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a.
K-Map:
- K-Map stands for Karnaugh Map which is used to reduce the logic functions more easily and quickly.
- It will minimize the Boolean expressions without using Boolean algebra theorems.
- By using K-Map, the Boolean expressions with two to four variables are easily reduced.
Explanation of Solution
Simplification of Boolean expression using K-Map:
Given:
The K-Map for the given expression is as follows:
The following steps are used to obtain the simplified Boolean expressions.
Step1:
Then group another possible 1’s in the table. Then write the Boolean expression according to the mapping. Write 0 term’s as complemented variable like x’ and 1 term’s as it is like x.
Step2:
The group the 1’s in the table. Then write the Boolean expression according to the mapping. Write 0 term’s as complemented variable like x’ and 1 term’s as it is like x.
Step3:
The group the 1’s in the table. Then write the Boolean expression according to the mapping. Write 0 term’s as complemented variable like x’ and 1 term’s as it is like x.
Step4:
Group all the expressions
Therefore, the simplified expression is “
b.
K-Map:
- K-Map stands for Karnaugh Map which is used to reduce the logic functions more easily and quickly.
- It will minimize the Boolean expressions without using Boolean algebra theorems.
- By using K-Map, the Boolean expressions with two to four variables are easily reduced.
Explanation of Solution
Simplification of Boolean expression using K-Map:
Given:
Simplifying the given equation into 4 variable terms as shown below:
The K-Map for the given expression is as follows:
The following steps are used to obtain the simplified Boolean expressions.
Step1:
The group the 1’s in the table. Then write the Boolean expression according to the mapping. Write 0 term’s as complemented variable like x’ and 1 term’s as it is like x.
Step2:
The group the 1’s in the table. Then write the Boolean expression according to the mapping. Write 0 term’s as complemented variable like x’ and 1 term’s as it is like x.
Step3:
The group the 1’s in the table. Then write the Boolean expression according to the mapping. Write 0 term’s as complemented variable like x’ and 1 term’s as it is like x.
Step4:
Group all the expressions
Therefore, the simplified expression is “
c.
K-Map:
- K-Map stands for Karnaugh Map which is used to reduce the logic functions more easily and quickly.
- It will minimize the Boolean expressions without using Boolean algebra theorems.
- By using K-Map, the Boolean expressions with two to four variables are easily reduced.
Explanation of Solution
Simplification of Boolean expression using K-Map:
Given:
Simplifying the given equation into 4 variable terms as shown below:
The K-Map for the given expression is as follows:
The following steps are used to obtain the simplified Boolean expressions.
Step1:
Then group another possible 1’s in the table. Then write the Boolean expression according to the mapping. Write 0 term’s as complemented variable like x’ and 1 term’s as it is like x.
Step2:
The group the 1’s in the table. Then write the Boolean expression according to the mapping. Write 0 term’s as complemented variable like x’ and 1 term’s as it is like x.
Step3:
The group the 1’s in the table. Then write the Boolean expression according to the mapping. Write 0 term’s as complemented variable like x’ and 1 term’s as it is like x.
Step4:
Group all the expressions
Therefore, the simplified expression is “
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Chapter 3 Solutions
Essentials of Computer Organization and Architecture
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