(&#$>"$*$(&,(:-'.'1?((
(
(
(
(
! !"#"$ "%&'&()"#$ %&*+),-+,$ +*$ .*$ !""!#$ ./&0&1+$ ($ 2(/3($ %&#+&/($ )($ $%&'()&$*+,!#$+$,+0+'&()+$!""#$%&'()%*(!%($*+).4$$$! "#!$%%&'!()*+,-!.,-/-*01!
!!!! "#!$%%&'!23,0)4,-!.,-/-*051!
!!!! 6#!$%%&'!()*+,-!.,-/-*01!
!!!!! 6#!$%%&'!23,0)4,-!.,-/-*051!
!
! !"#"$ "%&'&()"#$ %&*+),-+,$ +*$ .*$ !""!#$ ./&0&1+$ ($ 2(/3($ %&#+&/($ )($ $%&'()&$*+,!#$+$,+0+'&()+$!""#$%&'()%*(!%($*+).4$$$! "#!$%%&'!()*+,-!.,-/-*01!
!!!! "#!$%%&'!23,0)4,-!.,-/-*051!
!!!! 6#!$%%&'!()*+,-!.,-/-*01!
!!!!! 6#!$%%&'!23,0)4,-!.,-/-*051!
!
! !"#"$ "%&'&()"#$ %&*+),-+,$ +*$ .*$ !""!#$ ./&0&1+$ ($ 2(/3($ %&#+&/($ )($ $%&'()&$*+,!#$+$,+0+'&()+$!""#$%&'()%*(!%($*+).4$$$! "#!$%%&'!()*+,-!.,-/-*01!
!!!! "#!$%%&'!23,0)4,-!.,-/-*051!
!!!! 6#!$%%&'!()*+,-!.,-/-*01!
!!!!! 6#!$%%&'!23,0)4,-!.,-/-*051!
!
! !"#"$ "%&'&()"#$ %&*+),-+,$ +*$ .*$ !""!#$ ./&0&1+$ ($ 2(/3($ %&#+&/($ )($ $%&'()&$*+,!#$+$,+0+'&()+$!""#$%&'()%*(!%($*+).4$$$! "#!$%%&'!()*+,-!.,-/-*01!
!!!! "#!$%%&'!23,0)4,-!.,-/-*051!
!!!! 6#!$%%&'!()*+,-!.,-/-*01!
!!!!! 6#!$%%&'!23,0)4,-!.,-/-*051!
!
! !"#"$ "%&'&()"#$ %&*+),-+,$ +*$ .*$ !""!#$ ./&0&1+$ ($ 2(/3($ %&#+&/($ )($ $%&'()&$*+,!#$+$,+0+'&()+$!""#$%&'()%*(!%($*+).4$$$! "#!$%%&'!()*+,-!.,-/-*01!
!!!! "#!$%%&'!23,0)4,-!.,-/-*051!
!!!! 6#!$%%&'!()*+,-!.,-/-*01!
!!!!! 6#!$%%&'!23,0)4,-!.,-/-*051!
!
!"#$$$
$$
%&'($)*$!""!#$&$+,-.',/($,$(+&00,$1,0$0&)0$1(1,0$+,/,+(-1,2,0$&*$)*$3-13+(1,'4$
$
EXEMPLOS: !"#$$$
$$
%&'($)*$!""!#$&$+,-.',/($,$(+&00,$1,0$0&)0$1(1,0$+,/,+(-1,2,0$&*$)*$3-13+(1,'4$
$
EXEMPLOS:
!"#$$
$
$
$
%&'$()$*&+,-+-,)$!"#$$.),)$&*/*"0'1),$-2)$()&$3-)+,'$'.*,)45*&$*$2'&+,)1('$6$
,*&-/+)('7$
$
$
!"#$$
$
$
$
%&'$()$*&+,-+-,)$!"#$$.),)$&*/*"0'1),$-2)$()&$3-)+,'$'.*,)45*&$*$2'&+,)1('$6$
,*&-/+)('7$
$
$
20
EXEMPLOS: !"#$
%&'()*$*$*+,-./$0'$!""!#$123$
$
$
$
!"#$
%&'()*$*$*+,-./$0'$!""!#$123$
$
$
$
EXEMPLOS:
!"#$$%"&'()*$+"$,)-(&./0$)/+*)$/$12$"$"345&6*)$/$7(86&/8*9"8'/:$
!"#$$%"&'()*$+"$,)-(&./0$)/+*)$/$12$"$"345&6*)$/$7(86&/8*9"8'/:$
!"#$$
%&'()*+$,-$.(/0)123$(24+($2$56$,$,789)'+($&,0$"0:')2:+-,:*2;$
!"#$$
%&'()*+$,-$.(/0)123$(24+($2$56$,$,789)'+($&,0$"0:')2:+-,:*2;$
!"#$%&%'()#*#+*&,)%&-.'*#/-#*./(#/*#0%.(1#.(#-.')(/(#/*#(&*0')(/*)#*2#/*#
+*.3-)0*)#456#+*%1')*#,(00(89(%:(#+*)-;<=.+%(#/-#+*)'-#7+#
0-1-+%*.(/(#,()(#,(00()#0*&-.'-#(#7)-;<=.+%(#&>:%&(#7&#/(#7*)&(#/-#
*./(?#
#
@"#A-1-+%*.()#(#7)-;<=.+%(#/-#(&*0')(B-&##.*#&C.%&*#@#3-D-0#(#7)-;<=.+%(#
&>:%&(#/*#-0,-+')*#/-#E*2)%-)#/(#7*)&(#/-#*./(#(,1%+(/("#
F(#,)>'%+(G#-&#&2%'*0#0%0'-&(0#H#+*&2&#')(9(1I()#
+*&#J#(#K#3-D-0#(#7)-;<=.+%(#/-#(&*0')(B-&"#
!" ## !"!
