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Truth Tables Logic Gates: AND Logic Gates: OR Logic Gates: NOT Summary of Logic Gates and Truth Tables Combinational Logic Circuits Logic Circuit #1: Car s Hot Engine Logic Circuit #2: Central Heating Pump Logic Circuit #3: Greenhouse Heater Summary of Combinational Logic Circuits V ! ,  D$  Nиgֳgֳ?#" `G BContents  ff6  ZHgֳgֳ8c? PTLD___PPT9& PPage Title Clocks A Simple Oscillator Circuit How an Oscillator Circuit Works How an Oscillator Circuit Works (Alternative) How to Change a Clock s Frequency Counters Counting in Decimal Devices Using Counters f !  ,  D$\  C 4A Gate - AND 1a(0c z  s DAm?Gate - OR 1a"` 0 |  s FA3?Gate - NOT 1a"` 0H  0޽h ? ̙33___PPT10i.T{P6&+D=' = @B + % @&w(  ?  ZGfgֳgֳo?"`P0J ,$0 s+ Electronics Section 4.4 Digital Processes ,,$  ! NOfgֳgֳ?#" `G \"Electronics 4.4: Digital Processes##ffX " C 0ALED DiagramZ*:g # C XA@Electronic Symbol - LED CorrectZj`d $ C <A$Gate - XOR Detailh PX % C 0Aled-circuit `:N & C &A OBJ115Zj`H  0޽h ? ̙33y___PPT10Y+D=' = @B +E \ T P  (       ZXfgֳgֳo?"`2*"___PPT9    Transistor as a Switch (G) State that a transistor can be used as a switch. (G) State that a transistor may be conducting or nonconducting, ie on or off. Simple Switching Systems (G) Draw and identify the circuit symbol for an NPN transistor. (G) Identify from a circuit diagram the purpose of a simple transistor switching circuit. (C) Explain the operation of a simple transistor switching circuit. Digital Logic Gates (G) Draw and identify the symbols for two-input AND, OR and NOT gates. (G) State that logic gates may have one or more inputs and that a truth table shows the output for all possible input combinations. (G) State that high voltage = logic 1, low voltage = logic 0. (G) Draw the truth tables for AND OR and NOT gates. (C) Identify the following gates from truth tables: AND, OR, NOT. Combinational Logic Circuits (G) Explain how to use combinations of digital logic gates for control in simple situations. (C) Complete a truth table for a simple combinational logic circuit. Clock Signals (G) State that a digital circuit can produce a series of clock pulses. (C) Explain how a simple oscillator built from a Resistor, Capacitor and Inverter operates. (C) Describe how to change the frequency of a clock. Counters (G) Give an example of a device containing a counter circuit. (G) State that there are circuits which can count digital pulses. (G) State that the output of the counter circuit is in binary. (G) State that the output of a binary counter can be converted to decimal.!!D!=!B!]!E!G!!  !  2  K      =      W    A    D    ;  1  ?       $$ Z$$ (( B(( ,, ,, 00 D00 44 Y44 44 244 88 88 << ;<< << ?<< << <<< << H<< } WC#h   Nfgֳgֳ?#" `G b(4.4 Digital Processes: Learning Outcomes))ffH   0޽h ? ̙33___PPT10i.N+D=' = @B + ` l(  l"  l NԔ?"`} ,$@0 l Nfgֳgֳ?#" `G QIntroducing TransistorsffB l HD)?l ,$@0B l HD)?Y,$@0B l ND)?l ,$@0B l NZD)?,$D0l  l TХfgֳgֳo?"` ,,$D0 *This is the symbol for an NPN transistor.3*+ ) + UvgIIt  l TЯfgֳgֳ֭o?"`,A,$D0  Transistors are process devices.<!   ! UvgIIH l 0޽h ? ̙33___PPT10i.\ө+:+D' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* l%(D' =-o6Bdissolve*<3<* lD ' =%(Dw ' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* l%(D' =-o6Bdissolve*<3<* lD3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*l%(D' =-o6Bdissolve*<3<*lD3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*l%(D' =-o6Bdissolve*<3<*lD3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*l%(D' =-o6Bdissolve*<3<*lD3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*l%(D' =-o6Bdissolve*<3<*lD' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* l%(D' =-o6Bdissolve*<3<* l+p+0+ lO ++0+ lO ++B#style.visibility<* p%(D' =-o6Bdissolve*<3<* pD3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =-o6Bdissolve*<3<*pD3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =-o6Bdissolve*<3<*pD3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =-o6Bdissolve*<3<*pD3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =-o6Bdissolve*<3<*pD' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* p%(D' =-o6Bdissolve*<3<* pD' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* p%(D' =-o6Bdissolve*<3<* pD' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* p%(D' =-o6Bdissolve*<3<* p++0+ po ++0+ po ++0+ pO +3 7/t(  t"  t NԔ?"`dC ,$@0 t Nfgֳgֳ?#" `G PTransistor as a SwitchffB t HD)? ,$@0B t HD)? ,$@0B t ND)? } ,$@0B t NZD)? P ,$D03  t T jgֳgֳo?"