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EE2731_Class_Notes_02-14

# EE2731_Class_Notes_02-14 - Combinational logic circuits...

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Classification of Digital Circuits Combinational logic circuits. Output depends only on present input. Sequential circuits. Output depends on present input and present state of the circuit.

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Combinational Logic Design procedure: Start with the problem statement. Determine the number of inputs variables and the required number of output variables. Derive a truth table that defines the required relationship between input and output. Simplify each output function (Karnaugh maps). Draw the logic diagram.
Half Adder Design Example A half adder computes the sum of two one bit Boolean inputs, which can be at most 102. This requires two outputs. Inputs: X, and Y. Outputs: S and C. X Y C S 0 0 0 0 0 1 0 1 1 0 0 1 1 1 1 0

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Half Adder Design Example C = XY S = X Y
Decoders A decoder is a multiple-input multiple-output logic circuit that converts coded inputs into coded outputs, where the inputs and outputs codes are different.

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Function Realization With Decoders The outputs of a binary decoder provides 2 n minterms for its n inputs, and a Boolean functions can be represented as a sum of minterms, therefore a decoder and one or more OR gates can be used to realize sums of minterms of n variables.
Multiplexers Combinational logic circuit that selects binary information from one of many input lines and directs it to a single output line. The input is selected by the binary value on the select lines.

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Function Realization With Multiplexers A multiplexer is basically a binary decoder whose outputs were ORed together and some extra input lines were added to each product term. A sum of minterms can be realized by setting the corresponding input line of the chosen minterms to 1 and setting the input lines of the remaining minterms to 0.
Demultiplexers Combinational logic circuit that receives binary information on a single input and sends this information to one of many possible output lines. The output is selected by the binary value on the select lines.

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Open Collector Devices Entire upper half of output circuit is omitted. External pull-up resistor is needed. If any input is low, then Q2 and Q3 are cutoff and the voltage Z is high.
Open Collector Devices Can be used to drive a load, such as LEDs, relays or other device. It is important to calculate a suitable resistor R. The current through the load must not exceed IOLMax .

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Open Collector Devices Wired AND Logic – When two or more open-collector outputs are tied together with an external pull-up resistor, the circuit behaves as if the gates were connected to an AND gate.
Open Collector Devices Common Bus – Several open collector outputs may be connected together to create a common bus.

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EE2731_Class_Notes_02-14 - Combinational logic circuits...

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