41B2&(0#/%+(0#,()(#(&*0')(B-&#/-#(1'(#7%/-1%/(/-#
!"#$%&%'()#*#+*&,)%&-.'*#/-#*./(#/*#0%.(1#.(#-.')(/(#/*#(&*0')(/*)#*2#/*#
+*.3-)0*)#456#+*%1')*#,(00(89(%:(#+*)-;<=.+%(#/-#+*)'-#7+#
0-1-+%*.(/(#,()(#,(00()#0*&-.'-#(#7)-;<=.+%(#&>:%&(#7&#/(#7*)&(#/-#
*./(?#
#
@"#A-1-+%*.()#(#7)-;<=.+%(#/-#(&*0')(B-&##.*#&C.%&*#@#3-D-0#(#7)-;<=.+%(#
&>:%&(#/*#-0,-+')*#/-#E*2)%-)#/(#7*)&(#/-#*./(#(,1%+(/("#
F(#,)>'%+(G#-&#&2%'*0#0%0'-&(0#H#+*&2&#')(9(1I()#
+*&#J#(#K#3-D-0#(#7)-;<=.+%(#/-#(&*0')(B-&"#
!" ## !"!
41B2&(0#/%+(0#,()(#(&*0')(B-&#/-#(1'(#7%/-1%/(/-#
!"#$%&%'()#*#+*&,)%&-.'*#/-#*./(#/*#0%.(1#.(#-.')(/(#/*#(&*0')(/*)#*2#/*#
+*.3-)0*)#456#+*%1')*#,(00(89(%:(#+*)-;<=.+%(#/-#+*)'-#7+#
0-1-+%*.(/(#,()(#,(00()#0*&-.'-#(#7)-;<=.+%(#&>:%&(#7&#/(#7*)&(#/-#
*./(?#
#
@"#A-1-+%*.()#(#7)-;<=.+%(#/-#(&*0')(B-&##.*#&C.%&*#@#3-D-0#(#7)-;<=.+%(#
&>:%&(#/*#-0,-+')*#/-#E*2)%-)#/(#7*)&(#/-#*./(#(,1%+(/("#
F(#,)>'%+(G#-&#&2%'*0#0%0'-&(0#H#+*&2&#')(9(1I()#
+*&#J#(#K#3-D-0#(#7)-;<=.+%(#/-#(&*0')(B-&"#
!" ## !"!
41B2&(0#/%+(0#,()(#(&*0')(B-&#/-#(1'(#7%/-1%/(/-#
!"#$%&%'()#*#+*&,)%&-.'*#/-#*./(#/*#0%.(1#.(#-.')(/(#/*#(&*0')(/*)#*2#/*#
+*.3-)0*)#456#+*%1')*#,(00(89(%:(#+*)-;<=.+%(#/-#+*)'-#7+#
0-1-+%*.(/(#,()(#,(00()#0*&-.'-#(#7)-;<=.+%(#&>:%&(#7&#/(#7*)&(#/-#
*./(?#
#
@"#A-1-+%*.()#(#7)-;<=.+%(#/-#(&*0')(B-&##.*#&C.%&*#@#3-D-0#(#7)-;<=.+%(#
&>:%&(#/*#-0,-+')*#/-#E*2)%-)#/(#7*)&(#/-#*./(#(,1%+(/("#
F(#,)>'%+(G#-&#&2%'*0#0%0'-&(0#H#+*&2&#')(9(1I()#
+*&#J#(#K#3-D-0#(#7)-;<=.+%(#/-#(&*0')(B-&"#
!" ## !"!
41B2&(0#/%+(0#,()(#(&*0')(B-&#/-#(1'(#7%/-1%/(/-#
!"#$%#&#'("&)*"+",#-.'-/'0&'("12/&#'-/'340"1"56.'-/'("7#"1'
!"#$%#&#'("&)*"+",#-.'-/'0&'("12/&#'-/'340"1"56.'-/'("7#"1'
!"##"$%&'(
!"#$%"&'()*
+#$'%,*-'
."$'*)"%('
!"#$%"&'
/#$%*)*
0#*&123-*
4*5)*(0#*&123-*
/#$%*)*64*5)*
7323$*&
!"#$*)"%'89
:3;'%89<<<
)(&%*'(#
+,-)-./0-12343567/0./-/74
/8"9#"$".:%.;<(*(=.'>?8*(.:%.@$".?<"*"./-1.
!"##"$%&'(
!"#$%"&'()*
+#$'%,*-'
."$'*)"%('
!"#$%"&'
/#$%*)*
0#*&123-*
4*5)*(0#*&123-*
/#$%*)*64*5)*
7323$*&
!"#$*)"%'89
:3;'%89<<<
)(&%*'(#
+,-)-./0-12343567/0./-/74
/8"9#"$".:%.;<(*(=.'>?8*(.:%.@$".?<"*"./-1.
