5.2 Design
Procedure
Part 5.2.1 Step
by Step Design Procedure
The design of
combinational logic circuits starts from the statement of the problem and ends
in a circuit diagram or a set of Boolean functions from which the logic circuit
can be easily drawn. The procedure involves the following steps:
1. The problem is stated.
2.
The number of
available input variables and required output variables is determined.
3.
The input and
output variables are assigned letter symbols.
4.
The truth table
that defines the required relationships between the inputs and outputs is
derived.
5.
The simplified
function for each output is obtained.
6.
The logic circuit
is drawn
Example
No. 1
Design a
combinational circuit with three inputs and one output. The output is equal to
logic-1 when the binary value of the input is less than 3. The output is
logic-0 otherwise. Implement using all NAND gates.
Solution
No. 1
Step
1, 2 and 3: The three inputs
can be designated with any letters, say, A, B, and C. The output is to be
represented by F. Construct the truth table having three columns for the inputs
and one column for the output. The number of rows corresponds to the number of
possible input combinations 23=8. Thus,
Step
4:
|
Input |
Output |
||
|
A |
B |
C |
F |
|
0 |
0 |
0 |
1 |
|
0 |
0 |
1 |
1 |
|
0 |
1 |
0 |
1 |
|
0 |
1 |
1 |
0 |
|
1 |
0 |
0 |
0 |
|
1 |
0 |
1 |
0 |
|
1 |
1 |
0 |
0 |
|
1 |
1 |
1 |
0 |
Step
5: Output values are derived using the
condition, ABC < 3, F = 1, ABC ≥ 3, F = 0
Forming the SOP
expression of the output:
F = A'B'C' +
A'B'C + A'BC'
The simplified
expression is F = A'B' + A'C' or F = A'(B' + C')
Step
6: Draw the Logic Circuit
Figure 2. Logic Circuit for F = A'B' + A'C'
Figure 3. Logic Circuit using Universal Gate (NAND)
Example
No 2.
Design a
combinational circuit with three inputs and six outputs. The output binary
number should be the square of the input binary number.
Solution
No. 2
Constructing the
truth table having three inputs x, y, and z and six outputs F1 to F6. The
outputs are obtained by getting the square of the input binary, (ABC)22=
(F1 F2 F3 F4 F5 F6)2
|
Input |
Output |
|||||||
|
x |
y |
z |
F1 |
F2 |
F3 |
F4 |
F5 |
F6 |
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
1 |
|
0 |
1 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
|
0 |
1 |
1 |
0 |
0 |
1 |
0 |
0 |
1 |
|
1 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
|
|
1 |
0 |
1 |
0 |
1 |
1 |
0 |
0 |
1 |
|
1 |
1 |
0 |
1 |
0 |
0 |
1 |
0 |
|
|
1 |
1 |
1 |
1 |
1 |
0 |
0 |
0 |
1 |
The simplified
expression for each of the output is obtained, and the logic circuit drawn. The
circuit given below is just one of the many possible combinational logic
circuits for this particular example.
F1 = xy
F2 = xy' + xz
F3 = x'yz + xy'z
F4 = yz'
F5 = 0
F6 = z
Figure 4 Simplified Logic Circuit