`7 %Transistors can be used as switches.1*& $ & UvgII  t Th3jgֳgֳo?"`R 7j,$D 0 7Transistors can either conduct or not conduct current.2 !    8 UvgII  t T,jgֳgֳo?"`7,$D0 )ie, transistors can either be on or off.2r*  * UvgII"  t NԔ?"`& ,$@0B t HD)?,$@ 0B t HD)? ,$@ 0B t HD)?9,$D 0J t TTKjgֳgֳo?"` ] ,$D0  Transistor(      UvgIIF t TlSjgֳgֳo?"` c ,$D 0 Switch(   UvgIIH t 0޽h ? ̙33##___PPT10e#.^pǁ+KwDY"' = @B D"' = @BA?%,( < +O%,( < +D ' =%(Dw ' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* t%(D' =-o6Bdissolve*<3<* tD3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =-o6Bdissolve*<3<*tD3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =-o6Bdissolve*<3<*tD3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =-o6Bdissolve*<3<*tD3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =-o6Bdissolve*<3<*tD' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =-o6Bdissolve*<3<*tD ' =%(D< ' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* t%(D' =-o6Bdissolve*<3<* tD3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =-o6Bdissolve*<3<*tD3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =-o6Bdissolve*<3<*tD3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =-o6Bdissolve*<3<*tD' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =-o6Bdissolve*<3<*tD' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* t%(D' =-o6Bdissolve*<3<* tD' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* t%(D' =-o6Bdissolve*<3<* t++0+ to ++0+ to ++0+to ++0+to +    = (    NXjgֳgֳ?#" `G NHow Transistors Workff"  NԔ?"`V5 1 pB  HD)?| | pB  HD)?x{ xvB  ND)?Z| o vB   NZD)?| B    Tjjgֳgֳ֭o?"` C,$D0 HSwitching is controlled by the voltage between the Base and the Emitter.hI    I UvgII   Tajgֳgֳo?"`d   Collector(      UvgII   T4|jgֳgֳo?"`! S  Emitter(   UvgII   Tjgֳgֳo?"` ~Base(   UvgII  TDjgֳgֳ֭o?"` T ,$D0 IgWhen VBE < 0.7V the transistor switches off and no current flows between the Collector and the Emitter.0 8  ' h UvgIIn  T̊jgֳgֳ֭o?"` T,$D0 When VBE e" 0.7V the transistor switches on and current flows between the Collector and the Emitter./ 5   ' d UvgIIH  0޽h ? ̙33  ___PPT10 .`@+-D ' = @B D ' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*++0+ q ++0+q ++0+q +M ;3$(    Njgֳgֳ?#" `G jTransistor Switching Example150ffff  Tjgֳgֳo?"`H T` ,$D0 9MWhen VBE is less than 0.7V the transistor is off and the lamp does not light.1    N UvgII  Tjgֳgֳo?"` T8,$D0 3GWhen VBE is greater than 0.7V the transistor is on and the lamp lights.3     H UvgIIpB  HD)? g pB  HD)?g pB   HD)?` pB   HD)?mpB   HD)? pB   HD)?mmpB   HD)?wZ  N)?"` PpB  HD)?}}pB  HD)? vB  ND)?2pB  HD)?pB  HD)?pB  HD)?gg}pB  HD)?gg vB  ND)?ggvB  NZD)? vB  ND ?" pB  HD)?` ` pB  HD)?` ` vB ! NZD ? ` 2  Np?"`    fTj1?  SX  " T\jgֳgֳo?"`9%  Variable Voltage Supply$  UvgII $ Zj1?j O12V  H  0޽h ? ̙33___PPT10.pͧ+z)D' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*+p+0+q ++0+q +t    xb (  x x Nlgֳgֳ?#" `  m5Transistor Circuit #1: Temperature-Controlled Circuit66ff x <lA  kW)  "  x T4lgֳgֳ֭o?"`m RS,$D0 .This transistor circuit contains a Thermistor.D!  # / UvgII x T\lgֳgֳ֭o?"`m R-,$D0 DBecause of the thermistor, this circuit is dependent on temperature.6E 8 E UvgII x Tlgֳgֳ֭o?"`}m R ,$D0 TThe purpose of this circuit is to turn on the LED when the temperature reaches . . .U UU UvgIIq  x Th!lgֳgֳo?"`b >M ,$D0 9Input = Voltage Divider Process = Transistor Output = LED: :: UovgIIX  x T*lgֳgֳo?"`o m Rt$D0@8___PPT9 JLED = Off. Heat the Thermistor. RThermistor . VThermistor . Voltage across 10kW resistor . Transistor switches on. LED = On.! !   $F       F U iIH x 0޽h ? ̙33JB___PPT10"._`u+xD' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =-o6Bdissolve*<3<*xD' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =-o6Bdissolve*<3<*xD' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =-o6Bdissolve*<3<*xD' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* x%(D' =-o6Bdissolve*<3<* xD' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* x%(D' =-o6Bdissolve*<3<* x++0+xq ++0+xq ++0+xq ++0+ xq ++0+ xq +    | (  | | N;lgֳgֳ?#" `G i/Transistor Circuit #2: Light-Controlled Circuit00ff | <^lA  ZT@ m  "  | Tp1lgֳgֳ֭o?"`m RS,$D0 <This transistor circuit contains a Light-Dependent Resistor.D!  #= UvgII | Th5lgֳgֳ֭o?"`m Rm,$D0 7Because of the LDR, this circuit is dependent on light.68 18 UvgII  | Tplgֳgֳ֭o?"`m RT,$D0 ]The purpose of this circuit is to turn on the LED when the light reaches a certain intensity.^ ^^ UvgIIq  | Tlwlgֳgֳo?"