!"#$
!!"#$%!&!'()*)"$(+&"(,+')-#./+%!%$%$&'($
$
)*+,*-.-$/01234-/+%$
!$,0*0453-*$/316+13237+1$0$3420*8-5019$
!$8-53:32-*$-$3412-:-;<+$0$+$*05+4=053.042+$/0$6:-5-1$'>?9$
!$,0*0453-*$5-4-31$0$2-*08-1$/-$6:-5-$3412-:-/-9$
!$5*3-*$015-:-1$6-*-$+1$3412*@.042+1$73*2@-31$ABCD9$
!$5+483,@*-*$0%,1!%#9$
!$0E6+*2-*$0$3.6+*2-*$-*F@37+1$/0$5+483,@*-;<+G$$
$
)*+50/3.042+1$HI135+1%$!"#$%&%'() *+') ,-,.*&+() %) *&%/%) 012) 10345467) "+)
/+.*8$%9+') *,##+%&) ,) %) :+'",;'%) *%'%) *,'.;$;') %)
/+",-<+)9+#)#;"%;#)9,),"$'%9%),=+8)#%>9%?$
)*+8G$':0E-4/*0$J-:H34+2$
'1$6*34536-31$5-*-520*K1235-1$/-$6:-5-$'>?$>'LMNMOP$1<+%$
!M$042*-/-19$
NO$1-K/-19$
#NNGNNN$#"&./!#$6+*$10,@4/+9$
!O$H321$.@:238@4;<+$CQRG$!"#$
!!"#$%!&!'()*)"$(+&"(,+')-#./+%!%$%$&'($
$
)*+,*-.-$/01234-/+%$
!$,0*0453-*$/316+13237+1$0$3420*8-5019$
!$8-53:32-*$-$3412-:-;<+$0$+$*05+4=053.042+$/0$6:-5-1$'>?9$
!$,0*0453-*$5-4-31$0$2-*08-1$/-$6:-5-$3412-:-/-9$
!$5*3-*$015-:-1$6-*-$+1$3412*@.042+1$73*2@-31$ABCD9$
!$5+483,@*-*$0%,1!%#9$
!$0E6+*2-*$0$3.6+*2-*$-*F@37+1$/0$5+483,@*-;<+G$$
$
)*+50/3.042+1$HI135+1%$!"#$%&%'() *+') ,-,.*&+() %) *&%/%) 012) 10345467) "+)
/+.*8$%9+') *,##+%&) ,) %) :+'",;'%) *%'%) *,'.;$;') %)
/+",-<+)9+#)#;"%;#)9,),"$'%9%),=+8)#%>9%?$
)*+8G$':0E-4/*0$J-:H34+2$
'1$6*34536-31$5-*-520*K1235-1$/-$6:-5-$'>?$>'LMNMOP$1<+%$
!M$042*-/-19$
NO$1-K/-19$
#NNGNNN$#"&./!#$6+*$10,@4/+9$
!O$H321$.@:238@4;<+$CQRG$!"#$
!!"#$%!&!'()*)"$(+&"(,+')-#./+%!%$%$&'($
$
)*+,*-.-$/01234-/+%$
!$,0*0453-*$/316+13237+1$0$3420*8-5019$
!$8-53:32-*$-$3412-:-;<+$0$+$*05+4=053.042+$/0$6:-5-1$'>?9$
!$,0*0453-*$5-4-31$0$2-*08-1$/-$6:-5-$3412-:-/-9$
!$5*3-*$015-:-1$6-*-$+1$3412*@.042+1$73*2@-31$ABCD9$
!$5+483,@*-*$0%,1!%#9$
!$0E6+*2-*$0$3.6+*2-*$-*F@37+1$/0$5+483,@*-;<+G$$
$
)*+50/3.042+1$HI135+1%$!"#$%&%'() *+') ,-,.*&+() %) *&%/%) 012) 10345467) "+)
/+.*8$%9+') *,##+%&) ,) %) :+'",;'%) *%'%) *,'.;$;') %)
/+",-<+)9+#)#;"%;#)9,),"$'%9%),=+8)#%>9%?$
)*+8G$':0E-4/*0$J-:H34+2$
'1$6*34536-31$5-*-520*K1235-1$/-$6:-5-$'>?$>'LMNMOP$1<+%$
!M$042*-/-19$
NO$1-K/-19$
#NNGNNN$#"&./!#$6+*$10,@4/+9$
!O$H321$.@:238@4;<+$CQRG$
21
!"#$%&'()$*+,-./0&,$1.+23/'4$
564.$(,&&.7,/4.$(8/93'/.$9'7'$87.$
3/4,&(.9,$,/4&,$.6$:+.9.6$*;<$=9'7$
0&3>,&6$:.&.$?.2@A5BC$,$0,7.36$
036:'6343>'6$0,$ADE$9'7$'$?.2@A5B)$
*+F7$0366'G$:,&734,$.$&,.+3H.IJ'$0,$
4,64,6$:&,+373/.&,6$9'7$,66,6$
036:'6343>'6)$K,68730.7,/4,$.:&,6,/4.$
#$9.4,L'&3.6$0,$9'/(3L8&.IJ'M$
!
!
