Wed Oct 14

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

+8 For any Boolean values \(X\) and \(Y\), can \((X+Y)'\) be rewritten as \(X' + Y'\)?

yes / noJustify 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).+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.

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

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