Gates and Logic Hakim Weatherspoon CS 3410 Spring 2011 Computer Science Cornell Universty See P H Appendix C 0 C 1 C 2 Gates and Logic See P H Appendix C 0 C 1 C 2 http www xkcd com 74 Announcements Class newsgroup created Posted on web page Use it for partner finding First assignment is to find partners Sections start next week Use this weeks section to find a partner Note about class No Verilog or VHDL Clickers not required but will use them from time to time 3 A switch Acts as a conductor or insulator Can be used to build amazing things 4 Better Switch One current controls another larger current Static Power Keeps consuming power when in the ON state Dynamic Power Jump in power consumption when switching 5 Atoms e e e e e e PNN P P PN P NN NPNP e e hole e e e e e e 6 Elements e e e B e Boron e e e Si e Silicon e P e e e Phosphorus 7 Silicon Crystal e e e e e Si e e e e e Si e e Si e e e e e e Si e e e e e Si e e e Silicon e e e e e Si e e Si e e Si e e e e e e e e Si e e Si e e e e e Si e e Si e e Si e e e e e e e e Si e e Si e e e e e Si e e Si e e Si e e e e e e e e Si e e Si e e e e e e Si e e Si e e Si e e e e e e e e Si e e Si e e e e e e Si e e Si e e Si e e e e e e e e Si e e Si e e e e Si e e Si e e Si e e e e e Si e e Si e e 8 Phosphorus Doping e e e e e e e e N Type e eSilicon e Phosphorus e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e ee e e P e e e e e e e e e e e e e e e e e e e e e e e P e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e P e e e ee e e e e e e e e e e e e e e e e P e e e e e ee e e e e e e e e e e e e e e 9 Boron Doping e e e e e e e e e e e e e e e e e e e e e e e e Silicon e Boron eP Type e e e e e e e e e e e e e e e e e e e e e e e e e B e e e e e e e e e e e e e e e e e B e e e e e e e e e e e e e e e e e B e e e e e e e e e e e e e e e e e B e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e 10 Semiconductors Insulator p type Si Boron has mobile holes low voltage depleted insulator high voltage mobile holes conductor n type Si Phosphorus has mobile electrons low voltage mobile electrons conductor high voltage depleted insulator 11 Bipolar Junction P Type N Type e e e e e e e e e e e e e low v insulator high v conductor e low v conductor high v insulator 12 Reverse Bias P Type N Type e e e e e e e e e e e e e low v insulator high v conductor e low v conductor high v insulator 13 Forward Bias P Type N Type e e e e e e e e e e e e e e e low v insulator high v conductor e e e e e e e low v conductor high v insulator 14 Diodes PN Junction Diode p type Conventions vdd vcc 1 2v 5v hi vss vee 0v gnd n type 15 PNP Junction p type n type p type 16 Bipolar Junction Transistors Solid state switch The most amazing invention of the 1900s Emitter input Base switch Collector output PNP Transistor C p n p E vdd NPN Transistor vss E n p n B E B C B vdd C B C E vss 17 Field Effect Transistors P type FET N type FET Drain vdd Gate Drain Gate Source Connect Source to Drain when Gate lo Drain must be vdd or connected to source of another P type transistor Source vss Connect Source to Drain when Gate hi Source must be vss or connected to drain of another N type transistor 18 Multiple Transistors 5v Vdd in out 0v t Vss In Out Gate delay transistor switching time voltage propagation fanout temperature CMOS design complementary symmetry metal oxide voltage semiconductor Power consumption dynamic leakage 19 Digital Logic 5v Vdd in out Vss 2v 0 5v 0v t In Out 5v 0v 0v 5v In Out voltage truth table Conventions vdd vcc 1 2v 5v hi true 1 vss vee 0v gnd false 0 20 NOT Gate Inverter Function NOT Symbol Vdd in out in out Vss In Out 0 1 1 0 Truth table 21 NAND Gate Vdd A Function NAND Symbol Vdd B out B A a b out A B out Vss 0 0 1 1 0 1 0 1 1 1 1 0 22 NOR Gate Function NOR Symbol Vdd A a b B out out B A Vss A B out Vss 0 0 1 1 0 1 0 1 1 0 0 0 23 Building Functions AND OR NOT 24 Universal Gates NAND is universal so is NOR Can implement any function with just NAND gates De Morgan s laws are helpful pushing bubbles useful for manufacturing E g XOR A B A or B but not both exclusive or Proof 25 Logic Equations Some notation constants true 1 false 0 variables a b out operators AND a b ab a b a b a b a b a a b a OR a b NOT a 26 Identities Identities useful for manipulating logic equations For optimization ease of implementation a 0 a a 1 1 a 1 a0 0 a1 a a 0 a b a b …
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