"#$%&#'!()*!+),#-.(&#'M$$
,-32,$'$N.&0O.&,$3/64.+.0'$,$0,4,94.0')$
P,&>,$ 4.72F7$ :.&.$ 3/9+83&$ 843+34Q&3'6G$
9'/(3L8&.&$ ,$ 4,64.&$ 036:'6343>'6)$E6$0'36$
843+34Q&3'6$ :&3/93:.36$ 6J'6$ !"#$%"&'%($ ,$
)%(&*!+,%-()$
"(,(!/#%0123-133*M$$
9'/4F7$ '6$ 9./.36$ >3&48.36G$7'64&./0'$
'6$ 9./.36$ >3&48.36$ 9'/(3L8&.0'6$
./4,&3'&7,/4,$,$('&/,9,$843+34Q&3'6$:.&.$
4,64,6$ ,$ &,9'/(3L8&.IR,6$ 0,66,6$
9./.36$ >3&48.36)$ S.72F7$ ('&/,9,$
.9,66'$.'$;*T$<N.//,+$B3H.&0$'/0,$
>'9U$:'0,$9&3.&$/'>'6$9./.36$>3&48.36)$
$
!"#$%&'()$*+,-./0&,$1.+23/'4$
564.$(,&&.7,/4.$(8/93'/.$9'7'$87.$
3/4,&(.9,$,/4&,$.6$:+.9.6$*;<$=9'7$
0&3>,&6$:.&.$?.2@A5BC$,$0,7.36$
036:'6343>'6$0,$ADE$9'7$'$?.2@A5B)$
*+F7$0366'G$:,&734,$.$&,.+3H.IJ'$0,$
4,64,6$:&,+373/.&,6$9'7$,66,6$
036:'6343>'6)$K,68730.7,/4,$.:&,6,/4.$
#$9.4,L'&3.6$0,$9'/(3L8&.IJ'M$
!
!
"#$%&#'!()*!+),#-.(&#'M$$
,-32,$'$N.&0O.&,$3/64.+.0'$,$0,4,94.0')$
P,&>,$ 4.72F7$ :.&.$ 3/9+83&$ 843+34Q&3'6G$
9'/(3L8&.&$ ,$ 4,64.&$ 036:'6343>'6)$E6$0'36$
843+34Q&3'6$ :&3/93:.36$ 6J'6$ !"#$%"&'%($ ,$
)%(&*!+,%-()$
"(,(!/#%0123-133*M$$
9'/4F7$ '6$ 9./.36$ >3&48.36G$7'64&./0'$
'6$ 9./.36$ >3&48.36$ 9'/(3L8&.0'6$
./4,&3'&7,/4,$,$('&/,9,$843+34Q&3'6$:.&.$
4,64,6$ ,$ &,9'/(3L8&.IR,6$ 0,66,6$
9./.36$ >3&48.36)$ S.72F7$ ('&/,9,$
.9,66'$.'$;*T$<N.//,+$B3H.&0$'/0,$
>'9U$:'0,$9&3.&$/'>'6$9./.36$>3&48.36)$
$
!"#$
%&'$&$()*&+,)*-')+.&$/0.&'1.-*&$2/$34/*/$56%$657#8#9:$&0$2/$
2-;3&+<=)4>$*4-*/($+&;$-.)+;$!"#$%"&'()*'+),"-.(%"&$)$/+0!1234'!"#$%"&$
!"#$%&'()*+#&
,-./01230+4.#&
,.103&5'-2'-&
10,0+10+1.&1'&
50-#6.&1.&789:&
3'#&.&/.+/024.&;&
.&30#3.$&
?(&@A$54)B/+2()$C/4D-+&.$
NImyDAQ
!"#$
%&'(')*+,$(+*+'-$.$/0+(+$%12$1%3454678$20'(+,$*)-$'9:*-$!"#"$%&'()*+,)++-;$
.,"-'#'+/"0$%12!34$5',#6"0$7)"//&08$:$3--$7)"//&0$
!"#$
%&'()*+,)-.'$*)$('-/+01&234'$*'$(2-256$728.2$(5+(2&$-'$+.),$9$)8:1)&*2$
!"#$%&'"$(')*+',-%&./0'12/""$0$
!""#
$%&%'()#*)#+,-)#*%#.%/.)0#)1#2%*,*3#*%.%43*35#-)0#%6%2-&)5#+%/.()#%&7+0,835#
8)00%/+%#%&7+0,835#+%02)-30#+,-)#95#%/+0%#)1+03.#-)..,:,&,*3*%.;#$%&%8,)/305#-303#%.+%#
%6-%0,2%/+)5#+%/.()#%&7+0,83#<!"#$%&'=#
>0)?;#@&%63/*0%#A3&:,/)+#
!""#
$%&'(%#)%*%#+',-&-*#.&-+%+'/#0!"#$%12#,%-3%#0&'"()1#45&-4%#'#463-4%#+%#4'+-+%#
078/'*9%*#7/#(-4-:'/#+%#)(%;%#<=>#.:-(-?%+%1@#=-A-:%*#B#0B7(:/1#&7#'/)%C7#!"#$%#'#
.:-(-?%*#%#,%-3%#*)+',-$@##
D*7,@#<('3%&+*'#E%(8-&7:#
!"#$
%&'()*+,)-.'$/0&0$1)2)34'$*0$/20(0$567$)$*0$('-8+9:&034'$*'$(0-02$*)$)-.&0*0;$
72+(0&$),$!"#$%&'(;$$
%&'8;$52)<0-*&)$=02>+-'.$
!"!#
$%&'()*+(,-&#./%/#0*,/1*2/%#/#'%*/34&#)&5#'/,/*5#)(#(,-%/)/#6,(5-(#(7(+.1&8#-%95#
