Test2_5200_sol - ELEC 5200/ELEC 6200 Computer Architecture...

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ELEC 5200/ELEC 6200 Computer Architecture and Design Class Test II, October 27, 2004 Total 24 points Broun 306, 8:00-8:50AM Instructions: Please read all questions before writing your answers and attempt all four (4) questions. Be sure to revise your answers before turning them in. Please number your answer sheets, and on the first page identify the test as shown above, write your name and write the total number of pages you are submitting. You must return the question sheet with your answers. Thank you. Problem 1: 6 points Consider the following cases of addition of 4-bit two’s complement integers: (i) 0111 (ii) 1001 +0100 +0010 1011 1011 (a) Although the numbers being added are different, why are the result same? (3 points) (b) Express the two additions using equivalent decimal integers. (3 points) Answer: (a) In (i), both numbers being added have the same sign (positive) but the sum is negative. This condition indicates overflow and the sum is not correct. There is no overflow in (ii) and the sum is correct. (b) (i) 7+4 = -5 (incorrect due to overflow); (ii) -7+2 = -5 Problem 2: 6 points We wish to multiply 6 ten by -6 ten using the Booth multiplication algorithm and 4-bit two’s complement representation: (a) Show the steps of multiplication leading to the final result.
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