`b >M ,$D0 9Input = Voltage Divider Process = Transistor Output = LED: :: UovgII  | Tlgֳgֳo?"`m Ri t$D0@8___PPT9 zLED = Off. Cover LDR. RLDR . VLDR . Transistor switches on. LED = On.H!   "H U iIH | 0޽h ? ̙33JB___PPT10"._+n+%(D' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*|%(D' =-o6Bdissolve*<3<*|D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*|%(D' =-o6Bdissolve*<3<*|D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* |%(D' =-o6Bdissolve*<3<* |D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* |%(D' =-o6Bdissolve*<3<* |D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* |%(D' =-o6Bdissolve*<3<* |++0+|Y ++0+|Y ++0+ |Y ++0+ |Y ++0+ |Y +&  !(    <0lA  U@  "   Nlgֳgֳ?#" `G h.Transistor Circuit #3: Time-Controlled Circuit//ff  T(lgֳgֳ֭o?"`m RS,$D0 -This transistor circuit contains a Capacitor.D!   # . UvgII  Tlgֳgֳ֭o?"`m R,$D0 oBecause of the capacitor, this circuit is dependent on the time taken to charge and discharge of the capacitor.6p 77p UvgII   Tlgֳgֳ֭o?"`7m R ,$D0 ZThe purpose of this circuit is to turn on the LED a short time after the switch is opened.[ [[ UvgII_   Tdlgֳgֳ֭o?"` m R ,$D0 +Where would this circuit be found in a car?, ,, UvgIIq   T|lgֳgֳo?"` >M : ,$D0 9Input = Voltage Divider Process = Transistor Output = LED: :: UovgII   Tlgֳgֳo?"` @ %$D0^V___PPT980 |Open Switch. VC . Transistor switches on after a short delay. LED = On.0!    !   I U iI   Ttlgֳgֳo?"` @ t$D0@8___PPT9 ;Switch closed. VC = 0V. Transistor switches off. LED = Off.:<!  +< U iIH  0޽h ? ̙33___PPT10.__+D' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* ++0+q ++0+q ++0+ Y ++0+ Y ++0+ Y ++0+ Y ++0+ Y += &(    Nlgֳgֳ?#" `G b(Summary of Transistor Switching Circuits))ff  Tlgֳgֳo?"`$z,$D0 jYou are expected to know the purpose of a transistor switching circuit: the last three pages should help.4.k i k UvgII   T(ngֳgֳ֭o?"`,$D0 2In each of the three circuits the input device is:63 " 3 UvgIIg   TH+ngֳgֳ֭o?"`6jB,$D0 A Voltage Divider using a6   UvgII>   T(#ngֳgֳo?"` ,$@0 x Thermistor     UvgII7   T:ngֳgֳo?"` ,$@0 qLDR  UvgII=  TBngֳgֳo?"`  ,$D 0 w Capacitor     UvgII  TKngֳgֳ֭o?"` F ,$D0 3In each of the three circuits the output device is:64 " 4 UvgIIF  TElectronic Symbol - Thermistor[,$D0  C HA0Electronic Symbol - LDRzV,$D0B  HD)?R 99 ,$@ 0B  HD)?R  ,$@ 0B  HD)?  ,$@ 0B  HD)? : ,$@ 0  C 0ALED Diagram FY,$D0H  0޽h ? ̙33'++___PPT10*.``a\+1D)' = @B D(' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D+' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D+' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D ' =%(D ' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*++0+Y ++0+ Y ++0+ Y ++0+ Y ++0+ Y ++0+Y ++0+Y ++0+Y +( ?7(    Ndngֳgֳ?#" `G ?Logicff   <W?LogicComic Sans MS"`dH  0޽h ? ̙33___PPT10i..PR+D=' = @B +. \ (  \ \ Tmngֳgֳo?"`l7,$D0 BbFrom Section 4.2 Output Devices, remember that digital signals have only two values,7  1 and  _ , or  High Voltage and  ___ _______ , or  On and  ___ , or  True and  _____ .V \ T  " UvII" \ TLo?"` ],$@0" \ TG$*Hb\IԔ?7  ,$@0" \ TG%*HIԔ?7 Z? ,$@0"  \ TG$*Hb\IԔ?7 z ,$@0"  \ TG%*HIԔ?7 @ %,$@0  \  `un1?,$0 7Off  \  `Dn1?  ,$ 0 6On  \  `n1? -) ,$ 0 @ High Voltage   \  `n1?,$ 0 ? Low Voltage   \ Nngֳgֳ?#" `G SRevision: Digital Signalsff \  `hn1? 7 ,$ 0 51 \  ` n1?,$ 0 50H \ 0޽h ?O\\ \ \ ̙33aY___PPT109.t+(D' = @B D@' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*\%(D' =-o6Bdissolve*<3<*\D' =%(D'' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*\%(D' =-o6Bdissolve*<3<*\D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*\%(D' =-o6Bdissolve*<3<*\D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*\%(D' =-o6Bdissolve*<3<*\D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* \%(D' =-o6Bdissolve*<3<* \D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* \%(D' =-o6Bdissolve*<3<* \D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* \%(D' =-o6Bdissolve*<3<* \D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* \%(D' =-o6Bdissolve*<3<* \D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* \%(D' =-o6Bdissolve*<3<* \D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*\%(D' =-o6Bdissolve*<3<*\D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*\%(D' =-o6Bdissolve*<3<*\D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*\%(D' =-o6Bdissolve*<3<*\++0+\ ++0+ \ ++0+ \ ++0+ \ ++0+\ ++0+\ ++0+\ ++ -(    Nxngֳgֳ?#" `G OIntroduction to Logicff   fxngֳgֳƍرdo?" `&,$D0 Many digital electronic processes are designed around  logic circuits.