F(A, B, C) = A B C + A B C + A B C + A B C + A B C(sum-of-minterms)F(A, B, C) = (A + B + C) (A + B + C) (A + B + C)(product-of-maxterms)G(A, B, C) = Sm (0, 1, 4, 7)G(A, B, C) = ?M (2, 3, 5, 6)010001010 0 1ECE 2030 -- Introduction to Computer Engineering EXAM #2 SOLUTION February 26, 2007 Page 1 of 5 Problem 1. (10 points) A. (4 points) F(A, B, C) = A B C + A B C + A B C + A B C + A B C (sum-of-minterms) F(A, B, C) = (A + B + C) (A + B + C) (A + B + C) (product-of-maxterms) B. (4 points) G(A, B, C) = Σm ( 0, 1, 4, 7 ) G(A, B, C) = ΠM ( 2, 3, 5, 6 ) C. (2 points) Problem 3. (12 points) A. (6 points) B. (4 points) X Y = 0 0 0 1 1 0 1 1 FUNCTION LF0 LF1 LF2 LF3 X 1 1 0 0 X + Y 0 1 1 0 X + Y 1 0 1 1 + = exclusive-OR A B C G 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 1 00 01 11 10 CDAB00 0 x 1 x 01 0 0 1 x 11 1 x 0 1 10 x1 1 0 0 1 2 3 0 CFA B 0 1 2A 3B 4C 5 6 7C. (2 points) I0 I1 I2 I3 I4 I5 I6I7 D2D1D0 1 0 1 1 0 1 0 1 0 1 0 0 1 0 0 0 1 0 1 0 0 1 FECE 2030 -- Introduction to Computer Engineering EXAM #2 SOLUTION February 26, 2007 Page 2 of 5 Problem 2. (18 points) A. (8 points) work copy Final SOP Final POS F(A, B, C, D) = B D + A C D + A C D + A B C (2 essential) F(A, B, C, D) = (C + D) (A + B + C) (A + B + D) (A + B + C + D) (4 essential) B. (10 points) work copy Final SOP Final POS G(A, B, C, D) = B D + B D + { A B C or A C D } (0 essential) G(A, B, C, D) = (B + D) (A + B + D) { (A + B + C) or (B + C + D) } (2 essential) Problem 4. (10 points) A. (4 points) F = A IA + A B IB + A B C IC OR F = A IA + A B IB + A B IC VALID = EN (A + B + C) 00 01 11 10 CD AB 00 1 1 x 0 01 1 0 x 1 11 1 x 0 x 10 0 1 1 x 00 01 11 10 CDAB00 1 1 x 0 01 1 0 x 1 11 1 x 0 x 10011x00 01 11 10 CD AB00 1 1 x 0 01 1 0 x 1 11 1 x 0 x 10 0 1 1 x00 01 11 10 CD AB00 0 1 1 1 01 0 1 0 1 11 0 0 1 1 10 0 1 1 000 01 11 10 CDAB00 0 1 1 1 01 0 1 0 1 11 0 0 1 1 10011000 01 11 10 CD AB 00 0 1 1 1 01 0 1 0 1 11 0 0 1 1 10 0 1 1 0 B. (6 points) Solutions will vary, depending on equations
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