fa10-sw-s2 - ECE 2030 B 12:00pm 4 problems 4 pages Computer...

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ECE 2030 B 12:00pm Computer Engineering Fall 2010 4 problems, 4 pages Exam Two Solutions 27 October 2010 Problem 1 (4 parts, 40 points) Safety in Numbers Part A (10 points) Convert the following notations: binary notation decimal notation 1 0111 1100. 256 + 64 + 32 + 16 + 8 + 4 = 380 1100.1011 8 + 4 + .5 + .125 + .0625 = 12.6875 1000101.0111 69.4375 binary notation hexadecimal notation 101 1001 0101.0101 101 595.5A 1000 1011 0110.0011 11 8B6.3C Part B (12 points) For the 28 bit representations below, determine the most positive value and the step size (difference between sequential values). All answers should be expressed in decimal notation . Fractions (e.g., 3/16ths) may be used. Signed representations are two’s complement. representation most positive value step size unsigned fixed-point (26 bits) . (2 bits) 64M 1/4 signed integer (28 bits) . (0 bits) 128M 1 signed fixed-point (21 bits) . (7 bits) 1M 1/128 signed fixed-point (14 bits) . (14 bits) 8K 1/16K Part C (6 points) A 40 bit floating point representation has a 30 bit mantissa field, a 9 bit exponent field, and one sign bit. What is the largest value that can be represented (closest to infinity)?
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