Combinational logic With Multiplexers and Decoders. Topic From GTU Syllabus Of Digital Electronics Subject

1. Combinational Logic With
Multiplexer and Decoders
Prepared By: Harsh Parmar (160410116079)

2. 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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3. 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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4. Classification of Combinational Logic
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5. • 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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6. • 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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7. 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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8. 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
oselect decoder that has no of inputs equal to the number of input
ovariables in the given functions,
oselect the proper external gate
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9. • 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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10. 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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11. 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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12. 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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