$Id: review1.txt,v 1.1 2006/02/03 00:52:12 locasto Exp $
Spring 2006 COMS 1001
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0. Translate the following numbers from binary (base 2) to decimal
    (base 10).

    a) 10011001
    b) 00000001  
    c) 10000000  
    d) 11011010  
    e) 00000000010110110000000111110111

    answers:
    a) 153
    b) 1
    c) 128
    d) 218
    e) 5964279

1. Translate the following numbers from decimal to binary.

    a) 1,024
    b) 554
    c) 4,342,119
    d) 4490
    e) 2048
    f) 4096
    g) 11223

    answers:
    a) 10000000000
    b) 1000101010
    c) 10000100100000101100111
    d) 1000110001010
    e) 100000000000 
    f) 1000000000000
    g) 10101111010111

2. Add these binary numbers.

   a) 10010000 + 00110111
   b) 0000 + 1111
   c) 01 + 01
   d) 1000 + 0010

   answers:
   a) 11000111
   b) 1111
   c) 10
   d) 1010

3. Show the truth table for the following expressions:

   a) p AND q
   b) p OR q
   c) NOT p
   d) p AND q OR q
   e) (q IMPLIES p) AND (q OR p)
   f) p AND q AND r
   g) (p OR q) IMPLIES r

   answers:
   a)     p| q| p AND q|    b) p| q| p OR q|
          --------------       -------------
          T  T    T            T  T    T
          T  F    F            T  F    T
          F  T    F            F  T    T
          F  F    F            F  F    F

   c)  p  !p           d) p  q  p AND q OR q
       -----              ------------------
       T   F              T  T       T
       F   T              T  F       F
                          F  T       T
                          F  F       F

   e) p  q   q->p AND q OR p
      ----------------------
      T  T       T      
      T  F       T     
      F  T       F     
      F  F       F      

   f)  p  q  r    p and q and r  |g) p or q -> r 
       ----------------------------------------
       T  T  T        T                 T
       T  T  F        F                 F 
       T  F  T        F                 T
       T  F  F        F                 F
       F  T  T        F                 T
       F  T  F        F                 F
       F  F  T        F                 T
       F  F  F        F                 T


4. Draw the circuits (using AND, NOT, and OR gates) for the following
  expressions:

   a) a OR b AND c OR d
   b) a AND b OR (NOT c OR NOT d)

   answers:
   a)

      a ---\---\
            >   >------------+----\
      b ---/---/             |    |
                             |     )------
      c ---\---\             |    |
            >   >------------+----/
      d ---/---/

   b)

      a ---+--|
           |   )------------\------\
      b ---+--|              \      \
                              >      >----
      c ---+--|              /      /
           |   )------------/------/
      d ---+--|

    
5. What is a computer?

   A computer is a device for receiving, storing, and processing 
   information. A digital computer uses a composition of electronic
   circuits to process information.