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Classification of Digital Circuits Combinational. Output depends only on current input values. Sequential. Output depends on current input values and present state of the circuit, where the present state of the circuit is the current value of the devices memory. Also called finite state machines. State of a Circuit The contents of storage elements. A collection of know internal signal values that contain information about the past necessary to account the future behavior of the circuit. Bi-stable Element (Simple Memory) The simplest sequential circuit. It consist of a pair of inverters connected as shown below. Notice the feedback loop. A B Digital Analysis Two stable states. If A is HIGH then the lower inverter has a HIGH at its input and a LOW at its output. This in turn forces the upper inverters input to be LOW and its output to be HIGH. If A is LOW then the lower inverter has a LOW at its input and a HIGH at its output. This in turn forces the upper inverters input to be HIGH and its output to be LOW. Analog Analysis Considering the steady state behavior of the bistable element. V in1 = V out2 V in1 = T(V in2 ) V in1 = T(V out1 ) V in1 = T(T(V in1 )) V out1 = V out2 V in1 = V in2 stable metastable stable Transfer function: V out1 = T ( V in1 ) V out2 = T ( V in2 ) V in1 V out1 V out2 V in2 Q Q_L Analog Analysis Metastable behavior: Consider the middle intersecting point in the diagram shown below. What would happen if a small amount of noise varies either input voltage. V out1 = V out2 V in1 = V in2 stable metastable stable Analog Analysis The drawing on this slide shows a very good analogy to the stable and metastable behavior of a bi- stable element. stable stable metastable Clock Signal that determines the change of state in most sequential circuits. CLK t per t H t L t L t H t per state changes occur here (a) state changes occur here CLK_L (b) duty cycle = t H / t per frequency = 1 / t per period = t per duty cycle = t L / t per Latches and Flip-Flops Binary cells capable of storing 1 bit of information. Generates one of two possible stable states. Two outputs labeled Q and Q. One or more inputs. Latches and Flip-Flops These sequential devices differ in the way their outputs are changed: The output of a latch changes independent of a clocking signal. The output of a flipflop changes at specific times determined by a clocking signal. Basic Latch Memory element Alarm Sensor Reset Set On Off Reset Set Q S-R Latch S R Q a Q b 1 1 1 1 0/1 1/0 1 1 (a) Circuit (b) Truth table Time 1 1 1 1 R S Q a Q b Q a Q b ? ? (c) Timing diagram R S t 1 t 2 t 3 t 4 t 5 t 6 t 7 t 8 t 9 t 10 (no change) S-R Latch R S Q 1 1 1 1 S R 1 last Q Q 1 ( a) (b) QN last QN QN SR latch based on NOR gates.... View Full Document

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