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Announcements mid-term on Thursday 12:30 – be on time. Calculators allowed (required!) No assignment due this week Assignment 6 posted on Thursday Project ideas to me by Nov 1st

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Lecture 15 Overview Digitization Logic families Logic and Gates

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A jump ahead - Lab Information: The Data Flipflop A signal on the D INPUT is transferred to the Q OUTPUT during the positive going transition of the clock pulse. CLEAR and PRESET are independent of the clock and accomplished by a low on the appropriate input. http://fac-web.spsu.edu/cs/faculty/bbrown/web_lectures/sequential/

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Digitization How do we convert a time varying signal into digital bits? Sampling rate and resolution.

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Digitizing a signal 0

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Digitizing a signal

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Digitizing a signal

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Camera 1.8 m 499 PMTs Photonis XP2970 0.15º spacing

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Data Acquisition PMT signals digitised with 500MHz sampling FADCs Data rates –24 samples/channel –13.5 kb/event @ 100 Hz –5 Gb/hour Integrated Pulse

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Cosmic Ray showers measured by VERITAS (each frame 2 ns long)

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Transistor switches How do we generate the 1's and 0's? 1= high voltage, 0= low voltage How do we switch between these states? Can't use mechanical switches in a circuit

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Transistor as a voltage-controlled switch Use a voltage controlled switch instead: Ground the input V BE =0 (reverse biased) BJT in cutoff state Collector current=0 V out =V CC ="1" Transistor behaves like an open switch to ground Connect the input to V CC Generates a base current I B =V CC /R B Collector current of I C = β I B tries to flow V CC =V RL +V CE =I C R L +V CE Maximum collector current is I C =V CC /R L when V CE =0 so V out =V CE =0 (BJT is saturated) Transistor behaves like a closed switch to ground RBRB RLRL Control the switch by applying suitable V in : 0V=open, large +'ve V= closed V CC V CE

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Transistor as a voltage-controlled switch Use a voltage controlled switch instead: Ground the input V BE =0 (reverse biased) BJT in cutoff state Collector current=0 V out =V CC ="1" Transistor behaves like an open switch to ground Connect the input to V CC Generates a base current I B =V CC /R B Collector current of I C = β I B tries to flow V CC =V RL +V CE =I C R L +V CE Maximum collector current is I C =V CC /R L when V CE =0 so V out =V CE =0 (BJT is saturated) Transistor behaves like a closed switch to ground RBRB RLRL Control the switch by applying suitable V in : 0V=open, large +'ve V= closed V CC V CE

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Transistor as a voltage-controlled switch Use a voltage controlled switch instead: Ground the input V BE =0 (reverse biased) BJT in cutoff state Collector current=0 V out =V CC ="1" Transistor behaves like an open switch to ground Connect the input to V CC Generates a base current I B =V CC /R B Collector current of I C = β I B tries to flow V CC =V RL +V CE =I C R L +V CE Maximum collector current is I C =V CC /R L when V CE =0 so V out =V CE =0 (BJT is saturated) Transistor behaves like a closed switch to ground Control the switch by applying suitable V in : 0V=open, large +'ve V= closed

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Logic Gates How do you process a digital signal?

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Logic Families: TTL TTL = transistor-transistor logic TTL output: LOW 2.4V TTL input: LOW 2.0V Based on BJTs Supply voltage = 5V 2.4V 0.4V

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CMOS CMOS logic = Complementary MOS Based on MOSFETs CMOS levels depend upon the supply voltage and provide larger noise margins than TTL Many other logic families and subtle variations exist - NIM, ECL, LVDS etc. Generally simple to connect devices from the same logic families together - interfacing different families is more complex (See Horowitz and Hill Ch 9.01)

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How do you process a digital signal? Have only two states –1,0 map naturally to logic states True/False – Use Boolean algebra – Carry out calculations using a "truth table": list all possible combinations of inputs and corresponding output e.g. A, B and C are digital signals n inputs give 2 n combinations Each logic function can be performed with logic gate circuit. Digital logic designers do not need to care about what is inside a gate Today's microprocessors can contain >100 million logic gates

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The AND gate The output of an AND gate is TRUE if, and only if, both inputs are TRUE The symbol for an AND operation is the multiplication symbol "" This is often omitted, so "A AND B" is written "AB" Note that the truth table looks correct for the multiplication of A and B

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The NOT gate Also known as an inverter Symbol is the overbar ¯. An apostrophe ' is also used (e.g. A') There are several realizations of a NOT gate possible 1)This is the usual schematic symbol 2)Sometimes it is shown explicitly as a gate 3)Tying the inputs of a NAND gate together yields a NOT 4)Tying the inputs of a NOR gate also yields a NOT

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The NAND gate Note the connection between NAND and AND. The output of a NAND gate is the opposite of AND (NAND=NOT AND). Note the symbol for the NAND operation (AND, NOTed). Schematically, the small circle at the output end of the AND symbol means NOT NAND is one of the most heavily used binary operations

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The OR gate The output is TRUE if any of the inputs are TRUE Symbol is +

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The NOR gate The output is TRUE only if all of the inputs are FALSE Inverse of OR

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Gate Combination Which of the following inputs gives D=1 ? Answer: a and c

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Gate Combinations What is the truth table for this circuit? The effect of this circuit is the same as an XOR gate. ABDEC 00 01 10 11 ABDEC 00010 01111 10111 11100

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The XOR gate Exclusive OR The output is TRUE only if one or the other, but not both, inputs are TRUE Symbol is The XOR gate can be used as an "optional inverter" e.g. to invert or not invert an input signal at B, based on a controlling input at A C C=A XOR B C=A B ABC (in) (out) 000 011 101 110

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The XNOR gate Inverse of XOR The output is TRUE only if both inputs are the same. "logical equality" C C=A NOR B C=A B ABC (in) (out) 001 010 100 111

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