Combinational Logic Circuits
Unlike sequentcial logic blocks whose outputs are dependant on both their present inputs and
their previous output state giving them some form of Memory, the outputs of Combinational
Logic Circuits are only determined by the logical function of their current input state, logic "0"
or logic "1", at any given instant in time as they have no feedback, and any changes to the signals
being applied to their inputs will immediately have an effect at the output. In other words, in a
Combinational Logic Circuit, the output is dependant at all times on the combination of its
inputs and if one of its inputs condition changes state so does the output as combinational circuits
have "no memory", "timing" or "feedback loops".
Combinational Logic
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. These
logic gates are the building blocks of combinational logic circuits. An example of a
combinational circuit is a decoder, which converts the binary code data present at its input into a
number of different output lines, one at a time producing an equivalent decimal code at its
output.
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.
The three main ways of specifying the function of a combinational logic circuit are:
1. 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.
2. 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.
3. 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.
The Multiplexer
A data selector, more commonly called a Multiplexer, shortened to "Mux" or "MPX", are
combinational logic switching devices that operate like a very fast acting multiple position rotary
switch. They connect or control, multiple input lines called "channels" consisting of either 2, 4, 8
or 16 individual inputs, one at a time to an output.
The Demultiplexer
The data distributor, known more commonly as a Demultiplexer or "Demux", is the exact
opposite of the Multiplexer we saw in the previous tutorial. The demultiplexer takes one single
input data line and then switches it to any one of a number of individual output lines one at a
time. The demultiplexer converts a serial data signal at the input to a parallel data at its output
lines as shown below.
The Digital Encoder
Unlike a multiplexer that selects one individual data input line and then sends that data to a
single output line or switch, a Digital Encoder more commonly called a Binary Encoder takes
ALL its data inputs one at a time and then converts them into a single encoded output.
So we can say that a binary encoder, is a multi-input combinational logic circuit that
converts the logic level "1" data at its inputs into an equivalent binary code at its
output. Generally, digital encoders produce outputs of 2-bit, 3-bit or 4-bit codes depending
upon the number of data input lines. An "n-bit" binary encoder has 2n input lines and n-bit
output lines with common types that include 4-to-2, 8-to-3 and 16-to-4 line configurations.
The output lines of a digital encoder generate the binary equivalent of the input line whose
value is equal to "1" and are available to encode either a decimal or hexadecimal input pattern
to typically a binary or B.C.D. output code.
Unlike sequentcial logic blocks whose outputs are dependant on both their present inputs and
their previous output state giving them some form of Memory, the outputs of Combinational
Logic Circuits are only determined by the logical function of their current input state, logic "0"
or logic "1", at any given instant in time as they have no feedback, and any changes to the signals
being applied to their inputs will immediately have an effect at the output. In other words, in a
Combinational Logic Circuit, the output is dependant at all times on the combination of its
inputs and if one of its inputs condition changes state so does the output as combinational circuits
have "no memory", "timing" or "feedback loops".
Combinational Logic
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. These
logic gates are the building blocks of combinational logic circuits. An example of a
combinational circuit is a decoder, which converts the binary code data present at its input into a
number of different output lines, one at a time producing an equivalent decimal code at its
output.
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.
The three main ways of specifying the function of a combinational logic circuit are:
1. 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.
2. 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.
3. 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.
The Multiplexer
A data selector, more commonly called a Multiplexer, shortened to "Mux" or "MPX", are
combinational logic switching devices that operate like a very fast acting multiple position rotary
switch. They connect or control, multiple input lines called "channels" consisting of either 2, 4, 8
or 16 individual inputs, one at a time to an output.
 |
| Multiplexer Symbol |
The Demultiplexer
The data distributor, known more commonly as a Demultiplexer or "Demux", is the exact
opposite of the Multiplexer we saw in the previous tutorial. The demultiplexer takes one single
input data line and then switches it to any one of a number of individual output lines one at a
time. The demultiplexer converts a serial data signal at the input to a parallel data at its output
lines as shown below.
 |
| 1-to-4 Channel De-multiplexer |
The Digital Encoder
Unlike a multiplexer that selects one individual data input line and then sends that data to a
single output line or switch, a Digital Encoder more commonly called a Binary Encoder takes
ALL its data inputs one at a time and then converts them into a single encoded output.
So we can say that a binary encoder, is a multi-input combinational logic circuit that
converts the logic level "1" data at its inputs into an equivalent binary code at its
output. Generally, digital encoders produce outputs of 2-bit, 3-bit or 4-bit codes depending
upon the number of data input lines. An "n-bit" binary encoder has 2n input lines and n-bit
output lines with common types that include 4-to-2, 8-to-3 and 16-to-4 line configurations.
The output lines of a digital encoder generate the binary equivalent of the input line whose
value is equal to "1" and are available to encode either a decimal or hexadecimal input pattern
to typically a binary or B.C.D. output code.
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