>& " 7H UvgII   fngֳgֳƍرdo?" ` ,$D0 bThe Inputs and Outputs in logic have only two values: 0 & 1; High & Low; On & Off; True and False.66 - 6-c Uv,` ` B B    fngֳgֳƍرdo?" `j  ,$D0 `Logic is ideally suited to help design digital electronic circuits because of its binary nature.>' : R a UvgIIt   fngֳgֳƍرdo?" `D v,$D0 0We will look at some fundamental logic circuits.1 11 UvgIIH  0޽h ? ̙336.___PPT10.dE +D ' = @B D ' = @BA?%,( < +O%,( < +D' =%(D' =%(DG' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+v4 ,0B*O3> B<*D' =%(D' =%(DG' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+v4 ,0B*O3> B<*D' =%(D' =%(DG' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+v4 ,0B*O3> B<*D' =%(D' =%(DG' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+v4 ,0B*O3> B<*++0+ ++0+ ++0+ ++0+ +  WO `(  `2 ` N)?"` >vB  `@ ND)? .vB  ` ND)? .pB  ` HD)?>  | ` Npgֳgֳ?#" `G SLogic: Switches in SeriesffpB ` HD)?|7}pB ` HD)?| |pB  ` HD)?6 pB  ` HD)?SpB ` HD)?\\pB ` HD)?66pB ` HD)?\66|pB ` HD)?  pB ` HD)?}pB ` HD)? }j ` Tngֳgֳ֭o?"`  ,$D0 8The bulb will light only under certain conditions: what?9 99 UvgII `  `p1?m 6S1 `  `hp1?   6S2 ` TXpgֳgֳ֭o?"`[ Y,$D0 JComplete the following: The bulb will turn on only when switches S1 ___ S2 are closed, for all other combinations the bulb is off.v k   7 UvgII ` Nlp}})?"`U,$@0 V"S1 S2 Lit 0 0 0 0 1 0 1 0 0 1 1 1##B ` HD)?,$@0B ` NZD)?3,$D0pB ` HD)?}  ~H ` 0޽h ? ̙33`X___PPT108.ba+Dd' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*`%(D' =-o6Bdissolve*<3<*`D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*`%(D' =-o6Bdissolve*<3<*`Df' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*`%(D' =-o6Bdissolve*<3<*`D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*`%(D' =-o6Bdissolve*<3<*`D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*`%(D' =-o6Bdissolve*<3<*`++0+` ++0+` ++0+` +e  0"h=(  h h N\vB h@ ND)? .vB h ND)?~ .pB h HD)?> pB  h HD)?|=}pB  h HD)? pB  h HD)?pB h HD)?\s*\pB h HD)?pB h HD)? pB h HD)? } h  `Cp1?  6S1pB h HD)? '6  h  `Gp1?& ~ F  6S2pB h HD)?] e h TlKpgֳgֳ֭o?"`  ,$D0 3The bulb will light under certain conditions: what?4 44 UvgII h TSpgֳgֳ֭o?"`> <,$D0 }Complete the following: The bulb will turn on when switches S1 ___ S2 are closed, for all other combinations the bulb is off.J f '<~ UvgIIpB h HD)? < pB h HD)?}N ~pB h HD)? M   h TWpm)??"`D,$@0 V"S1 S2 Lit 0 0 0 0 1 1 1 0 1 1 1 1##B !h ND)??z,z,$@0B "h TZD)??99,$D0H h 0޽h ? ̙33`X___PPT108.2+v^\Dd' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*h%(D' =-o6Bdissolve*<3<*hD' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*h%(D' =-o6Bdissolve*<3<*hDf' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* h%(D' =-o6Bdissolve*<3<* hD3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*!h%(D' =-o6Bdissolve*<3<*!hD3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*"h%(D' =-o6Bdissolve*<3<*"h++0+h ++0+h ++0+ h +K$ @C(    N\xpgֳgֳ?#" `G KLogic: Opposites!ff2  N)?"`~ >vB @ ND)? .vB  ND)?~ .pB   HD)?> }pB   HD)? pB   HD)?pB   HD)?\s*\pB  HD)?pB  HD)? pB  HD)?z    `@p1?z  5SpB  HD)?]}e  Tpgֳgֳ֭o?"`p ,$D0 3The bulb will light under certain conditions: what?4 44 UvgII  Tpgֳgֳ֭o?"`  ,$D0 kComplete the following: The bulb will turn on when switch S is ____, and turn off when switch S is ______.` T ' l UvgIIpB  HD)?  z  Tp3)??"`D,$@0 BS Lit 0 1 1 0B  ND)??z,z,$@0B  TZD)??,$D0pB  HD)?| }pB  HD)?  }  Tpgֳgֳ֭o?"` ,$D0 }This circuit is for illustration only! If this was a real circuit, what would happen to the battery when switch S was closed?,d  ~$% X UvgIIH  0޽h ? ̙33@8___PPT10./` +HྤD ' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*++0+ ++0+ ++0+ ++0+ +s0 ?7P (    N@pgֳgֳ?#" `G F Truth Tables  ffz  Tpgֳgֳ֭o?"`M,$D0 2The tables on the previous pages are truth tables.03 % 3 UvgII  Tpgֳgֳ֭o?"`,$D0 hTruth Tables list: All combinations of all possible inputs, Every Output for each combination of inputs.f V  !i UvII  Ttpgֳgֳ֭o?"``x ,$D0 VThere are special circuits called logic gates which can be used in control situations.>4 # " *$3 # UvgII  Np}})?"` ,$@0 V"S1 S2 Lit 0 0 0 0 1 0 1 0 0 1 1 1##B   HD)?u iu ,$@0B   NZD)? vv,$D0   TTpm)??"` j,$@0 V"S1 S2 Lit 0 0 0 0 1 1 1 0 1 1 1 1##B   ND)??u Ru ,$@ 0B   TZD)?? _ _ ,$D 0   T+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*Df' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* Df' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* Df' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*+P+0+ ++0+ ++0+ ++0+ ++0+  ++0+ +p# m e ` 4 (  4 4 Npgֳgֳ?