5-M1-soln

5-M1-soln - Midterm 1 ECE 25, Fall 2007 Thursday November 8...

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For each binary vector below, what does it represent if it is interpreted as a Decimal number in conventional binary form (positive only), a Decimal number in 2’s complement form (positive and negative), an Octal number, and a Hexadecimal number? Decimal conventional 2’s complement Binary form form Octal Hexadecimal 001111 15 15 17 0F (just “F” also OK) 100000 32 -32 40 20 111111 63 -1 77 3F 100110 38 -26 46 26 1
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F ( A, B, C, D )= X m (0 , 5 , 6 , 10 , 14 , 15) d ( A, B, C, D X m (2 , 4 , 8) Answer: 1 x 1 x x 1 1 1 1 00 01 11 10 00 01 11 10 AB CD a) Identify all the prime and essential prime implicants. Prime Essential −− 10 C ¯ D 0 0 ¯ B ¯ D 0 0 ¯ A ¯ D 111 ABC X 010 ¯ AB ¯ C X b) Find the minimum two-level logic implementation. F = ABC + ¯ AB ¯ C + C ¯ D + ¯ B ¯ D OR F = ABC + ¯ AB ¯ C + C ¯ D + ¯ A ¯ D OR F = ABC + ¯ AB ¯ C + ¯ B ¯ D + ¯ A ¯ D 2
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Given following logic equations, minimize the number of literals (e.g. by using common subexpres- sions, Boolean rules, etc). H = ¯ ABC ¯ E + ¯ ABCF J = ADE + AD ¯ F + ¯ BDE + ¯ BD ¯ F + ¯ CDE + ¯ CD ¯ F K = ¯ ABC ¯ EF + ¯ EFG + ¯ G L
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5-M1-soln - Midterm 1 ECE 25, Fall 2007 Thursday November 8...

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