ECE 2030 Introduction to Computer Engineering February 14 2012 EXAM 1 SOLUTION Page 1 of 3 Problem 1 15 points total 2 pts each parts i vi 3 pts part vii i 1010110102 28 26 24 23 21 256 64 16 8 2 34610 ii 84 2510 64 16 4 0 25 26 24 22 2 2 1010100 012 iii 101010112 010 101 0112 2538 iv 437 48 4x82 3x81 7x80 4x8 1 256 24 7 0 5 287 510 v 5CE16 0101 1100 11102 101110011102 vi 60110 2x256 5x16 9 2x162 5x161 9x160 25916 vii A19D16 1010 0001 1001 11012 001 010 000 110 011 1012 1206358 Problem 2 20 points A 15 points i S M 0 1 2 5 6 m 3 4 7 A B C A B C A B C ii U m 0 1 2 5 A B C A B C A B C A B C A C A B B C iii T A B A B C B C A B A C B A B C B C ABC ACB BA BAC BC AB BC ABC iv Q B C D A B D A B D B C D A B D A B D BCD ABD ABD v P A C B AC AC B AC AC BA BC AB AC BC B 5 points NOTE Other solutions possible F B D A C B C A D A C D B D A C BC A D AC D A B A D B C C D B C A D A C D AB AD BC CD BCD A CD AB AD BC CD ABCD ECE 2030 Introduction to Computer Engineering February 14 2012 EXAM 1 Page 2 of 3 Problem 3 12 points A 6 points J A B C A C B A C A 0 0 0 0 1 1 1 1 B 0 0 1 1 0 0 1 1 C 0 1 0 1 0 1 0 1 K A B C A B C A C B A 0 0 0 0 1 1 1 1 J 1 0 1 1 1 0 1 0 J A B C m 0 2 3 4 6 B 0 0 1 1 0 0 1 1 C 0 1 0 1 0 1 0 1 K 0 1 1 0 1 0 1 0 K A B C M 0 3 5 7 B 6 points A B F C D F A B B B C C D PHYSICAL gates 1 AND 1 OR 3 NAND 0 NOR 4 INVERTER Problem 4 14 points X A 6 points A 0 0 0 0 1 1 1 1 B 0 0 1 1 0 0 1 1 Z C 0 1 0 1 0 1 0 1 Fpu 0 0 1 1 1 0 1 0 Fpd 0 0 0 1 0 1 0 1 Y F float float 1 short 1 0 1 0 X Y G Z Y B 8 points G X Y Z X Y X Z Y Z Z X Y X Y X X Y ECE 2030 Introduction to Computer Engineering February 14 2012 EXAM 1 Page 3 of 3 Problem 5 14 points A 6 points Prime implicants CD 00 01 11 10 00 0 0 1 1 01 1 0 1 11 0 1 10 0 1 AB AC ess ACD ess BC ess ess 1 CD ess ess 0 1 ABD ess ess 1 1 ABD ess ess B 8 points CD CD 00 01 11 10 00 0 0 1 1 01 0 0 1 11 1 1 10 0 1 AB CD 00 01 11 10 00 0 0 1 1 1 01 0 0 1 0 1 11 1 1 1 1 10 0 1 Final SOP version 1 AB 00 01 11 10 00 0 0 1 1 1 01 0 0 1 1 0 1 11 1 1 0 1 1 1 10 0 1 1 1 Final SOP version 2 AB Final POS F A B C D AC CD ABC ABD minimal sum of products SOP version 1 F A B C D AC BC ABD ACD minimal sum of products SOP version 2 F A B C D A C B C D A B C D minimal product of sums POS
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