#" `G JLogic Gates: ANDff 4 C 4A Gate - AND 1a A,$D0! 4 Zr}}o?"`z7 ,$D0 UTwo-Input AND Gate5& i 4 N\r}})?"`<I ,$@0 3AND Truth Table8,16 A B Q 0 0 0 0 1 0 1 0 0 1 1 1Z4   B 4 HD)?}C},$@0B  4 NZD)? ,$D0X  4 N r}}o?"`Y T< ,$D0 :The output of an AND gate is 1 only when all inputs are 1.B; i  4 Nr}}o?"` T<$,$D0 5Only when Input A AND Input B are 1, the output is 1.X6   4 Trgֳgֳo?"`eT3 q,$D 0 JSee page  Logic: Switches in Series .& && UvgIIH 4 0޽h ? ̙33___PPT10.m"+  D?' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =-o6Bdissolve*<3<*4D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =-o6Bdissolve*<3<*4D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* 4%(D' =-o6Bdissolve*<3<* 4D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* 4%(D' =-o6Bdissolve*<3<* 4Df' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =-o6Bdissolve*<3<*4D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =-o6Bdissolve*<3<*4D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* 4%(D' =-o6Bdissolve*<3<* 4D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* 4%(D' =-o6Bdissolve*<3<* 4++0+4 ++0+4 ++0+ 4 ++0+ 4 ++0+ 4 +#   p 8# (  8 8 N>rgֳgֳ?#" `G ILogic Gates: ORff& 8  `Brmo??"`zF] ,$D0 TTwo-Input OR Gate5& ` 8 TxGrm)??"`<w ,$@0 2OR Truth Table8,16 A B Q 0 0 0 0 1 1 1 0 1 1 1 1L3  B 8 ND)??}C},$@0B 8 TZD)?? ,$D0V 8 Trmo??"`Y  ,$D0 2The output of an OR gate is 1 when any input is 1.B3 h  8 TTrmo??"` $,$D0 .When Input A OR Input B is 1, the output is 1.X/  8 s DAm?Gate - OR 1a"` @,$D0  8 T\rgֳgֳo?"`e q,$D 0 NSee page  Logic: Switches in Parallel .( (( UvgIIH 8 0޽h ? ̙33___PPT10.m"+_wJLD?' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* 8%(D' =-o6Bdissolve*<3<* 8D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =-o6Bdissolve*<3<*8D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =-o6Bdissolve*<3<*8D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* 8%(D' =-o6Bdissolve*<3<* 8Df' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =-o6Bdissolve*<3<*8D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =-o6Bdissolve*<3<*8D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =-o6Bdissolve*<3<*8D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* 8%(D' =-o6Bdissolve*<3<* 8++0+8 ++0+8 ++0+8 ++0+ 8 ++0+ 8 +'    <* (  < < Nrgֳgֳ?#" `G JLogic Gates: NOTff <  `|r3o??"`z/ ,$D0 K NOT Gate5&  O < Tr3)??"`<w> ,$@0 !NOT Truth Table8,16 A Q 0 1 1 0L"   B < ND)??}C},$@0B < TZD)??,$D 0Z < Tr3o??"`v  ,$D0 6The output of a NOT gate is the opposite of the input.B7 j < Tr3o??"` ',$D0 FWhen Input A is 0, the output is 1. When Input A is 1, the output is 0BG  < s FA3?Gate - NOT 1a"`z C,$D0$  < Tr3o??"`  ,$D0 ^(Note that NOT gates have only one input.))p  < T rgֳgֳo?"`e@ q,$D 0 :See page  Logic: Opposites! .  UvgIIH < 0޽h ? ̙33___PPT10.m"+? zD7' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* <%(D' =-o6Bdissolve*<3<* <D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =-o6Bdissolve*<3<*<D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* <%(D' =-o6Bdissolve*<3<* <D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =-o6Bdissolve*<3<*<D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =-o6Bdissolve*<3<*<Df' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =-o6Bdissolve*<3<*<D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =-o6Bdissolve*<3<*<D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =-o6Bdissolve*<3<*<D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* <%(D' =-o6Bdissolve*<3<* <+P+0+< ++0+< ++0+< ++0+< ++0+ < ++0+ < +6 @(  @ @ N|rgֳgֳ?#" `G a'Summary of Logic Gates and Truth Tables((ff @ Trgֳgֳo?"` ,$D0 %ATruth Tables list:6 Every Output for every combination of inputs.f .    :   UvYIIA @ N8r}})?"`0P ,$@0 'AND Gate A B Q 0 0 0 0 1 0 1 0 0 1 1 1>  B @ HD)?8,$@0B @@ NZD)?@E ,$D08 @ Txrm)??"`0` ,$@0 r&OR Gate A B Q 0 0 0 0 1 1 1 0 1 1 1 10B @ ND)??,$@ 0B  @ TZD)??U Y ,$D 0'  @ Tr3)??"`00?,$@ 0 aNOT Gate A Q 0 1 1 00   B  @ ND)??,$@ 0B  @@ TZD)??,$D0  @ C 4A Gate - AND 1aP P ,$D0 @ s DAm?Gate - OR 1a"`P : ,$D0 @ s FA3?Gate - NOT 1a"`P F ,$D 0q @ Trgֳgֳo?"