CS/ECE 252 Introduction to Computer Engineering

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
   1.75
2. 10111110110000000000000000000000
   -0.375

Problem 2 (5 points)

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

1. Draw the transistor level circuit for Z
   Z = (A NOR B) NAND C
   
2. Draw the gate-level circuit for Z using a minimal number of NAND, NOT, and NOR gates
   

Problem 3 (4 points)

Given the following transistor level circuit:

1. Fill out the truth table for Z
   

   A	B	Z
   0	0	0
   0	1	1
   1	0	1
   1	1	1

2. What is Z in terms of A and B
   Z = A OR 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
   

   A	B	C	Z
   0	0	0	0
   0	0	1	0
   0	1	0	0
   0	1	1	1
   1	0	0	0
   1	0	1	1
   1	1	0	1
   1	1	1	1

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
   

   A	B	Z
   0	0	0
   0	1	1
   1	0	1
   1	1	0

2. Is there a logic gate that implements this function? Give reasons for your answer.
   Yes, the XOR gate.

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)?
2048 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
   We use DeMorgan's Law on the OR gate and get the following:
   

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.)

4C 61 73 74 1 51 75 65 73 74 69 6F 6E 21 00