CS 316: Gates and Logic
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1 CS 36: Gtes nd Logi Kvit Bl Fll 27 Computer Siene Cornell University Announements Clss newsgroup reted Posted on we-pge Use it for prtner finding First ssignment is to find prtners
2 P nd N Trnsistors PNP Trnsistor B E NPN Trnsistor B E C Connet E to C when se = C Connet E to C when se = Inverter in Funtion: NOT Clled n inverter Symol: in In Out Truth tle Useful for tking the inverse of n input CMOS: omplementry-symmetry metl oxide semiondutor 2
3 NAND Gte Funtion: NAND Symol: A B +Vdd NOR Gte Funtion: NOR Symol: Vss A B 3
4 NOT: Building Funtions AND: OR: NAND nd NOR re universl Cn implement ny funtion with NAND or just NOR gtes useful for mnufturing NOT: Building Funtions AND: OR: NAND nd NOR re universl Cn implement ny funtion with NAND or just NOR gtes useful for mnufturing 4
5 Logi Equtions AND = = & = OR = + = = NOT = =! = Identities Identities useful for mnipulting logi equtions For optimiztion & ese of implementtion + = + = + = = = = (+) = + ( + ) = ( ) = + + = + 5
6 Logi Mnipultion Cn speify funtions y desriing gtes, truth tles or logi equtions Cn mnipulte logi equtions lgerilly Cn lso use truth tle to prove equivlene Exmple: (+)(+) = LHS RHS (+)(+) = = + (+) + = ( + (+)) + = + Logi Minimiztion A ommon prolem is how to implement desired funtion most effiiently One n derive the eqution from the truth tle minterm for ll puts tht re, tke the orresponding minterm, OR the minterms to otin the result in sum of produts form How does one find the most effiient eqution? Mnipulte lgerilly until stisfied Use Krnugh mps 6
7 Krnugh mps Enoding of the truth tle where djent ells differ in only one it truth tle for AND Corresponding Krnugh mp Bigger Krnugh Mps 3-input fun y d 4-input fun y d 7
8 8 Minimiztion with Krnugh mps () Sum of minterms yields Minimiztion with Krnugh mps (2) Sum of minterms yields Krnugh mps identify whih inputs re (ir)relevnt to the put
9 Minimiztion with Krnugh mps (2) Sum of minterms yields Krnugh mp minimiztion Cover ll s Group djent loks of 2 n s tht yield retngulr shpe Enode the ommon fetures of the retngle = + Krnugh Minimiztion Triks () Minterms n overlp = + + Minterms n spn 2, 4, 8 or more ells = + 9
10 Krnugh Minimiztion Triks (2) d d The mp wrps round = d = d Krnugh Minimiztion Triks (3) d x x x x x d x x x x x Don t re vlues n e interpreted individully in whtever wy is onvenient ssume ll x s = = d ssume middle x s = ssume 4 th olumn x = = d
Lec 2: Gates and Logic
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