`0,$D0 )Logic gates may have one or more inputs.6(* ( ) UvYIIH @ 0޽h ? ̙33m'e'___PPT10E'.m"+aD&' = @B D%' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =-o6Bdissolve*<3<*@D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* @%(D' =-o6Bdissolve*<3<* @Df' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =-o6Bdissolve*<3<*@D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =-o6Bdissolve*<3<*@D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =-o6Bdissolve*<3<*@D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =-o6Bdissolve*<3<*@Df' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =-o6Bdissolve*<3<*@D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =-o6Bdissolve*<3<*@D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* @%(D' =-o6Bdissolve*<3<* @D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =-o6Bdissolve*<3<*@Df' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* @%(D' =-o6Bdissolve*<3<* @D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* @%(D' =-o6Bdissolve*<3<* @D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* @%(D' =-o6Bdissolve*<3<* @D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =-o6Bdissolve*<3<*@++0+@ ++0+@ ++0+@ ++0+ @ ++0+@ + D<(  D D Nugֳgֳ?#" `G l Combinational Logic Circuits9,170!ffff D THugֳgֳ֭o?"`,$D0 ^Combinational Logic Circuits are simply circuits using a combination of AND, OR and NOT gates.>9 & 9 $8 & UvgII& D T@ugֳgֳ֭o?"`(,$D0 `bYou are expected to design Logic Circuits and Truth Tables of simple combinational logic circuits.T. 5  )f     5 UvgII D C 4A Gate - AND 1a',$D0 D s DAm?Gate - OR 1a"`:S ,$D0 D s FA3?Gate - NOT 1a"`M  ,$D0H D 0޽h ? ̙33{s___PPT10S.m"+*D' = @B Dr' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D' =-o6Bdissolve*<3<*DD' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D' =-o6Bdissolve*<3<*DD' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D' =-o6Bdissolve*<3<*DD' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D' =-o6Bdissolve*<3<*DD' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D' =-o6Bdissolve*<3<*D+p+0+D ++0+D +< H (  H H N4ugֳgֳ?#" `G ~DLogic Circuit #1: Car s Hot Engine##ff  H T(8ugֳgֳ֭o?"`S,$D0 ZWhen a car s engine becomes too hot an LED should light but only when the ignition is switched on.D8 + 8(c UvgIIr H N3fp?"`c o,$@0B H HD)?o,$@ 0B H HD)?sY s,$@ 0B H HD)?Y ,$@ 07  H TEugֳgֳ֭o?"`(,$@ 0 qLED  UvgIIC  H TMugֳgֳo?"`+,$@ 0 }Ignition Switch  UvgIIR  H  `Vugֳgֳfo?"`8+ ,$@0 Temperature Sensor  UvgII  H N^u)?"` P P,$@0 oTruth Table Ignition Temperature Output Switch Sensor LED Off Cold Off Off Hot Off On Cold Off On Hot On(p d,B H HD)? p ,$@0B H NZD)? ),$D0q H TXjugֳgֳ֭o?"` 0 P ,$D0 5Here, the truth table is simply that for an AND Gate.6 65 UvgIIF H T`sugֳgֳ֭o?"` 0 P`,$D0 For the LED to light, the Ignition Switch must be on and the Temperature Sensor must be  hot .j_ 2!^ UvgII H  fvu1? z,$0 U1  H  flu1? z,$0 U1 H H 0޽h ? ̙33((___PPT10(.m"+D`&' = @B D&' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =-o6Bdissolve*<3<*HDf' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* H%(D' =-o6Bdissolve*<3<* HD3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =-o6Bdissolve*<3<*HD3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =-o6Bdissolve*<3<*HD' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =-o6Bdissolve*<3<*HD' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =-o6Bdissolve*<3<*HD' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =-o6Bdissolve*<3<*HD3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =-o6Bdissolve*<3<*HD3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =-o6Bdissolve*<3<*HD3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =-o6Bdissolve*<3<*HD@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* H%(D' =-o6Bdissolve*<3<* HD@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* H%(D' =-o6Bdissolve*<3<* HD@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* H%(D' =-o6Bdissolve*<3<* HD@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =-o6Bdissolve*<3<*HD@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =-o6Bdissolve*<3<*H++0+H ++0+ H ++0+ H ++0+ H ++0+ H ++0+H ++0+H ++0+H ++0+H +H ;(    Nugֳgֳ?#" `G `&Logic Circuit #2: Central Heating Pump''ffT  Tugֳgֳ֭o?"`,$D0 Derive a logic circuit that will turn on a Central Heating System s pump when the house is cold and the Central Heating System is turned on.  UvgII<  Tԣugֳgֳ֭o?"`d,$D0 vThis time let s find the truth table first: House is Cold = 0 ; House is Hot = 1 CHS is Off = 0; CHS is On = 1*, C o,P  UvgIIm  Nu)?"`v ,$@0 OTruth Table House CHS Pump Cold Off Off Cold On On Hot Off Off Hot On Off(P DKB  HD)?0,$@0B   NZD)? ,$D0<   Nu)?"` j,$@0 |, House CHS Pump 0 0 0 0 1 1 1 0 0 1 1 0--KB   HD)? 0 ,$@0B   NZD)? 0,$D 0B  HD)? 0 ,$@ 0B  HD)? 0 ,$@ 0a  Thugֳgֳ̙o?"`bpv ,$@ 0 Central Heating ,  UvgII  T3fp?` ( ,$@ 0B  HD)? K ,$@0r   N3fp?"