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Consider the following specifications of an alarm system: Four sensors w, x, y, and z are used as inputs and the alarm's sound S is used as output. If sensors w and z together detect an event, the output S must go ON. If sensors w, x, and y together detect an event, the output S must go ON. Otherwise, the output S remains OFF. a) Build a truth table for this system. b) From the truth table, derive a Boolean expression in both canonical and standard SOP forms. c) Using Boolean Algebra, simplify your expression to the minimum number of literals. d) Using K-map, find the simplified expression that you found in c). e) Implement the simplified expression with gates.

Consider the following specifications of an alarm system: Four sensors w, x, y, and z are used as inputs and the alarm's sound S is used as output. If sensors w and z together detect an event, the output S must go ON. If sensors w, x, and y together detect an event, the output S must go ON. Otherwise, the output S remains OFF. a) Build a truth table for this system. b) From the truth table, derive a Boolean expression in both canonical and standard SOP forms. c) Using Boolean Algebra, simplify your expression to the minimum number of literals. d) Using K-map, find the simplified expression that you found in c). e) Implement the simplified expression with gates.

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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Consider the following specifications of an alarm system: Four sensors w, x, y, and z are used as inputs and the alarm's sound S is used as output. If sensors w and z together detect an event, the output S must go ON. If sensors w, x, and y together detect an event, the output S must go ON. Otherwise, the output S remains OFF. a) Build a truth table for this system. b) From the truth table, derive a Boolean expression in both canonical and standard SOP forms. c) Using Boolean Algebra, simplify your expression to the minimum number of literals. d) Using K-map, find the simplified expression that you found in c). e) Implement the simplified expression with gates.
Transcribed Image Text:Consider the following specifications of an alarm system: Four sensors w, x, y, and z are used as inputs and the alarm's sound S is used as output. If sensors w and z together detect an event, the output S must go ON. If sensors w, x, and y together detect an event, the output S must go ON. Otherwise, the output S remains OFF. a) Build a truth table for this system. b) From the truth table, derive a Boolean expression in both canonical and standard SOP forms. c) Using Boolean Algebra, simplify your expression to the minimum number of literals. d) Using K-map, find the simplified expression that you found in c). e) Implement the simplified expression with gates.
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