'/,/*5#0&%/+#'&,0*:;%/)&5<=##
$%&0=#>1(7/,)%(#?/1@*,&-#
!"#$
%&'()*+,)-.'$*)$.)/.)$*)$0,$*'/$(1-1+/2$3'-)(.1&$0,$/+-14$*)$)-.&1*1$5&)/6)+.1&$'$
.+6'$*)$/+-14$)$1/$71+81/$('-7+90&1*1/$-'$:;<=$1//+,$(','=$*1$641(1$;>3?2$34+(1&$
-'$@'.A'$!"#$2$$
%&'72$;4)81-*&)$B14@+-'.$!"#$
%&'()*+,)-.'$*)$.)/.)$*)$0,$*'/$(1-1+/2$3'-)(.1&$0,$/+-14$*)$)-.&1*1$5&)/6)+.1&$'$
.+6'$*)$/+-14$)$1/$71+81/$('-7+90&1*1/$-'$:;<=$1//+,$(','=$*1$641(1$;>3?2$34+(1&$
-'$@'.A'$!"#$2$$
%&'72$;4)81-*&)$B14@+-'.$
!"#$%&'()*+,-")&.+(/0,#1& 234&
22
!"#$%$&'()*+),-*(%).()/-01234)
526,!7)89!,2:2;5!/)
)
!"#$%#&%'()*'+#$&,-,$-%,.*/,-0$
$"12$34,.56*',$
$"12$7!"!#$%&&$
$8+49,:+-$
526,!7<=)
$
8+49-+.,:+-$;!"#$%"<$:,#$
=%-#>%#$?,*#$,9@,*#$:+$
A,B!"CD0$$
$!"#$ &,-,$ %E%'@9,-$ @?,$
9,-%),F$
$G?,$ #H-*%$ :%$ !*#$ &,-,$
9+:+#$+#$9*&+#$:%$?%:*I>%#$
!"#$%$&'()*+),-*(%).()/-01234)
526,!7)89!,2:2;5!/)
)
!"#$%#&%'()*'+#$&,-,$-%,.*/,-0$
$"12$34,.56*',$
$"12$7!"!#$%&&$
$8+49,:+-$
526,!7<=)
$
8+49-+.,:+-$;!"#$%"<$:,#$
=%-#>%#$?,*#$,9@,*#$:+$
A,B!"CD0$$
$!"#$ &,-,$ %E%'@9,-$ @?,$
9,-%),F$
$G?,$ #H-*%$ :%$ !*#$ &,-,$
9+:+#$+#$9*&+#$:%$?%:*I>%#$
!"#"$%"&'("()#*#+",-./0#12*1*23'*4"#5#$'1*6#()#!"#$%"&#
1"2"#"7%'6'89*#()#("(*6:#
!
!!!"#$%&%'(#)*+,-./0"!#$%!$"%12"3!&'!()*+%!,-.'/!012*/*3)&%#!'4!.'5#6'#!),2*7)#!&%!
8)(9:;<=! '! )*,&)! #$%! 4),2*&)#! '4! >1,?$%! &)! @%4A)2*(*/*&)&'! &)#! .'5#6'#B! C!
A5DA5*)!E)2*%,)/! #D! )@%,#'/F)! #'1!1#%!'4!#*21)?6'#!,'@'##G5*)#! '! H1'!',.%/.)4!
&*#A%#*2*.%#!),2*7%#I!
!
!!4,3*567"233"! *,25%&13*&%!,)!.'5#$%!JBK!'!)A5'#',2)!)!A%##*(*/*&)&'!&'!12*/*3)?$%!
&'!.G5*%#!9:#!'!4)*%5!@)A)@*&)&'!&'!A5%75)4)?$%I!
!
!!+,-./086"! *,25%&13*&%#! 2)4(L4! ,)! .'5#$%! JBKB! CA5'#',2)! &*.'5#)#! .),2)7',#!
@%4! 5'/)?$%! )%! 4L2%&%! 25)&*@*%,)/M! @%4%! A%5! '+'4A/%M! 4)*%5! *,2'75)?$%! @%4! )!
>'55)4',2)!NCOM!14!,-.'/!&'!)(#25)?$%!4)*%5M!@)A)@*&)&'!&'!41/2*A5%@'##%M!4)*%5!
5%(1#2'3M!4)*%5!'#2)(*/*&)&'M!',25'!%125%#!>)2%5'#!4',%#!*4A%52),2'#B!
!
E)#!/P4*,)#!A%#2'5*%5'#!)A5'#',2%!)#!Q!A%##*(*/*&)&'#!&'!@D&*7%!A)5)!)H1*#*?$%!&'!
&)&%#B!
!
!"#"$%"&'("()#*#+",-./0#12*1*23'*4"#5#$'1*6#()#!"#$%"&#
1"2"#"7%'6'89*#()#("(*6:#
!
!!!"#$%&%'(#)*+,-./0"!#$%!$"%12"3!&'!()*+%!,-.'/!012*/*3)&%#!'4!.'5#6'#!),2*7)#!&%!
8)(9:;<=! '! )*,&)! #$%! 4),2*&)#! '4! >1,?$%! &)! @%4A)2*(*/*&)&'! &)#! .'5#6'#B! C!
A5DA5*)!E)2*%,)/! #D! )@%,#'/F)! #'1!1#%!'4!#*21)?6'#!,'@'##G5*)#! '! H1'!',.%/.)4!
&*#A%#*2*.%#!),2*7%#I!
!
!!4,3*567"233"! *,25%&13*&%!,)!.'5#$%!JBK!'!)A5'#',2)!)!A%##*(*/*&)&'!&'!12*/*3)?$%!
&'!.G5*%#!9:#!'!4)*%5!@)A)@*&)&'!&'!A5%75)4)?$%I!
