CSC103 Homework 1 Solution 2013

--D. Thiebaut (talk) 09:19, 21 September 2013 (EDT)

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This solution page is for the homework assignment that was due on Tuesda Sept. 17th, at 9:00 a.m.

Question #1

Count in binary and write down the first 35 numbers of the series. In other words, complete the second column in the list below.

   0    0
  1    1
  2    10
  3    11
  4    100
  5    101
  6    110
  7    111
  8    1000
  9    1001
 10    1010
 11    1011
 12    1100
 13    1101
 14    1110
 15    1111
 16    10000
 17    10001
 18    10010
 19    10011
 20    10100
 21    10101
 22    10110
 23    10111
 24    11000
 25    11001
 26    11010
 27    11011
 28    11100
 29    11101
 30    11110
 31    11111
 32    100000
 33    100001
 34    100010

Perform the following additions in binary:

    10110 + 10011 = 101001

    11110 + 10110 = 110100

Question #2

• Write the first 30 numbers of a system with 6 digits. To help you out, I will start with the first 9 numbers of the series:

  0    0
  1    1
  2    2
  3    3
  4    4
  5    5
  6    10
  7    11
  8    12
  9    13
 10    14
 11    15
 12    20
 13    21
 14    22
 15    23
 16    24
 17    25
 18    30
 19    31
 20    32
 21    33
 22    34
 23    35
 24    40
 25    41
 26    42
 27    43
 28    44
 29    45
 30    50

Continue on until you have 20 consecutive numbers of a system in base 6.

Question #3

In base 4.

    1003 + 2301 = 3310

    2232 + 3101 = 11333

Question #4

       f = ( a and b ) or ( a and not c )  or ( not b )

a b c f
0 0 0 1
0 0 1 1
0 1 0 0
0 1 1 1
1 0 0 1
1 0 1 1
1 1 0 1
1 1 1 1

a b c f
F F F T
F F T T
F T F F
F T T T
T F F T 
T F T T 
T T F T 
T T T T