# CS/ECE 252 Introduction to Computer Engineering

Fall 2011 Section 1
Instructor Guri Sohi
TAs Newsha Ardalani and Rebecca Lam

URL: http://www.cs.wisc.edu/~sohi/cs252/Fall2011/

## Homework 3 // Due at lecture Mon, Sep 26

Primary contact for this homework: Rebecca Lam [rjlam@cs.wisc.edu]

You must do this homework in groups of two. Please write the full name and the student id of each member on every pages and staple multiple pages together.

### Problem 1 (2 points)

Write the decimal equivalents for these IEEE floating point numbers

1. 00111111111000000000000000000000
2. 10111110110000000000000000000000

### Problem 2 (5 points)

Given the logic equation Z = A OR B OR (NOT C)

1. Draw the transistor level circuit for Z
2. Draw the gate-level circuit for Z using a minimal number of NAND, NOT, and NOR gates
*Hint: Use DeMorgan's Law

### Problem 3 (4 points)

Given the following transistor level circuit:

1. Fill out the truth table for Z
2. What is Z in terms of A and B

### Problem 4 (5 points)

Given the logic equation Z = (A AND B) OR (B AND C) OR (A AND C)

1. Fill out the truth table
2. Draw the gate-level circuit for Z using 2-input AND and OR gates

### Problem 5 (4 points)

Given the logic equation Z = (A AND (NOT B)) OR ((NOT A) AND B)

1. Fill out the truth table
2. Is there a logic gate that implements this function? Give reasons for your answer.

### Problem 6 (2 points)

Given an address size of 10 bits with 16 bits stored at each address, what is the total size of accessible memory(in bytes)?

### Problem 7 (6 points)

Given the following truth table

1. Draw the gate-level circuit using NOT gates and 3-input AND and OR gates.
2. Convert the circuit of part a into a circuit that uses only NAND gates. *Hint: Use DeMorgan's Law
 A B C Z 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 0

### Problem 8 (2 points)

Using ASCII 8-bit, null-terminated string patterns, represent each of the characters in the string "Last Question!" using the hexadecimal value. (Only represent the characters between the quotation marks.)

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