Classnotes digital 1_ gates (Fri., Mar. 14)

Classnotes digital 1_ gates (Fri., Mar. 14) - Class Digital...

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Unformatted text preview: Class Digital 1: Gates REV 0; March I4, 2008_ rTopics: - OLD: —- ‘Old’: group project: what’s worth recalling? * truism #1: harder to build than to sketch. Some ofthe easie-St sketches were troublesome: clipper. and amplfier (hard to stabilize; we skipped that task, this term) t truism #2: in design, don’t forget simple methods, just because you know fancier ways: exam- ples: v to shift DC level, don’t use op amp shifter unless you need to transfer DC informatioa Blocking cap plus divider is much simpler, if all you need is to pass a wiggle (AC). the usual case - don’t forget the humble switch (preferable to, say, current source or follower) - don’t design a push-pull follower if you need only “push” (that is, source, never sink) 0 NEW: - very general: analog versus digital (demo of crude digital audio) - Boolean logic: essential functions * ’truth tables’ >lr “active low“ signals - silly example: missile launch scheme A h0w to draw it; how to minimize strain on brain — how to build a gate >2: early gates (from early 70‘s to mid ’80’s): “'ITL" from bipolar transistors >k better: CMOS logic takes over (from mid ‘80’s) » dopey MOSFET inverter - elegant CMOS inverter (you’ve seen this before) - ...and more interesting gates, all with the virtues of CMOS 2k noise immunity: TTL versus CMOS versus diflerential (“LVDS”) (demo) — PALS, GALs and FPGA’s make small packages (SSI) obsolete * dense and progrzu‘runable =lc and allow use of clever software: t. , - ABEL (obsolescent, but easy to learn): we may use this for one design (you‘ll load it onto W your own PC to do a homework design) tofu/Ir - VHDL" & Verilog (competitors; more powerful than ABEL, and harder to learn and more ‘ t remote from hardware) We‘ll use Verilog to do some designs, as HW (just another option in W )0 the software that you will have downloaded to your own PC) ‘— one more, peculiar gate (iftime): “three—state” pi 011 ““Low Voltage Differential Signalling.” l’Vl—lDL: “Very [High Speed Integrated Circuit] Hardware Design Language"oof! (class.gates.mar08.tex: March 14,2008) Physics 123 Midterm Fall 2006 " 5 3 Bad Project (10 points) Here‘s a sketch of an infrared transnutter-and-detector circuit like the one you just built. Imagine that yourjob is like the one that just faced us teachers: to help fix any defects that are fatal or nearly—fatal. You should n0t try to improve the circuit in lesser ways—for example, by making the detection differential. Nor should you Just Show us a working circuit—perhaps drawing your lab circuit from memory. The point, instead, is to look critically at what’s drawn below‘ and fix what needs fixing and nothing else. We will charge for fixes that weren’t required! Here’s an example of the sort of repair we’d like to see: :(u J] (-1 14,-‘1 \ .»k.~'(M-r. I Figure 3: sample of the sort of repair we’d like to see Quito SOH’ZQ (3m) Figure 4: Bad Project: show necessary changes Physics 123 Midterm Fall 2006 " 5 3 Bad Project (10 points) ' i Here’s a sketch of an infrared transmitter—and-detector circuit like the one you just built. Imagine that your job is like the one thatjust faced us teachers: to help fix any defects that are fatal or nearly—fatal. You should not try to improve the circuit in lesser ways—for example, by making the detection differential. Nor should you just show us a working circuit—perhaps drawing your lab circuit from memory. The point, in5tead. is to look critically at what’s drawn below, and fix what needs fixing and nothing else. We will charge for fixes that weren‘t required! Here‘s an example of the sort of repair we’d like to see: “‘fijbffi :(<J (Al “9.61 ‘ .akwhv‘u I Figure 3: sample of the sort of repair we'd like to see audio 3wer ($33) Figure 4: Bad Project: Show necessary changes Physics 123 Midterm Fall 2006 __ 5 3 Bad Project (10p0ints) Here’s a sketch of an infrared transmitter-and-detector circuit like the one you just built. Imagine that your job is like the one thatjust faced us teachers: to help fix any defects that are fatal or nearly-fatal. You should not try to improve the circuit in lesser ways—for example, by making the detection differential. weren’t required! Here’s an example ofthe sort of repair we‘d like to see: M51» ‘ l‘ A - 3" oh . ‘( J‘(x:Rr£Li1¢JJ Figure 3: sample of the sm-t of repair we’d like to see i l ‘ amino aware (gags) +Hrm'flfla! Brand 3'13 '13 "2:77.333?iii-":11: #- Hafimaf’flmnd 31-: 35% Thai??? Q5: 2.3;? '- .‘fii'ififi'éf hi note/33 should make you grateful that we’re only turning LED‘s On or Oil" in response to a toggle switch Or two! He proposes to render in mathematical symbols a passage from Cicero, treating conditional ' propositions. 775 'l' 15 'f 75 = l d :3? do 9+5, Boole presents an equation‘ ”y(l-x) + x(l-y) + (l-x)(l-y) = l." and explains. :3 L 30‘? Le“ The interpretation of which is: ——Either “Fabius was born at the rising of the 5%; .007} wank/d 7L0 dogsrar, and will not perish in the sea; or he was not born at the rising of the dogstar. EL g EB. WWI/bx. and will perish in the sea; or he was not born a! the rising ofthe dogstar, and will not 5 I 1’ Ti) perish in the sea. I 0 t W51 GrOne begins to appreciate the compactness of the notation, on reading the “interpretation” stated in; i I 0 words. (You‘ll recognize, if you care to parse the equatio , that Boole writes “(l-x)“ where we La m would write 5 (that is, x false)“. {Eli-aged: Comforting Truth #1 To build any digital device (including the i only three logic functions: st complex computer) we need \ j “a ‘1 “r m fl Yléfiw I 2D- D d>°~ ‘ k I to A) #7013 . Figure 7: Just three fundamental logic functions are necessary All logic circuits are combinations of these three functions, and only these. Comforting and remarkable Truth #2 Perhaps more surprising: it turns om thatjust one gate type (not three) will suffice to let one build any digital device. The gate type must be NAND or NOR; these two types are called “universal gates." Figure 8: "Universal" gates: NAND and NOR DeMorgan—a friend of Boole's~—-showed that what looks like an AND function can be transformed into OR (and vise-versa) with the help of some inverters. This is the powerful trick that allows one gate type to build the world. W ‘4 Text sec. 8074). 3.2 deMorgan’s '— a I 483 -___——t—__———'—-_'—. This is the only important rule of Boolean algebra you are likely to have to memorize (the others that we use are rett obvious: ro ositions like A + A* = l . deMorgan rs Theorem (in graphic rather than algebraic form) M W {Q You can swap shapes if at the same time you inven all inputs and outputs, etc. CLam Figure 9: deMorgan’s theorem in graphic form S \ WM {"9 w Rf ( When you do this you are changing only the symbol uscd to draw the gate; you are not anging the logicwthe hardware. (That laSt little observation is easy to say and hard to get used to. Don't be embarrassed if it takes you some time to get this idea straight.) ‘Hawking. Stephen ed.. God Created the Integers (2005), p. 808. A v.5- Narmna: E'Bramf .335: .' 2 1:"- 3" .' 5::siz' .. ~ ~ CHO§ I‘M?” 53% I103: (rmmunfij ...
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Classnotes digital 1_ gates (Fri., Mar. 14) - Class Digital...

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