!
!!+,-./086"! *,25%&13*&%#! 2)4(L4! ,)! .'5#$%! JBKB! CA5'#',2)! &*.'5#)#! .),2)7',#!
@%4! 5'/)?$%! )%! 4L2%&%! 25)&*@*%,)/M! @%4%! A%5! '+'4A/%M! 4)*%5! *,2'75)?$%! @%4! )!
>'55)4',2)!NCOM!14!,-.'/!&'!)(#25)?$%!4)*%5M!@)A)@*&)&'!&'!41/2*A5%@'##%M!4)*%5!
5%(1#2'3M!4)*%5!'#2)(*/*&)&'M!',25'!%125%#!>)2%5'#!4',%#!*4A%52),2'#B!
!
E)#!/P4*,)#!A%#2'5*%5'#!)A5'#',2%!)#!Q!A%##*(*/*&)&'#!&'!@D&*7%!A)5)!)H1*#*?$%!&'!
&)&%#B!
!
!"#$%&'()#*+,#!#!"#$%&%'(#)*+,-*
!"#$%&%'()%*#$+),)$
&-.,)%)$)-)/01'()$
2&-3$!"#$%&'()%*%+,'#4$-&,&#
./0(1'1,12+#
-)./0.1)#2%#34'#
2%256"2)'#"#
%.1&"2"'#%#'"72"'#
"."89:56"'#%#
25:51"5';#
6).1"2)&%'#%#
<&)6%25=%.1)'#2%#
6"85>&"?()+#
!"#$%&'()#*+,#!#!"#$%&%'(#)*+,-*
!"#$%&%'()%*#$+),)$
&-.,)%)$)-)/01'()$
2&-3$!"#$%&'()%*%+,'#4$-&,&#
./0(1'1,12+#
-)./0.1)#2%#34'#
2%256"2)'#"#
%.1&"2"'#%#'"72"'#
"."89:56"'#%#
25:51"5';#
6).1"2)&%'#%#
<&)6%25=%.1)'#2%#
6"85>&"?()+#
!"!#$%&'(#)*+,-./%+#0-*12.&3#
!"#$%&'()*+&,&-*./012&34%5&
!"#$%&'"()*+*,-"(&-".*.+*/)01-"$23"4!""#$%&'$()*+,(-,&..$)-*/)'0,1&%05"6(0"7-1*+*)-"-"1/&(8*1-9:/"1/&"-;"<+-1-;"=0"-6(*;*9:/"=0"=-=/;"!"
&-8)>&"1/&<-)*.*+*=-=0"1/&"-"?0@;:/"ABC"0"</;)0@*/@0;B"
DE3$FG!"#$H"I$EJK$H"J"D$L$3H
HJI"IJM2!E3N$FG!"4!2D3!L$O5
HJI"IE3PPJE"4!2D3!L$O5
OJE"!Q"JHDEJRJE"#$#!H
DOJ$E
E0;(&/"=0;)0"#$%&'S"1@*-@")-@07-;T"1/87*U(@-@")0&</@*,-9:/"0"
=*;<-@/T"+0@"0"0;1@0?0@"0"+*&<-@")-@07-"
!"#$%&'()*+&,&-*./012&34%5&
!"#$%&'"()*+*,-"(&-".*.+*/)01-"$23"4!""#$%&'$()*+,(-,&..$)-*/)'0,1&%05"6(0"7-1*+*)-"-"1/&(8*1-9:/"1/&"-;"<+-1-;"=0"-6(*;*9:/"=0"=-=/;"!"
&-8)>&"1/&<-)*.*+*=-=0"1/&"-"?0@;:/"ABC"0"</;)0@*/@0;B"
DE3$FG!"#$H"I$EJK$H"J"D$L$3H
HJI"IJM2!E3N$FG!"4!2D3!L$O5
HJI"IE3PPJE"4!2D3!L$O5
OJE"!Q"JHDEJRJE"#$#!H
DOJ$E
E0;(&/"=0;)0"#$%&'S"1@*-@")-@07-;T"1/87*U(@-@")0&</@*,-9:/"0"
=*;<-@/T"+0@"0"0;1@0?0@"0"+*&<-@")-@07-"
!"#$%&'()*+&,&-*./012&34%5&
!"#$%&'"()*+*,-"(&-".*.+*/)01-"$23"4!""#$%&'$()*+,(-,&..$)-*/)'0,1&%05"6(0"7-1*+*)-"-"1/&(8*1-9:/"1/&"-;"<+-1-;"=0"-6(*;*9:/"=0"=-=/;"!"
