Write out your answers to these problems neatly in a text file and submit your work by the due date.

Be sure to put your name on your paper.

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Note: Only problem 6 involves two's-complement notation.

1. (8 points) Convert the following binary numbers to their decimal representations:
   1. B'1001'

   2. B'10110'

   3. B'101110'

   4. B'101011'

2. (8 points) Convert the following hexadecimal numbers to their decimal representations:
   1. X'3C'

   2. X'A9'

   3. X'4E8'

   4. X'507'

3. (8 points) Convert the following decimal numbers to their hexadecimal and binary representations:
   1. 37

   2. 1194

   3. 359

   4. 2047

4. (8 points) Do the binary arithmetic:
   1. B'01110' + B'11011'

   2. B'10110' + B'01111'

   3. B'10101' - B'01100'

   4. B'11101' - B'01110'

5. (8 points) Do the hexadecimal arithmetic:
   1. X'2581' + X'94BD'

   2. X'F28' + X'31C'

   3. X'5BE7' - X'36C1'

   4. X'EAB' - X'B84'

6. (6 points) The integers in the following computations are indicated in hexadecimal, but represent 32-bit two's complement binary numbers. Perform the operations and indicate if overflow occurs and why. (If overflow occurs the result is invalid, but show it anyway.)

            
            a. X'D4C3B2A1'            b. X'754C4612'
             + X'3456ABCD'             + X'1003A642'
             -------------             -------------
   
   
   
   
   
            c. X'E044032F'            d. X'645C2041'   
             - X'A18492A2'             - X'781D30B1'
             -------------             -------------
   
   
   
   
   
            e. X'7FFFFFFF'            f. X'E8866541'
             + X'70000001'             - X'920B011F'
             -------------             -------------
   
   
   
   
   
   

7. (4 points) Assume that:
   • Register 0 contains X'00043E6C'
   • Register 1 contains X'0000007D'
   • Register 7 contains X'FF028CC4'

   Here are some expressions which may be D(X,B) addresses. If they are valid, calculate the values (in hexadecimal), and if they are not valid, explain why not:

   1. 38(0,1)

   2. 0(0,7,1)

   3. 117(0,7)

   4. 49(7,1)