Homework 2
CS 61 Fall 2005
Prof. Frank Vahid
See course web page for due date. 5% extra credit if working in study 
group of 3 or more -- see below.  SHOW WORK, not just answers, for every 
problem, to receive credit. 
Turn in your work electronically as a plain text file (e.g., not a Word doc) 
with the file named cs61_hw2_firstname_lastname.txt.
Exercise numbers (e.g., 2.4) refer to exercises in the Patt/Pattel textbook.

   1. (Encodings) There are ten University of California campuses.
      (a) If every campus is assigned a unique bit pattern, what is
          the minimum number of bits required?
      (b) List the names of all ten campuses, and using the minimum
          number of bits, give each a unique bit encoding. 

   2. (Ranges of binary numbers)
      (a) Exercise 2.4     (a question on range of binary number)
      (b) Exercise 2.8(c)  (a question on range of two's complement number)

   3. (Using AND/OR/NOT logic)
      (a) Exercises 2.30(a), 2.30(c), 2.30(e)   (questions on AND)
      (b) Exercise 2.34(a), 2.34(c)             (questions on AND, OR, and NOT)
      (c) Exercise 2.53                         (question using a truth table)

   4. (Hexadecimal numbers)
      (a) Convert the following binary numbers to 2-digit hex numbers:
          11110000 
          10100101
      (b) Convert the following decimal numbers to 2-digit hexadecimal 
          numbers, by first converting to binary, and then to hex:
          23 
          42
 
   5. ("Real" problems based on the above ideas)
      Say you are hired to write a program that controls a laser used during 
      laser surgery. The laser can be positioned from left to right by 
      setting an output S to any of 
             -20, -19, ..., -1, 0, 1, ..., 19, 20.
      -20 represents the further left the laser can point, 0 is the middle, 
      and 20 is the furthest right.

      (a) How many possible positions exist in the above range?
      (b) What is the minimum number of bits required to represent
          all those possible positions, using two's complement binary?
          Justify your answer!
      (c) The computer you'll be using represents numbers as 8-bit two's 
          complement. You want to write a program that starts by moving the 
          laser all the way left, then all the way right, and then rests the 
          laser in the center. So your program has some instructions like this:
 
                    POSITION -20
                    POSITION  20
                    POSITION   0

          Show how the computer would represent those three numbers
          of your program using 8-bit two's complement representation. 

      (d) The laser machine has eight "too-hot" sensors whose outputs 
          automatically get read into an 8-bit variable S, with each 
          bit in S representing the output of one sensor. Each sensor outputs 
          1 if the patient's skin is above a threshold temperature, 0 
          otherwise.  So if all the sensors indicated too-hot, S=11111111. 
          If only the rightmost sensor indicated too-hot, S=00000001. 

          You want to write a program that sets an output R to 1 if any of 
          the right four sensors indicate too-hot. Likewise, you want to set 
          an output L to 1 if any of the four left sensors indicate too-hot. 
          So you write a program something like this:
         
             T = S AND 00001111
             if T is not equal to 00000000, then R=1, else R=0
             U = S AND 11110000
             if U is not equal to 00000000, then L=1, else L=0

          (i) Show the results for T and U, if S=01010101. 
          (ii) Rewrite the above program by replacing the four 8-bit
               binary numbers by 2-digit hex numbers. To indicate
               that a number is in hex, precede it by x, like this: xFF. 
 
   6. (Transistors) Exercise 3.4 (refer to top p, bottom p, left n, right n
         in your answers, since you are submitting text only and not drawings)

   7. (Muxes/decoders)
      (a) Exercise 3.13
      (b) Exercise 3.14

   8. (Adders)
      Exercise 3.15

   9. If you worked in a study group of 3 or more people, 
      list names of study group partners, and date/time/place of meeting. 
      Submissions should each be unique, but explaining concepts,
      answering each others' questions, and comparing answers for 
      correctness is encouraged. 


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