Binary - Decimal Conversion Practice

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					                   LDU – Numeracy Support


        Binary - Decimal Conversion Practice

A) Convert the following binary numbers into decimal numbers:

  1)      1010100
  2)      1010
  3)      110011
  4)      101111
  5)      1110001
  6)      1010101010
  7)      10010010
  8)      10101
  9)      111111
  10)     1110001

B) Convert the following decimal numbers into binary numbers:

  1)      17
  2)      256
  3)      34
  4)      15
  5)      54
  6)      123
  7)      76
  8)      278
  9)      67
  10)     22



You will find the answers with some explanation on the next page ☺




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                       LDU – Numeracy Support


       Binary - Decimal Conversion Practice
                     Answers

A) Convert the following binary numbers into decimal numbers:

We will use the following binary place value table when converting
binary numbers to decimal numbers and visa versa.


29       28 27 26                  25 24          23     22     21       20
512      256 128 64                32 16          8      4      2        1
                          1        0     1        0      1      0        0

   1) 10101002 = 8410

We will start from the smallest place value, which is the right most
digit and will multiply the digit with the place value first then add
the values together.

0 x 20 + 0 x 21 + 1 x 22 + 0 x 23 + 1 x 24 + 0 x 25 + 1 x 26

We will only concentrate on the non 0 terms. We will work out the
index notations, multiplications then add the sum up:

1 x 4 + 1 x 16 + 1 x 64 = 4 + 16 + 64 = 84

   2) 10102 = 1010      3)    1100112 = 5110 4)        1011112 = 6110

   5) 11100012 = 7110         6)    10101010102 = 68210

   7) 100100102 = 13810       8)    101012 = 2110

   9) 1111112 = 6310          10) 11100012 = 11310

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                    LDU – Numeracy Support

B) Convert the following decimal numbers into binary numbers:

Converting decimal numbers to binary numbers are a bit more
“clumsy”. We will have to find the highest power of 2 that can be
subtracted from our number at each step and that way build up our
binary number. The binary place value table is a very handy visual aid
here:


29      28 27 26                 25 24           23     22     21        20
512     256 128 64               32 16           8      4      2         1
                                        1        0      0      0         1

  1)       1710 = 100012

Looking at the table above we can see that the highest power of 2
that we can subtract from 17 is 16, which is 24 and our remainder is
1 which is 20. All the other powers have not been used; therefore we
have to put 0 to those places in our number. (Just like you would do
in the decimal system for example with 407, where the 0 means that
we haven’t used any tens.)

2) 25610 = 1000000002        3) 3410 = 1000102        4) 1510 = 11012

5) 5410 = 1101102       6) 12310 = 11110112   7) 7610 = 10011002

8) 27810 = 1000101102        9) 6710 = 10000112       10) 2210 = 10112




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