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Lecture 32 Lecture 32 Digital Logic Gates Reading: Jaeger 6.1-6.4 and Notes Georgia Tech ECE 3040 - Dr. Alan Doolittle Basic Logic Gates NOT or Inverter Gate: (Asks, is the input false?) Output Input A Logic Function: Function: False=State 0 True=State 1 Z Z A Truth Table: Input A 0 1 Georgia Tech Output Z 1 0 ECE 3040 - Dr. Alan Doolittle Basic Logic Gates AND Gate: (Asks, are all inputs true?) Output Inputs A Z B Logic Function: Function: Z AB Truth Table: Inputs Georgia Tech A 0 0 1 1 Output B 0 1 0 1 Z 0 0 0 1 ECE 3040 - Dr. Alan Doolittle Basic Logic Gates OR Gate: (Asks, is any input true?) Inputs Output A Z B Logic Function: Function: Z A B Truth Table: Inputs Georgia Tech A 0 0 1 1 Output B 0 1 0 1 Z 0 1 1 1 ECE 3040 - Dr. Alan Doolittle Basic Logic Gates Any more complex functionality can be constructed from the th three basic gates by using DeMorgan s Law: ABC...N A B C... N A B C ... N ABC...N The complement of the product is replaced with the sum of the complements The complement of the sum is replaced with the product is replaced with the product of the complements Note: Only the AND, OR and Inverter gates are considered Basic logic Gates Georgia Tech ECE 3040 - Dr. Alan Doolittle Non-Basic Logic Gates NAND Gate: (Asks, is any input false?) Output Inputs A Z B Logic Function: Function: Z AB Truth Table: Inputs Georgia Tech A 0 0 1 1 Output B 0 1 0 1 Z 1 1 1 0 ECE 3040 - Dr. Alan Doolittle Non-Basic Logic Gates NOR Gate: (Asks, are all inputs false?) Inputs Output A Z B Logic Function: Function: Z A B Truth Table: Inputs Georgia Tech A 0 0 1 1 Output B 0 1 0 1 Z 1 0 0 0 ECE 3040 - Dr. Alan Doolittle Non-Basic Logic Gates XOR Gate, Exclusive OR Gate: (Asks, are the inputs not equal? Inequality test) Inputs Output A Z B Logic Function: Function: Z AB A B Truth Table: Inputs Georgia Tech A 0 0 1 1 Output B 0 1 0 1 Z 0 1 1 0 ECE 3040 - Dr. Alan Doolittle Non-Basic Logic Gates XNOR Gate, Exclusive NOR Gate: (Asks, are the inputs equal? An equality test) Inputs Output A Z B Logic Function: Function: Z AB AB A B A B Truth Table: Inputs Georgia Tech A 0 0 1 1 Output B 0 1 0 1 Z 1 0 0 1 ECE 3040 - Dr. Alan Doolittle Ideal Inverter Characteristics The easiest gate to analyze is the inverter (NOT) gate. By looking at the inverter we can learn a great deal about all gate physical implementations. The Voltage Transfer Characteristic (VTC) of an ideal inverter is: vi Definitions: VOH=Logic state 1 or True . The highest possible output voltage. VOL=Logic state 0 or False . The Lowest possible output voltage. VREF=Voltage for which the inverter switches from Logic state 1 to Logic state 0 The transition is abrupt. Georgia Tech ECE 3040 - Dr. Alan Doolittle Actual Inverter Implementation The simplest implementation of the inverter consists of a resistor and a switch. The switch can be an actual switch (user interaction required) or a transistor that is electrically turned on or off . Closed Switch, Vo=VOL Vo=0V Vo=VDS of Ms Vo=VCE of Qs Open Switch, Vo=VOH Vo=V+ Vo=V+ Vo=V+ Georgia Tech ECE 3040 - Dr. Alan Doolittle Actual Inverter Characteristics Practical Definitions: State 1 State 0 Georgia Tech VOH= Nominal output voltage defining a valid logic state 1 at the output VOL= Nominal output voltage defining a valid logic state valid logic state 0 at the output at the output VIL=Maximum input voltage resulting in a valid logic state 0 at the input (or a valid logic state valid logic state 1 at the output). at the output). VIH= Minimum input voltage resulting in a valid logic state 1 at the input (or a valid logic state 0 at the output) ECE 3040 - Dr. Alan Doolittle Actual Inverter Characteristics Noise Margins State 1 Safety Factor to insure that the th th output state does not change due to extra unwanted signals. State 0 Georgia Tech NMH=VOH- VIH NML=VIL-VOL ECE 3040 - Dr. Alan Doolittle Actual Inverter Characteristics V+ State 1 vo vi 1 VOH VIH 1 NMH State 0 VIL NML 0 VOL 0 V- Georgia Tech ECE 3040 - Dr. Alan Doolittle Actual Inverter Characteristics Actual inverter transitions from VOH to VOL is not abrupt. Definitions: VIL=Input voltage value (Larger than VOL, defined in a moment) where the State 1 slope of the VTC equals slope of the VTC equals -1 VIH=Input voltage value (Larger than VIL) where the slope of the VTC equals -1 VOH= The nominal output voltage for a state 1 at the output when the input State 0 voltage is VOL VOL=The nominal output voltage for a state 0 at the output when the input voltage is VOH VM=Voltage where the output voltage equals the input voltage Georgia Tech ECE 3040 - Dr. Alan Doolittle Inverter Time Response State transitions require finite amounts of time to occur. Thus, we can characterize th Ri the Rise, and Fall of the signals by: th Rise Time, tr, = The time required for the input/output to transition from 10% 10% to 90% of its total voltage excursion. I.E.: V= VOH- VOL V10%=VOL+0.1 V V90%=VOL+0.9 V Fall Time, tf, = The time required for the input/output to transition from 90% to 10% of its total voltage excursion. Georgia Tech ECE 3040 - Dr. Alan Doolittle Inverter Time Response State transitions require finite amounts of time to pass from the input of the gate to the output of the gate. This time required for a state change can be characterized by the propagation delays. Propagation Delay from high-to-low, PHL, = The time delay between the 50% 50% points on the input and output th waveforms during the high-to-low output transition Propagation Delay from low-to-high, PLH, = The time delay between the 50% points on the input and output 50% points on the input and output waveforms during the low-to-high output transition Average Propagation Delay, P=0.5( PHL+ PLH) The 50% points are: V50%=0.5(VOH+ VOL) Georgia Tech ECE 3040 - Dr. Alan Doolittle Rise and Fall Time Dependence on Power Since larger currents can charge a capacitor faster, high speed requires higher power (for a fixed capacitor load). Thus, there is a fundamental tradeoff in power and speed: Need high speed = Need higher power Need low power operation (example battery device) = will need to operate slower. Georgia Tech ECE 3040 - Dr. Alan Doolittle

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