Quiz 3 Solutions

Wed Oct 14

You have up to 20 minutes. You may not use text book or notes.

1. +8 For any Boolean values \(X\) and \(Y\), can \((X+Y)'\) be rewritten as \(X' + Y'\)?
   yes / no

   Justify your answer by creating a truth table to show the results of the two expressions for all possible values of \(X\) and \(Y\).

   The two expressions are not the same, because they have different values in the truth table (see the two columns in bold).

   

        

2. +6 In algebra, an operator is commutative if the order of its operands can be reversed. For example, standard addition is commutative because \(A+B = B+A\) for all numbers \(A\) and \(B\). Division is not commutative. For example, \(\frac45 \neq \frac54\) or in decimal notation, \(0.8 \neq 1.25\).

   Which of the Boolean operators (AND, OR, XOR) are commutative?

   All of those operators are commutative.

3. +6 Write the Boolean expression implemented by the following circuit diagram.

   

   Diagram for question 3

   \(A \cdot (B \oplus C)\)

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