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The truth table shown below is supposed to reflect the function F(x, y, z) = y(x + z') but some lines are in error. Identify the line numbers of the wrong lines and provide correct values.

The truth table shown below is supposed to reflect the function F(x, y, z) = y(x + z') but some lines are in error. Identify the line numbers of the wrong lines and provide correct values.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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### Understanding Truth Tables and Identifying Errors The truth table shown below is supposed to reflect the function F(x, y, z) = y(x + z') but some lines are in error. Identify the line numbers of the wrong lines and provide correct values. #### Truth Table: | # | X | Y | Z | F | |----|---|---|---|---| | 1 | 0 | 0 | 0 | 0 | | 2 | 0 | 0 | 1 | 0 | | 3 | 0 | 1 | 0 | 0 | | 4 | 0 | 1 | 1 | 1 | | 5 | 1 | 0 | 0 | 0 | | 6 | 1 | 0 | 1 | 1 | | 7 | 1 | 1 | 0 | 1 | | 8 | 1 | 1 | 1 | 1 | #### Explanation of the Function: The function F(x, y, z) = y(x + z') can be simplified as follows: - \(x + z'\) is an OR operation between x and the NOT of z. - \(y(x + z')\) is an AND operation between y and the above result. Given this function, let's calculate F for each row and identify any mistakes: 1. **Row 1**: \(F = 0(0 + 1) = 0\) 2. **Row 2**: \(F = 0(0 + 0) = 0\) 3. **Row 3**: \(F = 1(0 + 1) = 1\) – Error (Currently 0, should be 1) 4. **Row 4**: \(F = 1(0 + 0) = 0\) – Error (Currently 1, should be 0) 5. **Row 5**: \(F = 0(1 + 1) = 0\) 6. **Row 6**: \(F = 0(1 + 0) = 0\) – Error (Currently 1, should be 0) 7. **Row 7**: \(F = 1(1 + 1) = 1\
Transcribed Image Text:### Understanding Truth Tables and Identifying Errors The truth table shown below is supposed to reflect the function F(x, y, z) = y(x + z') but some lines are in error. Identify the line numbers of the wrong lines and provide correct values. #### Truth Table: | # | X | Y | Z | F | |----|---|---|---|---| | 1 | 0 | 0 | 0 | 0 | | 2 | 0 | 0 | 1 | 0 | | 3 | 0 | 1 | 0 | 0 | | 4 | 0 | 1 | 1 | 1 | | 5 | 1 | 0 | 0 | 0 | | 6 | 1 | 0 | 1 | 1 | | 7 | 1 | 1 | 0 | 1 | | 8 | 1 | 1 | 1 | 1 | #### Explanation of the Function: The function F(x, y, z) = y(x + z') can be simplified as follows: - \(x + z'\) is an OR operation between x and the NOT of z. - \(y(x + z')\) is an AND operation between y and the above result. Given this function, let's calculate F for each row and identify any mistakes: 1. **Row 1**: \(F = 0(0 + 1) = 0\) 2. **Row 2**: \(F = 0(0 + 0) = 0\) 3. **Row 3**: \(F = 1(0 + 1) = 1\) – Error (Currently 0, should be 1) 4. **Row 4**: \(F = 1(0 + 0) = 0\) – Error (Currently 1, should be 0) 5. **Row 5**: \(F = 0(1 + 1) = 0\) 6. **Row 6**: \(F = 0(1 + 0) = 0\) – Error (Currently 1, should be 0) 7. **Row 7**: \(F = 1(1 + 1) = 1\
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