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5. Draw the output X, Y and Z for the pattern of inputs shown in the figure below for three variable logical expressions: X = Not (A and B) and Not (B and C), this Boolean expression can also be depicted as X= (AB)' (BC)' Y = (Not A or B) and (A and Not B), this Boolean expression can also be depicted as Y = (A'+ B) (AB') Z = (A or B) and Not (A or C), this Boolean expression can also be depicted as

5. Draw the output X, Y and Z for the pattern of inputs shown in the figure below for three variable logical expressions: X = Not (A and B) and Not (B and C), this Boolean expression can also be depicted as X= (AB)' (BC)' Y = (Not A or B) and (A and Not B), this Boolean expression can also be depicted as Y = (A'+ B) (AB') Z = (A or B) and Not (A or C), this Boolean expression can also be depicted as

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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**Transcript for Educational Website** In this exercise, we are examining three variable logical expressions and their corresponding outputs X, Y, and Z based on given input patterns. Here's a breakdown of each expression: 1. **Expression for X**: - Defined as: Not (A and B) and Not (B and C) - Boolean expression: \( X = (AB)' (BC)' \) 2. **Expression for Y**: - Defined as: (Not A or B) and (A and Not B) - Boolean expression: \( Y = (A' + B)(AB') \) 3. **Expression for Z**: - Defined as: (A or B) and Not (A or C) - Boolean expression: \( Z = (A + B)(A + C)' \) **Graph/Diagram Explanation**: The diagram presents a series of logic waveforms with three input signals labeled A, B, and C. Each waveform shows a distinct high (1) and low (0) state over time, which represents binary input conditions. These inputs determine the outputs, X, Y, and Z, based on the logical expressions described above. - **Waveform A**: Alternates between high and low states more frequently. - **Waveform B**: Displays a combination of long periods of high and low states. - **Waveform C**: Alternates between states but maintains high or low states longer than A. While the diagram displays the lines for X, Y, and Z beneath the input waveforms A, B, and C, detailed calculations based on the logical operations with respect to the graph are needed to illustrate their waveforms. Each output should reflect the respective logical operations applied to the input waveforms.
Transcribed Image Text:**Transcript for Educational Website** In this exercise, we are examining three variable logical expressions and their corresponding outputs X, Y, and Z based on given input patterns. Here's a breakdown of each expression: 1. **Expression for X**: - Defined as: Not (A and B) and Not (B and C) - Boolean expression: \( X = (AB)' (BC)' \) 2. **Expression for Y**: - Defined as: (Not A or B) and (A and Not B) - Boolean expression: \( Y = (A' + B)(AB') \) 3. **Expression for Z**: - Defined as: (A or B) and Not (A or C) - Boolean expression: \( Z = (A + B)(A + C)' \) **Graph/Diagram Explanation**: The diagram presents a series of logic waveforms with three input signals labeled A, B, and C. Each waveform shows a distinct high (1) and low (0) state over time, which represents binary input conditions. These inputs determine the outputs, X, Y, and Z, based on the logical expressions described above. - **Waveform A**: Alternates between high and low states more frequently. - **Waveform B**: Displays a combination of long periods of high and low states. - **Waveform C**: Alternates between states but maintains high or low states longer than A. While the diagram displays the lines for X, Y, and Z beneath the input waveforms A, B, and C, detailed calculations based on the logical operations with respect to the graph are needed to illustrate their waveforms. Each output should reflect the respective logical operations applied to the input waveforms.
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