4. We have learned to simplify logic expressions using Boolean Algebra and K-Maps. We can also simplify logic expressions by "collapsing some rows" in their truth tables. For example, the function F(a,b,c) = Em(2,3,7) has the truth table below. We only need to consider the rows for which F-1. By collapsing rows 2 and 3, we can write abc = 01x, where x under c means that the value of c does not matter for this collapsed row. Similarly, by collapsing rows 3 and 7, we can write abc = x11. Then, we can drop the 'x' and simplify F = a'b + bc. The collapsed truth table is shown below the original one. Then use this method to simplify the function G(a,b,c) - [m(0,2,4,6,7). original truth table row # 0 1 2 3 4 5 6 7 row # 2,3 3,7 0,1,4,5,6 abc 000 001 010 011 100 101 110 111 F all others 0 0 1 1 0 0 0 1 collapsed truth table abc 01x x 11 F 1 1 0
4. We have learned to simplify logic expressions using Boolean Algebra and K-Maps. We can also simplify logic expressions by "collapsing some rows" in their truth tables. For example, the function F(a,b,c) = Em(2,3,7) has the truth table below. We only need to consider the rows for which F-1. By collapsing rows 2 and 3, we can write abc = 01x, where x under c means that the value of c does not matter for this collapsed row. Similarly, by collapsing rows 3 and 7, we can write abc = x11. Then, we can drop the 'x' and simplify F = a'b + bc. The collapsed truth table is shown below the original one. Then use this method to simplify the function G(a,b,c) - [m(0,2,4,6,7). original truth table row # 0 1 2 3 4 5 6 7 row # 2,3 3,7 0,1,4,5,6 abc 000 001 010 011 100 101 110 111 F all others 0 0 1 1 0 0 0 1 collapsed truth table abc 01x x 11 F 1 1 0
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need help simplifying equation
![**Simplifying Logic Expressions Using Boolean Algebra and K-Maps**
In logic design, we can simplify logic expressions using Boolean Algebra and Karnaugh Maps (K-Maps). Another method is by "collapsing some rows" in truth tables. Consider the function \( F(a,b,c) = \Sigma m(2,3,7) \), which has the truth table outlined below. The focus is on rows where \( F = 1 \).
By collapsing rows 2 and 3, the expression \( abc = 01x \) emerges, where \( x \) under \( c \) indicates that the value of \( c \) is immaterial for this collapsed row. Similarly, collapsing rows 3 and 7 yields \( abc = x11 \). Dropping the ‘\( x \)’ allows us to simplify and express \( F = ab' + bc \).
**Original Truth Table**
\[
\begin{array}{|c|c|c|c|c|}
\hline
\text{row \#} & a & b & c & F \\
\hline
0 & 0 & 0 & 0 & 0 \\
1 & 0 & 0 & 1 & 0 \\
2 & 0 & 1 & 0 & 1 \\
3 & 0 & 1 & 1 & 1 \\
4 & 1 & 0 & 0 & 0 \\
5 & 1 & 0 & 1 & 0 \\
6 & 1 & 1 & 0 & 0 \\
7 & 1 & 1 & 1 & 1 \\
\hline
\end{array}
\]
**Collapsed Truth Table**
\[
\begin{array}{|c|c|c|c|c|}
\hline
\text{row} & a & b & c & F \\
\hline
2,3 & 0 & 1 & x & 1 \\
3,7 & x & 1 & 1 & 1 \\
0,1,4,5,6 & \text{all others} & 0 \\
\hline
\end{array}
\]
This method further simplifies the function \( G(a,b,c) = \Sigma m(0,2,4,6,7) \).
This approach](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdaad9e7e-1f14-44d5-98ac-51623b651f9b%2Ffed2fae1-1865-421e-9124-5d50a9cb40ba%2Fplbfdhd_processed.png&w=3840&q=75)
Transcribed Image Text:**Simplifying Logic Expressions Using Boolean Algebra and K-Maps**
In logic design, we can simplify logic expressions using Boolean Algebra and Karnaugh Maps (K-Maps). Another method is by "collapsing some rows" in truth tables. Consider the function \( F(a,b,c) = \Sigma m(2,3,7) \), which has the truth table outlined below. The focus is on rows where \( F = 1 \).
By collapsing rows 2 and 3, the expression \( abc = 01x \) emerges, where \( x \) under \( c \) indicates that the value of \( c \) is immaterial for this collapsed row. Similarly, collapsing rows 3 and 7 yields \( abc = x11 \). Dropping the ‘\( x \)’ allows us to simplify and express \( F = ab' + bc \).
**Original Truth Table**
\[
\begin{array}{|c|c|c|c|c|}
\hline
\text{row \#} & a & b & c & F \\
\hline
0 & 0 & 0 & 0 & 0 \\
1 & 0 & 0 & 1 & 0 \\
2 & 0 & 1 & 0 & 1 \\
3 & 0 & 1 & 1 & 1 \\
4 & 1 & 0 & 0 & 0 \\
5 & 1 & 0 & 1 & 0 \\
6 & 1 & 1 & 0 & 0 \\
7 & 1 & 1 & 1 & 1 \\
\hline
\end{array}
\]
**Collapsed Truth Table**
\[
\begin{array}{|c|c|c|c|c|}
\hline
\text{row} & a & b & c & F \\
\hline
2,3 & 0 & 1 & x & 1 \\
3,7 & x & 1 & 1 & 1 \\
0,1,4,5,6 & \text{all others} & 0 \\
\hline
\end{array}
\]
This method further simplifies the function \( G(a,b,c) = \Sigma m(0,2,4,6,7) \).
This approach
Expert Solution
Step 1: Stating the problem:
We are going to design the truth table and Collapsed truth table for given function G as per the guidelines.
First we will draw the original truth table and for output values 1, we will check which rows can be collapsed.
I have attached the detailed solution below and designed the K-map also for better understanding.
Step by step
Solved in 3 steps with 1 images
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