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ch 2EC262_Marcovitz_Ch2_Solutions_Fall2011

# ch 2EC262_Marcovitz_Ch2_Solutions_Fall2011 - EC262 Digital...

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1 EC262 Digital Systems Fall 2011 Chapter 2 Solutions Textbook: Marcovitz, Introduction to Logic Design , 3 rd ed. Exercise 2 (e and f), Exercise 3(b), Exercise 5 ( a and c), Exercise 8 ( b, e and h), Exercise 9 ( a and b), Exercise 10 (a and b), Exercise 11 (a and c), Exercise 12 (b and c), Exercise 13, Exercise 17, Exercise 18 (b, c and d), Exercise 19 (a, b and c), Exercise 21 (a), Exercise 22 (b) and Exercise 26 (b). Exercise 2 : Show truth tables. e. A system has one output, F , and four inputs, ABCD . ( A,B ) represents one 2-bit unsigned binary number and ( C,D ) represents another 2-bit unsigned binary number. F is to be 1 iff the sum of the two numbers is odd. A B Dec (AB) C D Dec (CD) F 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 1 2 3 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 f. A system has one output, F , and four inputs, ABCD . ( A,B ) represents one 2-bit unsigned binary number in the range 0 to 2 (3 is not used) and ( C,D ) represents another 2-bit unsigned binary number in the same range. F is to be 1 iff the two numbers do not differ by more than 1. A B Dec (AB) C D Dec (CD) F 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 1 2 - 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 2 - 0 1 2 - 0 1 2 - 0 1 2 - 1 1 0 X 1 1 1 X 0 1 1 X X X X X

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2 Exercise 3 : Show a block diagram of a circuit using AND and OR gates. b. P8a: a(b +c) = ab + ac. Exercise 5 : Using truth tables to determine which expressions in each of the groups are equal. a. f = ac' + a' c + bc and g = (a + c) (a' + b + c') a b c ac' a' c bc f (a + c) (a' + b + c') g 0 0 0 0 1 1 1 1 0 0 1 1 0 0 1 1 0 1 0 1 0 1 0 1 0 0 0 0 1 0 1 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1 0 1 1 f = g c. f = ab + ac + a'bd and g = bd + ab'c + abd' a b c d ab ac a'bd f bd ab'c abd' g 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1
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