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sp04-jh-s1 - (B C(C A B ECE 2030 Introduction to Computer...

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ECE 2030 -- Introduction to Computer Engineering EXAM #1 SOLUTION (version A) February 5, 2004 Page 1 of 2 Problem 1. (20 points) A. (i) 110110101 2 = 437 10 (ii) 882 10 = `1101110010 2 (iii) 375 8 = 253 10 (iv) (2 9 + 2 6 ) = 512 + 64 = 576 (v) 365 10 = 101101101 2 = 0001 0110 1101 2 = 16D 16 (vi) 9C35 16 = 1001 1100 0011 0101 2 = 001 001 110 000 110 101 2 = 116065 8 B. (i) __S __ F(A, B, C) = Σ m (3, 5, 6) P) A B C + A B C + A B C (ii) __P __ F(A, B, C) = Π M (0, 1, 2, 5, 6) Q) A B + A C + B C (iii) __U __ (A + B) (A + B + C) (B + C) R) B C D + A B D + A B D (iv) __R __ (B + C + D) + (A + B D) + A B D S) A B C + A B C + A B C (v) __S __ B (A + C) + C (A + B) T) A B C + A B D (vi) __T __ A B + C (D + A) U) A B C + A B + B C Z) None of the above Problem 2. (15 points) A. B. One possible solution: C C A B C F 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 1 1 1 1 0 C B B B A B F C A 00 01 11 10 A BC 0 0 1 1 1 1 0 1 0 1 F(A, B, C) = Σ m ( 1, 2, 3, 5, 6 ) F PU = B C + C (A + B) F(A, B, C) = Π M ( 0, 4, 7 ) F PD = (B + C) (C + A B)
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Unformatted text preview: (B + C) (C + A B) ECE 2030 -- Introduction to Computer Engineering EXAM #1 SOLUTION (version A) February 5, 2004 Page 2 of 2 Problem 3. (20 points) A. B. 00 01 11 10 CD AB 00 0 0 0 0 01 1 1 1 0 11 1 0 1 1 10 1 1 0 1 00 01 11 10 CD AB 00 0 0 0 0 01 1 1 1 0 11 1 0 1 1 10 1 1 1 00 01 11 10 CD AB 00 1 x 0 x 01 0 x 1 0 11 1 1 0 0 10 1 x 1 00 01 11 10 CD AB 00 1 x 0 x 01 0 x 1 0 11 1 1 0 0 10 1 x 1 Final SOP Final POS Final SOP Final POS A. F(A, B, C, D) = A D + A B C + A B C + B C D Number of essential prime implicants: 2 (first two in above expression) F(A, B, C, D) = (A + B) (B + C + D) (A + C + D) (A + B + C + D) Number of essential prime implicates: 4 B. F(A, B, C, D) = B D + A C + A B D F(A, B, C, D) = (B + D) (A + B + D) (A + B + C) Problem 4. (20 points) A. F = (A + C) (B + D E) + B C E # of gates: _1_ AND _1 _ OR _2 _ NAND _2 _ NOR _5 _ INVERTER B. G Z Y W X G = ( W X + X Y ) ( W + Y Z ) # of gates: __6 _ ANDs __5 _ INVERTERs...
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