# combinational logic with multiplexers and decoders

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Combinational Logic Circuits

• Combinational Logic Circuits are made up from basic logic NAND, NOR or NOT gates that are “combined” or connected together to produce more complicated switching circuits. Add your second bullet point here

• These logic gates are the building blocks of combinational logic circuits.

• Combinational logic circuits can be very simple or very complicated and any combinational circuit can be implemented with only NAND and NOR gates as these are classed as “universal” gates.

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The three main ways of specifying the function of a combinational logic circuit are:

• Boolean Algebra – This forms the algebraic expression showing the operation of the logic circuit for each input variable either True or False that results in a logic “1” output.

• Truth Table – A truth table defines the function of a logic gate by providing a concise list that shows all the output states in tabular form for each possible combination of input variable that the gate could encounter.

• Logic Diagram – This is a graphical representation of a logic circuit that shows the wiring and connections of each individual logic gate, represented by a specific graphical symbol, that implements the logic circuit.

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• One of the most common uses of combinational logic is in Multiplexer and De-multiplexer type circuits.

• Here, multiple inputs or outputs are connected to a common signal line and logic gates are used to decode an address to select a single data input or output switch.

Combinational Logic Circuits

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• The outputs are a function of the present set of inputs only

• The inside of a combinational circuit is made of logic gates

• Combinational logic circuits are important components of digital systems

• Each output can be thought of as a function of all the inputs – if there are m outputs and n inputs then there are m Boolean functions, one describing each output

Combinational Circuits

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Decoders

• A decoder is a combinational logic circuit that converts binary information from n input lines to maximum of 2 nonunique outputs

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Combinational Circuit Implementation Using Decoder

• Since decoders produce 2n minterms of n- input variables, an external OR gates can be used to form a logical function in SOP form

• To implement a given function with decoder and external gates

oexpress the function as canonical SOP

o select decoder that has no of inputs equal to the number of input

o variables in the given functions,

o select the proper external gate

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• If the number of minterms > 2n/2 then express function as F’ and use NOR gate in the external gate to obtain the function F.

• If NAND gates are used to construct the decoder, then the external gate must be NAND gate (instead of OR gate)

Combinational Circuit Implementation Using Decoder

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Multiplexers

• A multiplexer or Data Selector is a combinational circuit that selects binary information from one of many input lines and directs the information to a single output line

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Multiplexers

• The multiplexer, shortened to “MUX” or “MPX”, is a combinational logic circuit designed to switch one of several input lines through to a single common output line by the application of a control signal.

• Multiplexers operate like very fast acting multiple position rotary switches connecting or controlling multiple input lines called “channels” one at a time to the output.

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The selection of a particular input line is controlled by a set of selection lines. For 2n data line we have n selection lines

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