Homework 4 Solutions - Computer Architecture and Design | ELEC 5200, Assignments of Computer Architecture and Organization

Download Homework 4 Solutions - Computer Architecture and Design | ELEC 5200 and more Assignments Computer Architecture and Organization in PDF only on Docsity! ELEC 5200-002/6200-002 Computer Architecture and Design Fall 2006 Homework 4 Solutions Assigned 9/25/06, due 10/2/06 Problem 1: Multiply 85ten by –16ten using the Booth multiplication algorithm and 8-bit two’s complement representation. Use 16 bits for the product. Answer: Booth multiplication: 0 1 0 1 0 1 0 1 = 85 1 1 1 1 0 0 0 0 (0) = –16 bit 1 of multiplier, pair 00 → no action bit 2 of multiplier, pair 00 → no action bit 3 of multiplier, pair 00 → no action bit 4 of multiplier, pair 00 → no action 1 1 1 1 1 0 1 0 1 0 1 1 0 0 0 0 bit 5 of multiplier, pair 10 → partial product = –85 bit 6 of multiplier, pair 11 → no action bit 7 of multiplier, pair 11 → no action bit 8 of multiplier, pair 11 → no action 1 1 1 1 1 0 1 0 1 0 1 1 0 0 0 0 16-bit product in two’s complement = –1360 Problem 2: The following flowchart gives a restoring algorithm for binary division of 32-bit positive integers. Modify the flowchart for non-restoring division. Initialize: Remainder, $R(33bits) = 0 Quotient, $Q(32bits) = dividend $M(33bits) = divisor Count = 0 Count = Count + 1 Count≤3 2 $Q = quotient $R = remainder $R = 2$R + MSB($Q) $Q = 2$Q $R = $R + $M MSB($R)= 1 $Q = $Q + 1 $R = $R – $M Y N Y N Left shift Restore Subtract divisor