&-8)>&"1/&<-)*.*+*=-=0"1/&"-"?0@;:/"ABC"0"</;)0@*/@0;B"
DE3$FG!"#$H"I$EJK$H"J"D$L$3H
HJI"IJM2!E3N$FG!"4!2D3!L$O5
HJI"IE3PPJE"4!2D3!L$O5
OJE"!Q"JHDEJRJE"#$#!H
DOJ$E
E0;(&/"=0;)0"#$%&'S"1@*-@")-@07-;T"1/87*U(@-@")0&</@*,-9:/"0"
=*;<-@/T"+0@"0"0;1@0?0@"0"+*&<-@")-@07-"
!"#$
!$
!$
!"#$%#&'#()*+(),-)./012)
!$
!$
%&'()$*+,-./0&,$1.+23/'4$ !"#$
!$
!$
!"#$%#&'#()*+(),-)./012)
!$
!$
%&'()$*+,-./0&,$1.+23/'4$ !"#$
!$
!$
!"#$%#&'#()*+(),-)./012)
!$
!$
%&'()$*+,-./0&,$1.+23/'4$!"#$
!$
!$
!"#$%#&'#()*+(),-)./012)
!$
!$
%&'()$*+,-./0&,$1.+23/'4$
!"#$
!$
!$
!"#$%#&'#()*+(),-)./012)
!$
!$
%&'()$*+,-./0&,$1.+23/'4$
!"#$
!$
!$
!"#$%#&'#()*+(),-)./012)
!$
!$
%&'()$*+,-./0&,$1.+23/'4$
23
!"#$%&'()$*+,-./0&,$1.+23/'4$
!"#$
!"#$"%%&%'()'$*+%(,$-$
.(/0123$4567$
%$&'$())*)+,-+,$,'$./0'($1,$01$268,9%%$2&,$&)($/)$34)$1/$567'8$9(0($:0*(0;$:/-.*<&0(0$,$,8,:&+(0$+(0,.()=$
>0/.=$6?,8(-10,$@(?A*-/+$ !"#$
!"#$"%%&%'()'$*+%(,$-$
.(/0123$4567$
%$&'$())*)+,-+,$,'$./0'($1,$01$268,9%%$2&,$&)($/)$34)$1/$567'8$9(0($:0*(0;$:/-.*<&0(0$,$,8,:&+(0$+(0,.()=$
>0/.=$6?,8(-10,$@(?A*-/+$!"#$
!"#$"%%&%'()'$*+%(,$-$
.(/0123$4567$
%$&'$())*)+,-+,$,'$./0'($1,$01$268,9%%$2&,$&)($/)$34)$1/$567'8$9(0($:0*(0;$:/-.*<&0(0$,$,8,:&+(0$+(0,.()=$
>0/.=$6?,8(-10,$@(?A*-/+$
!"#$%&'()*+,-")&.+(/0,#1& 223&
!"#$%&'()#*#+,'&,-$#+.'(/#(0$1(1%&-2134'(2'$(150-*-34'(/#(/1/'*(
6!"##$%$&'()*"+,+-+./7&
&
&
451)&106#&-)&+780509:#&6)";01)&8;&;)(<#"&=#,1"#()&5#/")&1#-+5&+5&)1+6+5&-+&
+780509:#&)&6"0,=06+(;),1)&58+&1);6#"0>+9:#%&?#,51"80"&,#&6+0,)(&$"#,1+(@&
!"#$%&'()*+,-")&.+(/0,#1& 223&
!"#$%&'()#*#+,'&,-$#+.'(/#(0$1(1%&-2134'(2'$(150-*-34'(/#(/1/'*(
6!"##$%$&'()*"+,+-+./7&
&
&
451)&106#&-)&+780509:#&6)";01)&8;&;)(<#"&=#,1"#()&5#/")&1#-+5&+5&)1+6+5&-+&
+780509:#&)&6"0,=06+(;),1)&58+&1);6#"0>+9:#%&?#,51"80"&,#&6+0,)(&$"#,1+(@&
!"#$%&'()*+,-")&.+(/0,#1& 223&
!"#$%&'()#*#+,'&,-$#+.'(/#(0$1(1%&-2134'(2'$(150-*-34'(/#(/1/'*(
6!"##$%$&'()*"+,+-+./7&
&
&
451)&106#&-)&+780509:#&6)";01)&8;&;)(<#"&=#,1"#()&5#/")&1#-+5&+5&)1+6+5&-+&
+780509:#&)&6"0,=06+(;),1)&58+&1);6#"0>+9:#%&?#,51"80"&,#&6+0,)(&$"#,1+(@&
!"#$%&'()*+,-")&.+(/0,#1& 223&
!"#$%&'()#*#+,'&,-$#+.'(/#(0$1(1%&-2134'(2'$(150-*-34'(/#(/1/'*(
6!"##$%$&'()*"+,+-+./7&
&
&
451)&106#&-)&+780509:#&6)";01)&8;&;)(<#"&=#,1"#()&5#/")&1#-+5&+5&)1+6+5&-+&
+780509:#&)&6"0,=06+(;),1)&58+&1);6#"0>+9:#%&?#,51"80"&,#&6+0,)(&$"#,1+(@&
!"#$%&'()*+,-")&.+(/0,#1& 223&
!"#"$%&'%()"$*&+,"+-).+./'(0.12&+0&)+.3-(#(12&+,"+
,.,&#+0&$*4$-.+&
&
4#,51"60"&67+&"#10,+&8+"+&")+(09+"&+:6050;<)5&=#,1>,6+5&-)&-+-#5%&4#7#&56?)51@#&
5)?6)&67&)*)78(#&-#&8+0,)(&$"#,1+(&)&-#&-0+?"+7+&-)&/(#=#5&56?)"0-#&A65)&56+&
