CMSC 250 Homework 3 Fall 2001

Due Wed Sept 19 at the beginning of your discussion section.

State what rule of inference is used in each of the following arguments:
1. If I walked to class, then I took the quiz.
  I did not take the quiz.
  Therefore, I did not walk to class.
2. I order salad or an appetizer or both with dinner.
  I do not order a salad with dinner.
  Therefore, I order an appetizer with dinner.
3. I went to the drugstore and the cleaners after work.
  Therefore, I went to the cleaners after work.
4. If it doesn't rain, then I will go on a picnic.
  If I go on a picnic, then I will eat a sandwich.
  Therefore, if it doesn't rain, I will eat a sandwich.
Construct a logical expression that is equivalent to the following circuit.
Use a truth table to determine if the following argument is valid:
$r\wedge q\to \sim p$
$p\wedge \sim q$
$p\to \sim r$
Therefore $p\vee r$ .
Write the following circuits as logical expressions and use a truth table to show that the following two circuits are equivalent.
Convert the following numbers from one base to another:
1. $19_{10} = \underline {\hskip 40pt}_{2}$
2. $82_{10} = \underline {\hskip 40pt}_{2}$
3. $1010111_{2} = \underline {\hskip 40pt}_{10}$
4. $1024_{10} = \underline {\hskip 40pt}_{2}$
5. $1010101_{2} = \underline {\hskip 40pt}_{10}$
6. $1011101_{2} = \underline {\hskip 40pt}_{16}$
7. $FADE_{16} = \underline {\hskip 40pt}_{2}$
Find the following:

$\begin{displaymath}$\begin{array}{c} \hskip 2pt 1010 \\ + 111 \\ \overline{\hskip 50pt} \end{array}$\ \end{displaymath}$

$\begin{displaymath}$\begin{array}{c} 1110110 \\ \hskip 2pt + 11010 \\ \overline{\hskip 50pt} \end{array}$\ \end{displaymath}$

$\begin{displaymath}$ \begin{array}{c} \hskip 9pt 100101010101 \\ +101010101111 \\ \overline{\hskip 80pt} \end{array}$\ \end{displaymath}$