3-M1-soln

3-M1-soln - Midterm 1 Solution ECE 25, Fall 2008 Thursday...

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a) Represent these numbers in 6-bit signed 2’s complement form or indicate that it is not possible. -1 111111 -7 111001 63 not possible -5 111011 34 not possible -32 100000 b) For each binary vector below, what does it represent in Octal and Hexadecimal? Binary Octal Hexadecimal 101111 57 2F 110000 60 30 011110 36 1E 1
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F ( A, B, C, D )= X m (1 , 6 , 7 , 10 , 11 , 12 , 13) d ( A, B, C, D X m (0 , 3 , 5 , 9 , 15) x x x 1 x 1 x 00 01 11 10 00 01 11 10 AB CD 1 1 1 1 1 a) Identify all the prime and essential prime implicants. Primes Essential Primes (including Essentials) Only —1 D 000- ¯ A ¯ B ¯ C 011- ¯ ABC X 110- AB ¯ C X 101- A ¯ BC X b) Find the minimum two-level logic implementation. F = ¯ ABC + AB ¯ C + 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. You can introduce new immediate equations for common sub-expressions if it helps to reduce the number of literals. Put a box around your Fnal answer, and indicate the number of literals in your Fnal answer. P =( ¯ A + ¯ B + ¯ C )( D + C + ¯ C ) ¯ A + ¯ B + ¯ C )( D +1) = ¯ A + ¯ B + ¯ C Q = ABC ¯ D + ABC ¯ E + ABC ¯ F = ABC ( ¯ D + ¯ E + ¯ F ) = ¯ P ¯ R R = ¯ BDEF + CDEF + DEF = ( ¯ B + C = S = A ¯ B ( ¯ A + B ) =0 T = +( ¯ A + ¯
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3-M1-soln - Midterm 1 Solution ECE 25, Fall 2008 Thursday...

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