` 0 ,$@0@  T+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*Df' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* Df' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D' =%(D'' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*+0+0+ ++0+ ++0+ ++0+  ++0+ ++0+ ++0+ ++0+ ++0+ ++0+ +tN |+(  B  T@ugֳgֳo?"`  ,$@ 0 |Heater  UvgII  N,ugֳgֳ?#" `G ]#Logic Circuit #3: Greenhouse Heater$$ff  Tugֳgֳ֭o?"`S,$D0 bDerive a logic circuit that will turn on a heater in a greenhouse only when it gets cold at night.c cb UvgII  Txgֳgֳ֭o?"`@ ,$D0 >Truth Table: Greenhouse Cold = 0 ; Hot = 1 Dark = 0; Light = 1*  2 ?,*  UvgII  N0 x)?"` ,$@0 eTruth Table Green Day/ Heater house Night Cold Night On Cold Day Off Hot Night Off Hot Day OffDf  GKB  HD)?`0`,$@0B  NZD)? ,$D0Z  Nx)?"`P :,$@0 . Green D/N Heater 0 0 1 0 1 0 1 0 0 1 1 06/ KB   HD)? 0 ,$@0B   NZD)? ,$D 0B   HD)? 0 ,$@ 0B   HD)? 0 ,$@ 0`   # lX xgֳgֳdo?"` bp ,$@ 0  Light Sensor     UvgII  T3fp?L ( ,$@0B  HD)? K ,$@0   f*x1? pF ,$0 U0    fx1?  ,$0 U1    f 2x1? pF ,$0 U0  ( T3fp?* (z ,$@0 )  f5x1?  ,$0 U1 R *  `9xgֳgֳfo?"`* Pp,$@0 Temperature Sensor  UvgIIr + N3fp?"`P P ,$D0H  0޽h ? ̙3366___PPT10p6.m"+/QD3' = @B D3' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*Df' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*Df' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =-o6Bdissolve*<3<*(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*)%(D' =-o6Bdissolve*<3<*)D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<**%(D' =-o6Bdissolve*<3<**D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*+%(D' =-o6Bdissolve*<3<*++h+0+o ++0+o ++0+o ++0+o ++0+o ++0+ o ++0+o ++0+o ++0+o ++0+)o ++0+*o +W    LE (  L L N8Gxgֳgֳ?#" `G a'Summary of Combinational Logic Circuits((ff L TKxgֳgֳ֭o?"`,$D0 NCombinational Logic Circuits are simply combinations of AND, OR and NOT gates.>5  ( $3  UvgII  L T`Lxgֳgֳ֭o?"`$D0LD___PPT9& [Constructing Logic Circuits Make a Truth Table. Get the logic circuit from the Truth Table.>  @! @[ U iIR L Tbxgֳgֳo?"` ` ,$D0 Tip: If the circuit has only one  high output then the circuit will probably use an AND Gate.v/ 0 ^ UvgIIZ L Tixgֳgֳo?"`N `f,$D0 Tip: If the circuit has more than one  high output then the circuit will probably use an OR Gate.v4 / b UvgII  L Tjxgֳgֳo?"``,$D0 #Tip: Note how useful NOT gates are!<$  # UvgIIH L 0޽h ? ̙33JB___PPT10".m"+D' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*L%(D' =-o6Bdissolve*<3<*LD' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*L%(D' =-o6Bdissolve*<3<*LD' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*L%(D' =-o6Bdissolve*<3<*LD' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*L%(D' =-o6Bdissolve*<3<*LD' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* L%(D' =-o6Bdissolve*<3<* L++0+Lo ++0+Lo ++0+Lo ++0+Lo ++0+ Lo +2 5P(  P P N̟xgֳgֳ?#" `G @Clocksff" P TLo?"`X,$@0" P TG$*HII Ԕ? : ,$@0" P TG%*H I.Ԕ?u Z ,$@0" P TG$*HII3Ԕ?  ,$@0" P TG%*H IԔ?[@ ,$@0" P TG$*HHI|Ԕ?(,$@0" P TG%*H IԔ?(,$@ 0" P TG$*HHI`Ԕ?l (,$@ 0= P Txgֳgֳ֭o?"` 9J ,$D 0 w!Clocks are normally square waves." "UvgII| P Txgֳgֳ֭o?"`,$D0 RClocks are regular waves of pulses, just like the ticking of a conventional clock:($ / SUvgII" 3P TG%*H IԔ? (,$D 0{ 4P Txgֳgֳo?"`Kc ,$D 0 CDigital circuits can be used to produce a series of clock pulses.106(  A UvgII6 5P Txgֳgֳ֭o?"` ,$D0 pThe circuits which produce clock pulses are sometimes called oscillators because they constantly oscillate between  on and  off .0 = ;UvgIIH P 0޽h ?PPPPP P P%3P ̙33""___PPT10".m"+4=D!' = @B Dd!' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =-o6Bdissolve*<3<*PD' =%(Dc' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =-o6Bdissolve*<3<*PD3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =-o6Bdissolve*<3<*PD3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =-o6Bdissolve*<3<*PD3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =-o6Bdissolve*<3<*PD3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =-o6Bdissolve*<3<*PD3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =-o6Bdissolve*<3<*PD3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =-o6Bdissolve*<3<*PD3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =-o6Bdissolve*<3<*PD3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*3P%(D' =-o6Bdissolve*<3<*3PD' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4P%(D' =-o6Bdissolve*<3<*4PD' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =-o6Bdissolve*<3<*PD' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*5P%(D' =-o6Bdissolve*<3<*5P++0+Pq ++0+Pq ++0+4Pq ++0+5Pq +- KC  (    C *Aoscline20PP ,$D0  Nxgֳgֳ?