2.6 Evaluation Of Logic Expression With The Use Of Truth Table
Boolean or logical expression can be simply
evaluated using a truth table or table of combinations of the variables
representing the relationship of all possible values that the variables may
take and result of the operation.
Part 2.6.1 Truth Table
A truth table is a tabular representation of a Boolean function.
It provides a clear and concise way to visualize the relationship between the
input values and the corresponding output value of a Boolean expression. Each
row in a truth table represents a unique combination of input values, while
each column represents an input variable or the output of the function. The
values in the table are typically 0 or 1, representing the logical values
"false" and "true," respectively. Truth tables are
essential for understanding Boolean functions, verifying the correctness of
Boolean expressions, and designing digital circuits.
Part 2.6.2 How we Draw a Truth Table
This is the step by step procedure how we
draw a truth table.
Step No. 1: Know the number of input.
The use the formula below to know the number of combination
you need to do.
Number of combination =
2n
Step No. 2 Draw the row of input, output and combination.
Step No. 3 Draw the combinations. Use the pattern.
Example no 1.
Draw a truth table with 3 input and 1 output variable.
Solution:
Step No. 1: Know the number of input.
The use the formula below to know the number of combination
you need to do.
Number of combination = 2n
Number of combination = 23
Number of combination = 8
Step No. 2 Draw the row of input, output and combination.
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Step No. 3 Draw the combinations. Use the pattern.
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And here is our truth table.
Example no 2.
Draw a truth table with 4 input and 1 output variable.
Solution:
Step No. 1: Know the number of input.
The use the formula below to know the number of combination
you need to do.
Number of combination = 2n
Number of combination = 24
Number of combination = 16
Step No. 2 Draw the row of input, output and combination.
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Step No. 3 Draw the combinations. Use the pattern.
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And here is our truth table.
Part 2.6.3 Conversion from Boolean Expression to
Truth Table.
This is the step by step procedure how we
convert Boolean expression to truth table.
Step No. 1: Know the number of input variables. The use the
formula below to know the number of combination you
need to do.
Number of combination =
2n
Step No. 2 Draw the row of input, output and combination.
Step No. 3 Draw the combinations. Use the pattern.
Step No. 4 Evaluate each term of the expression.
Example No 3.
Convert F=ABC+BC’+AC’ to truth table
Solution:
Step No. 1: Know the number of input variables. The use the
formula below to know the number of combination you
need to do.
Number of combination = 2n
Number of combination = 23
Number of combination =
8
Step No. 2 Draw the row of input, output and combination.
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Step No. 3 Draw the combinations. Use the pattern.
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F |
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Step No. 4 Evaluate each term of the expression.
Step No. 4.1
F=ABC+BC’+AC’
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C’ |
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Step No. 4.2
F=ABC+BC’+AC’
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C’ |
ABC |
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Step No. 4.3
F=ABC+BC’+AC’
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C’ |
ABC |
BC’ |
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0 |
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Step No. 4.4
F=ABC+BC’+AC’
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C’ |
ABC |
BC’ |
AC’ |
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Step No. 4.4
F=ABC+BC’+AC’
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Input |
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C |
C’ |
ABC |
BC’ |
AC’ |
ABC+BC’+AC’ |
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1 |
Step No. 4.5
Our Final truth table is:
F=ABC+BC’+AC’
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0 |
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