Homework 1
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_hw1_firstname_lastname.txt.

   1. Convert the following binary numbers to a decimal number. 
      (a) 0111
      (b) 1010
      (c) 1111100
     
   2. Convert the following decimal numbers to an 8-bit binary number. 
      (a) 8
      (b) 33
      (c) 254

   3. Perform the following additions using 4-bit binary numbers.
      (a) 9 + 5 = 14
      (b) 2 + 2 = 4
      (c) 8 + 7 = 15
      (d) 9 + 11 = 20 (note: overflow)

   4. Convert the following decimal numbers to an 8-bit binary number
      in two's complement format.
      (a) 1
      (b) -1
      (c) -17
      (d) 0
      (e) What is the range of possible numbers (smallest negative to 
          biggest positive, in decimal) for a 5-bit binary two's 
          complement representation? Express your answer as both
          as both binary and base 10 numbers.
 
   5. Perform the following computations using 4-bit two's complement
      binary numbers. 
      (a) 2 + 2 = 4
      (b) 2 - 1 = 1
      (c) -7 + 2 = -5
      (d) 3 - 5 = -2
      (e) -7 - 7 = -14 (note: overflow)

   6. 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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