1.1)   Convert the following binary numbers to decimal:

       011010101   011101   010000000000001   1101.10101

1.2)   Convert the following decimal numbers to binary:

       234   4567    513    2.75    1.1

1.3)   Convert the following hexadecimal numbers to binary:

        1AB2  3CF8   90D4   576E   3BBD   69FC

1.4)   Convert the binary numbers in problem 1.1 to hex.

1.5)   Convert the hex numbers in problem 1.3 to decimal.

1.6)   In your head convert the following hexadecimal numbers to
       decimal:

        59   66  7A  AB   FF   82   BC   D3   9C   C9   D5   E7

1.7)   Add the following binary numbers:

            0010101    00111000111     0011111111  011
            0011101    00010101010     0011111111  001
            -------    -----------     ----------  010
                                                   011
                                                   010
                                                   011
                                                   011
                                                  ----

1.8)   Subtract the following binary numbers.  Use the borrow
       technique.

               001001001   0100000000  010101010101
               001000111   0000000001  001111111111
               ---------   ----------  ------------

1.9)   Add the following hex numbers:

            0ABDEF   0AAAA   72ABCDEF  BEEF   BAD
            012345   09999   123EEEEE  BEEF   BAD
           -------   -----   --------  ----  ----

1.10)  Subtract the  hex numbers in problem 1.9.  Use the borrow
       technique.

1.11)  Take the two's complement of the following binary numbers.
       Give your answers in hex.  Assume a 16 bit word size.

         0101010101010101   1111111111111111    0011001100110011

1.12)  Redo problem 1.8 by adding the two's complement of the
       lower number in each subtraction.

1.13)  Reasoning analogously from your knowledge of two's
       complement numbers, figure out how to determine the 16's
       complement of a hex number.  Redo problem 1.10 by adding
       the 16's complement of the lower number in each
       subtraction.

1.14)  What is the ten's complement of 24.690?  Assume a 5 digit
       word size.

1.15)  What is 8K in decimal?  What is 4M in decimal?

1.16)  Is 1440K equal to 1.44M?  Explain.

1.17)  One disadvantage of sign-magnitude representation is that
       it requires sign analysis.  What is another disadvantage?
       Hint: how is zero represented?

1.18)  Prove that when two signed numbers with different signs
       are added, overflow never occurs.



1.28)  Convert the following octal (base 8) numbers to
       decimal:

            274   5555    651000   4000  40000

1.29)  Convert the following octal (base 8) numbers to decimal:

       1234  7777  111111 5555  10

1.30)  Add the following octal (base 8) numbers:

       1234   7777   4444   1111    7777
       1234   1111   4443   1111    7777
      -----  -----  -----  -----   -----

1.31)  Convert the following decimal numbers to octal (base 8): 
            999   2361   8   2000   4096

1.32)  Convert the following octal (base 8) numbers to
       binary:

          351   777    15741555634277554

1.33)  What is the range of 32-bit signed binary numbers? 


1.35)  Prove that extending to the left a negative two's
       complement number with ones never changes its value.