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Topic: Boolean Algebra Fill-in the boxes (those with arrows)  will give high rating if correct answers ty!!

Topic: Boolean Algebra Fill-in the boxes (those with arrows)  will give high rating if correct answers ty!!

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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Topic: Boolean Algebra

Fill-in the boxes (those with arrows) 

will give high rating if correct answers ty!!

 

Now let's use our Boolean algebra skills to revisit the full adder circuit from before. We want to create a circuit that turns on when there is a carry-out of 1, i.e. Cout =1. Here is the truth table that describes the operation of a full adder, focusing on just the Cout. Some remarks are included for rows where Cout = 1, and the corresponding Boolean expression is included for some entries. Complete the rest of the table. A B Cin Cout Cout is 1 when... Boolean expression 1 1 1 1 1 A is 0* AND B is 1 AND C is 1 АВС 1 1 1 A is 1 AND B is 0* AND C is 1 АВС 1 1 0 1 A is 1 AND B is 1 AND C is 0* 1 1 1 1 A is 1 AND B is 1 AND C is 1 *Note: X = 0 is the same as saying NOT (X = 1) or simply, NOT X. We denote NOT X as X'. We also say that X' is the complement of X. Looking at the table, we know that Cout will be 1 if any of the conditions where Cout=1 happens, i.e. the rows where we defined Boolean expressions above. Therefore, we OR all those four expressions in the table together, i.e. Cout = A'BC + AB'C + +
Transcribed Image Text:Now let's use our Boolean algebra skills to revisit the full adder circuit from before. We want to create a circuit that turns on when there is a carry-out of 1, i.e. Cout =1. Here is the truth table that describes the operation of a full adder, focusing on just the Cout. Some remarks are included for rows where Cout = 1, and the corresponding Boolean expression is included for some entries. Complete the rest of the table. A B Cin Cout Cout is 1 when... Boolean expression 1 1 1 1 1 A is 0* AND B is 1 AND C is 1 АВС 1 1 1 A is 1 AND B is 0* AND C is 1 АВС 1 1 0 1 A is 1 AND B is 1 AND C is 0* 1 1 1 1 A is 1 AND B is 1 AND C is 1 *Note: X = 0 is the same as saying NOT (X = 1) or simply, NOT X. We denote NOT X as X'. We also say that X' is the complement of X. Looking at the table, we know that Cout will be 1 if any of the conditions where Cout=1 happens, i.e. the rows where we defined Boolean expressions above. Therefore, we OR all those four expressions in the table together, i.e. Cout = A'BC + AB'C + +
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