## Assignment #2: Data Representation, and Boolean Logic and Circuits

Assigned: Monday, Sep. 10
Due: Monday, Sep. 17

### Overview

Topic: Signed Binary Numbers; Characters, Text, and ASCII; Boolean Logic, and Gates and Circuits
Related Reading: Class notes and Chapter 4

### Internet Requirements

For some of the problems in this assignment we will utilize the Logic Simulator Software. You will need to have an Internet connection to run this software.

### Practice Problems

• Complete Lab 7.1 associated with the Logic Simulator software. This lab walks you through the use of their Logg-O software, which we will be using for this assignment.

• Complete Lab 7.2 associated with the Logic Simulator software. This lab lets you start building some interesting circuits.

### Problems to be Submitted (25 points)

When you turn in your assignment, you must include a signed cover sheet (PDF) with your assignment (you're assignment will not be graded without a completed cover sheet).

You are allowed to submit your assignment via email, but if you choose to do so, you must bring a hardcopy of your assignment along with a completed cover sheet to the instructor at the next class. (Note: Do not email the instructor any .zip file attachments, as SLU's email may not deliver these emails, i.e. the instructor may not receive your email.)

1. (2 points)

Convert the decimal number 5710 into its 8-bit signed binary representation.

2. (3 points)

Convert the decimal number -8610 into its 8-bit signed binary representation.

3. (2 points)

Given the following bitstring:      10111001

What decimal number does it represent if interpreted as an 8-bit unsigned number?
What decimal number does it represent if interpreted as an 8-bit signed number?

4. (3 points)

The following text is represented in ASCII (characters are in hexadecimal). Translate the ASCII into the corresponding English text.

4E 65 65 64 20 61 73 70
69 72 69 6E 20 79 65 74
3F 00

5. (3 points)

Draw the circuit diagram for the Boolean logic equation:   (AB + C)D

Note: If you wish to use the Windows snipping tool (or similar screen capture tool), you may use the Logic Simulator software to construct the circuit and then include your screen capture of the circuit in your answer. (You have to use a screen capture tool; trying to print the web page unfortunately doesn't work.)

6. (5 points)

For the Boolean logic equation   BC + (C + B):

1. Draw the circuit diagram for this logic equation.
2. Give the truth table corresponding to this logic equation.
3. Does this circuit give the same output results (i.e. the same truth table) as the equation   X = C ?
Note: You may want to use the Logic Simulator software to verify your answer.

7. (4 points)

For the circuit in Exercise #62 at the end of Chapter 4 (p. 115):

1. Give the logic equation corresponding to this circuit.
2. Give the truth table corresponding to this circuit.
Note: You may want to use the Logic Simulator software to verify your answer.

8. (3 points)

Using truth tables, show that the answer for Exercise #12 (on p. 112 at the end of Chapter 4) is TRUE.
In other words, use truth tables to show that   (AB)   is equivalent to   A + B