In this section, I would like to outline the steps to be followed to design any Combinational circuit in a concise manner. Using a combination of basic logic gates (AND, OR, NOT) we can design any Combinational circuit.
A combinational circuit consists of input variables, logic gates and output variables.
The output of a combinational circuit depends only on the present input. They are memoryless, unlike sequential circuits.
Designing a combinational circuit requires the following steps:
1. From the given specifications, determine the required number of inputs and outputs.
2. Derive the truth table.
3. Obtain the simplified Boolean functions using reduction techniques such as K-Map.
4. Draw the logic diagram.
Consider the following design problem:
Construct a combinational circuit that takes a 2-bit number as input and triples it.
Aim: This circuit must multiply the input number by 3.
Step 1:
Input bits = 2
Output bits = 4 (since maximum output is 3*3 = 9 which can be represented using 4-bits)
Step 2:
Truth table
Input bits: A, B
Output bits: W, X, Y, Z
Step 3:
From the inputs, we can directly write the logical expression for the 4 outputs as shown below:
W = AB
X = AB'
Y = A'B + AB' = A ⊕ B
Z = A'B + AB = B
Since the equations are simple, reduction techniques are not required.
Step 4:
Logic Diagram
This can be obtained from the previous equations.
Thus given a 2-bit number AB, we obtain output WXYZ which is thrice of the input.
With these simple steps, it is possible to design any Combinational circuit. Remember, a Combinational circuit is one which performs a particular operation and returns some outputs. They cannot be used to design circuits which require memory.
Here is a list of a few common Combinational circuits that are commonly used in Digital Electronics:
A combinational circuit consists of input variables, logic gates and output variables.
The output of a combinational circuit depends only on the present input. They are memoryless, unlike sequential circuits.
Designing a combinational circuit requires the following steps:
1. From the given specifications, determine the required number of inputs and outputs.
2. Derive the truth table.
3. Obtain the simplified Boolean functions using reduction techniques such as K-Map.
4. Draw the logic diagram.
Consider the following design problem:
Construct a combinational circuit that takes a 2-bit number as input and triples it.
Aim: This circuit must multiply the input number by 3.
Step 1:
Input bits = 2
Output bits = 4 (since maximum output is 3*3 = 9 which can be represented using 4-bits)
Step 2:
Truth table
Input bits: A, B
Output bits: W, X, Y, Z
A
|
B
|
W
|
X
|
Y
|
Z
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
1
|
0
|
0
|
1
|
1
|
1
|
0
|
0
|
1
|
1
|
0
|
1
|
1
|
1
|
0
|
0
|
1
|
Step 3:
From the inputs, we can directly write the logical expression for the 4 outputs as shown below:
W = AB
X = AB'
Y = A'B + AB' = A ⊕ B
Z = A'B + AB = B
Since the equations are simple, reduction techniques are not required.
Step 4:
Logic Diagram
This can be obtained from the previous equations.
Thus given a 2-bit number AB, we obtain output WXYZ which is thrice of the input.
With these simple steps, it is possible to design any Combinational circuit. Remember, a Combinational circuit is one which performs a particular operation and returns some outputs. They cannot be used to design circuits which require memory.
Here is a list of a few common Combinational circuits that are commonly used in Digital Electronics:
- Encoders, Decoders
- Multiplexers, Demultiplexers
- Arithmetic circuits like adders, multipliers
- Code converters (Eg. Binary to BCD etc.)
- Solid state switches
- Bus Transceiver
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