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# 3-M1 - Midterm 1 ECE 25 Fall 2008 Thursday Oct 23 Name PID...

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1) Number representation (10 pts) a) Represent these numbers in 6-bit signed 2’s complement form or indicate that it is not possible. -1 -7 63 -5 34 -32 b) For each binary vector below, what does it represent in Octal and Hexadecimal? Binary Octal Hexadecimal 101111 110000 011110 1

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2) Two-level logic minimization (10 pts) F ( A, B, C, D ) = m (1 , 6 , 7 , 10 , 11 , 12 , 13) d ( A, B, C, D ) = m (0 , 3 , 5 , 9 , 15) 00 01 11 10 00 01 11 10 AB CD a) Identify all the prime and essential prime implicants. Primes Essential Primes (including Essentials) Only b) Find the minimum two-level logic implementation. F = 2
3) Multi-level logic minimization (10 pts) Given following logic equations, minimize the number of literals, e.g. by using common subexpres- sions, Boolean rules, etc. You can introduce new immediate equations for common sub-expressions if it helps to reduce the number of literals. Put a box around your final answer, and indicate the number of literals in your final answer. P = ( ¯ A + ¯ B + ¯ C )( D + C + ¯ C ) Q = ABC ¯ D + ABC

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