Concept explainers
a.
Sum-of-product:
- Sum-of-product is an equation written in the form of AND term for each input combination that produces output as logical 1.
- If the value is 1 write the input variables; otherwise write its complement.
- The OR and AND terms are the final combination of the expression.
Explanation of Solution
Truth table:
The given truth table is as follows:
x | y | z | F1 | F2 |
0 | 0 | 0 | 1 | 0 |
0 | 0 | 1 | 1 | 0 |
0 | 1 | 0 | 1 | 1 |
0 | 1 | 1 | 0 | 1 |
1 | 0 | 0 | 0 | 0 |
1 | 0 | 1 | 0 | 0 |
1 | 1 | 0 | 0 | 1 |
1 | 1 | 1 | 0 | 1 |
Sum-of-product form of F1:
The sum-of-product form of F1 for the above table is as follows:
Sum-of-product form of F2:
The sum-of-product form of F2 for the above table is as follows:
Therefore, the sum-of-product form of F1 and F2 are expressed.
Explanation of Solution
b.
Simplification of F1:
The simplifying the sum-of-product form of F1 is as follows:
Therefore, the simplified Boolean expression F1 is
Sum-of-product form of F2:
The sum-of-product form of F2 for the above table is as follows:
Therefore, the simplified Boolean expression F2 is
Explanation of Solution
c.
Circuit diagram:
The circuit diagram for the F1 and F2 is as follows:
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