07+?0,+;@#BC%&D)+(09+"&+:6050;<)5&=#7&+&8(+=+&EF.&A#6="#&G'H&-058#,>I)(C&)&
67&?)"+-#"&-)&50,+05%&
!"#$%&'()*+,-")&.+(/0,#1& 223&
!"#"$%&'%()"$*&+,"+-).+./'(0.12&+0&)+.3-(#(12&+,"+
,.,&#+0&$*4$-.+&
&
4#,51"60"&67+&"#10,+&8+"+&")+(09+"&+:6050;<)5&=#,1>,6+5&-)&-+-#5%&4#7#&56?)51@#&
5)?6)&67&)*)78(#&-#&8+0,)(&$"#,1+(&)&-#&-0+?"+7+&-)&/(#=#5&56?)"0-#&A65)&56+&
07+?0,+;@#BC%&D)+(09+"&+:6050;<)5&=#7&+&8(+=+&EF.&A#6="#&G'H&-058#,>I)(C&)&
67&?)"+-#"&-)&50,+05%&
!"#$%&'()*+,-")&.+(/0,#1& 223&
!"#"$%&'%()"$*&+,"+-).+./'(0.12&+0&)+.3-(#(12&+,"+
,.,&#+0&$*4$-.+&
&
4#,51"60"&67+&"#10,+&8+"+&")+(09+"&+:6050;<)5&=#,1>,6+5&-)&-+-#5%&4#7#&56?)51@#&
5)?6)&67&)*)78(#&-#&8+0,)(&$"#,1+(&)&-#&-0+?"+7+&-)&/(#=#5&56?)"0-#&A65)&56+&
07+?0,+;@#BC%&D)+(09+"&+:6050;<)5&=#7&+&8(+=+&EF.&A#6="#&G'H&-058#,>I)(C&)&
67&?)"+-#"&-)&50,+05%&
!"#$%&%&'"(")*'"+',-./%0.)*'1(2(%*'+'+3%4%&')*'"(")*'2)'5&67%1)8'9+.+1%)2(&'!"#$%&#'(%0(&('
:;;;')"#$<*='*+,,(-%)./('0(&('>;;;'+'?'"+'!"#$)%'0%&(#1'0(&('>;;;8'9+.+1%)2(&')*'1(2(%*'
@A+&%7%1(&')'$*)'"+'$,('+2/&("('"+'1)2/&).+'")'/%0)'*/&%25B'0(&(';=':='C')$';DC8'E)'1(2(.':'
1)2+1/(&'$,(')2"('*+2)%"(.'+'$,(')2"('#$("&(")'2)'1(2(.'C8'F)2*/&$%&')'*+5$%2/+'"%(5&(,('
"+'4.)1)*D'
'
!"#$%&%&'"(")*'"+',-./%0.)*'1(2(%*'+'+3%4%&')*'"(")*'2)'5&67%1)8'9+.+1%)2(&'!"#$%&#'(%0(&('
:;;;')"#$<*='*+,,(-%)./('0(&('>;;;'+'?'"+'!"#$)%'0%&(#1'0(&('>;;;8'9+.+1%)2(&')*'1(2(%*'
@A+&%7%1(&')'$*)'"+'$,('+2/&("('"+'1)2/&).+'")'/%0)'*/&%25B'0(&(';=':='C')$';DC8'E)'1(2(.':'
1)2+1/(&'$,(')2"('*+2)%"(.'+'$,(')2"('#$("&(")'2)'1(2(.'C8'F)2*/&$%&')'*+5$%2/+'"%(5&(,('
"+'4.)1)*D'
'
24
!"#$
!"#$%&'(')(*+',-."/%0$$
$
%&'()*'+$',$,&-.)/0&,$0'+&1',2$3&,&/45(4&+$.6'$+50)/'$7'+'$-&+'+$.6'$5/3'$
,&/5)3'($89.&$7&+6)0'$'(0&+'+$'$,.'$'67()0.3&$&$1+&9:;/<)'=$&$)/0&+<'('+$.6$>?$9.&$
'7+&,&/0&$5$<5++&,75/3&/0&$&,7&<0+5$35$,)/'($-&+'35$8@)@()50&<'2$!"#$%&'
()*+,--"$#.'/%0,1*)2'3,%-4),2,$5-.'!6,+5)%&'7%--"-5%$58=A$
!"#$
!"#$%&'(')(*+',-."/%0$$
$
%&'()*'+$',$,&-.)/0&,$0'+&1',2$3&,&/45(4&+$.6'$+50)/'$7'+'$-&+'+$.6'$5/3'$
,&/5)3'($89.&$7&+6)0'$'(0&+'+$'$,.'$'67()0.3&$&$1+&9:;/<)'=$&$)/0&+<'('+$.6$>?$9.&$
'7+&,&/0&$5$<5++&,75/3&/0&$&,7&<0+5$35$,)/'($-&+'35$8@)@()50&<'2$!"#$%&'
()*+,--"$#.'/%0,1*)2'3,%-4),2,$5-.'!6,+5)%&'7%--"-5%$58=A$
!"#$
!"#$%&'(')(*+',-."/%0$$
$
%&'()*'+$',$,&-.)/0&,$0'+&1',2$3&,&/45(4&+$.6'$+50)/'$7'+'$-&+'+$.6'$5/3'$
,&/5)3'($89.&$7&+6)0'$'(0&+'+$'$,.'$'67()0.3&$&$1+&9:;/<)'=$&$)/0&+<'('+$.6$>?$9.&$
'7+&,&/0&$5$<5++&,75/3&/0&$&,7&<0+5$35$,)/'($-&+'35$8@)@()50&<'2$!"#$%&'
()*+,--"$#.'/%0,1*)2'3,%-4),2,$5-.'!6,+5)%&'7%--"-5%$58=A$
!"#$%&'()*+,-")&.+(/0,#1& 234&
!"#$%&'()*+,-")&.+(/0,#1& 234&!"#$%&'()*+,-")&.+(/0,#1& 234&
!"#$%&'()*+,-")&.+(/0,#1& 232&