#" `G UA Simple Oscillator Circuitff  Tdxgֳgֳ֭o?"` P ,$D 0 Supply Voltage VS = V1 +V2    UvgII  Txgֳgֳ֭o?"` T @,$D 0 /?When the NOT-Gate outputs a 0, V2=0V and V1=5V: the LED lights.0    UvgII  T{gֳgֳ֭o?"` j;,$D 0 7GWhen the NOT-Gate outputs a 1, V2=5V and V1=0V: the LED does not light.0    UvgII  Tt{gֳgֳ֭o?"`d0,$D0 \Oscillator Circuits change between two values in a regular cyclical pattern: a clock output.*. / ]UvgII"   NH]IzԔ? 0P ,$@0"   NH`I%MԔ? P ,$@0"   NH`I%MԔ?  P ,$@0"  NH]IzԔ? `P ,$@0"  NH]IzԔ? pP ,$@0"  NH`I%MԔ? PP ,$D 0H  0޽h ?o    ̙33___PPT10+q}D' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D ' =%(D ' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*++0+q ++0+q ++0+q ++0+q +( _W (    C *Aoscline2 `h,$D0  N:{gֳgֳ?#" `G m!How an Oscillator Circuit Works180"ffff  TL{gֳgֳo?"`P $D0LD___PPT9& The Invertor s Input is 1, so its Output = 0: the Capacitor starts to discharge through the Resistor..! 8    XUiI  T\{gֳgֳ֭o?"`,$D0 6Capacitor C charges and discharges through Resistor R.P7   UvgII[  TD{gֳgֳo?"` ,$D0 -Start: ASSUME THE CAPACITOR IS FULLY CHARGED., ' .U7gIIL   TD{gֳgֳo?"` P $D0LD___PPT9& 2*As the Capacitor discharges the Invertor s Input eventually falls to 0, so its Output becomes 1: the Capacitor starts to charge through the Resistor.a! 5   * lUiI   Th{gֳgֳo?"` Pt$D0@8___PPT9 As the Capacitor charges the Invertor s Input eventually rises to 1, so its output becomes 0: the Capacitor discharges again.~! * WUiI   Tȁ{gֳgֳo?"`P$D0LD___PPT9& eThis sequence of charging and discharging continues ad infinitum to produce a series of clock pulses.BA! %  A%UiIH  0޽h ? ̙33e]___PPT10=.N+w[3D' = @B D|' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* +P+0+q ++0+q ++0+q ++0+ q ++0+ q ++0+ q +a    O (  R  C *Aoscline20PP   N{gֳgֳ?#" `G g-How an Oscillator Circuit Works (Alternative)..ffE  TĬ{gֳgֳo?"`V " ,$D0 / Capacitor NOT NOT V2 V1 LED Input Output 0  2U* A qgII_  T{gֳgֳo?"`@ L ,$D0  Charged 1 0 0V 5V On. 2U* A qgIIT  T{gֳgֳo?"`t  ,$D0 Discharged 0 1 5V 0V Off  f32U* A qgIIP   T<{gֳgֳo?"` ,$D0 Charged 1 0 0V 5V On  2U* A qgIIT   T{gֳgֳo?"`,$D0 Discharged 0 1 5V 0V Off  f32U* A qgIIH  0޽h ? ̙33JB___PPT10". ʧ+xD' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* ++0+t ++0+t ++0+t ++0+ t ++0+ t +v? qi0(  $  N$}gֳgֳ?#" `G FHow to Change a Clock s Frequency190$!ffff_   T}gֳgֳ֭o?"`,$D0 -The frequency of clock pulses can be altered:0.  !UvgII"   NHIԔ?`P,$@0"   NH۲IPԔ?`,$@0"  NHIԔ?`P,$@0"  NH۲IPԔ?`@,$@0"  TGHH,I"Ԕ?` ,$@ 0"  TG}6H'IP Ԕ?` p,$@ 0"  TG@H'I0Ԕ?`p,$@ 0"  NH,IԔ?` ,$@ 0(  T`}gֳgֳo?"`2,$@0 bHigh Frequency UvgII'  T}gֳgֳo?"`P 2,$D 0 a Low Frequency UvgII"  NHIԔ?` ,$D0  T8 }gֳgֳo?"`Qp ,$D0 vIf the value of the Capacitor is increased, charging and discharging takes longer so the clock frequency is decreased.Fw /UvgII  T5}gֳgֳo?"` Pp,$D0 uIf the value of the Resistor is increased, charging and discharging takes longer so the clock frequency is decreased.Fv /UvgIId  TA}gֳgֳo?"`~ P ,$D0 C then fN  UgIId  TK}gֳgֳo?"`n P,$D0 R then fN  UgIIH  0޽h ?        ̙33++___PPT10++@D)' = @B D)' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D' =%(D ' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D ' =%(D ' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*++0+ t ++0+t ++0+t ++0+t ++0+t ++0+t ++0+t +9 @(    NQ}gֳgֳ?#" `G BCounters  ff  T V}gֳgֳo?"`,$D0 OCounters are electronic circuits which can count digital pulses from a clock.126' ) M UvgIIV  T+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(Dc' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*+P+0+t ++0+t ++0+t ++0+t ++0+t ++0+t +Ur P$$$(    N}gֳgֳ?#" `G MCounting in Decimalff"  T`}gֳgֳ֭o?"`Y h,$@0 \Binary UvgII#  T}gֳgֳ֭o?"`QZ,$D0 ]Decimal UvgIIo  TĖ}gֳgֳo?"` h,$D0 % 0000 0001 0010 etc 0111 1000 1001 & && 0,6 /}.B @ HDPS?! ,$@0B @ NDPS? 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F ,$D 0B  @ NDPS?  ,$@ 0B  @ NDPS?  F ,$D 0B @ HDPS?) G) ,$@0B @ NDPS?V  ,$@0B @ NDPS?V  ,$@0B @ HDPS? F ,$@0B @ HDPS?F,$@0B @ NDPS?,$@0B @ NDPS?,$D0B @ HDPS?( ( ,$@0B @ NDPS?U ,, ,$@0B @ NDPS?U gg ,$@ 0B @ HDPS?  ,$@!0B @ HDPS?,$@"0B @ NDPS?,,,$D#0!   ft}1?6 V ,$0 Wetcf3 .  T\}gֳgֳo?"`,$D0 hCircuits called Binary-to-Decimal Convertors convert a counter s binary output into decimal.14N- 2 / " 3UvgIIB @ HDPS?) c) ,$@0B @ NDPS?V  ,$@0B @ NDPS?,$D0B  @ HDPS? &,$@0B !@ NDPS?"SS,$@0B "@ HDPS? %,$@0B #@ HDPS? % ,$@0B $@ NDPS? 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