3-F-soln

3-F-soln - 1) Two-level logic minimization (10 pts) Suppose...

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Suppose G ( A, B, C, D )= X m (1 , 3 , 4 , 6 , 9 , 11 , 14 , 15) and suppose F ( A, B, C, D ¯ G 1 0 0 1 1 1 1 0 0 1 1 0 0 0 0 1 00 01 11 10 00 01 11 10 A B C D a) Identify all the prime and essential prime implicants for the function F (not G). Primes Essential Primes (including Essentials) Only -0-0 ¯ B ¯ D ¯ B ¯ D 01-1 ¯ ABD ¯ ABD 110- AB ¯ C -101 B ¯ CD 1-00 A ¯ C ¯ D b) Find the minimum two-level logic implementation for the function F (again not G). F = ¯ B ¯ D + ¯ ABD + AB ¯ C (SHOULD JUST BE ONE SOLUTION) 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. (Use only AND, OR, or INVERT operators in the Boolean expressions.) X = ABC Y = DEF P = ABCDEF + ABCGH + ABCG ¯ H = ABC ( + GH + G ¯ H ) = ABC ( + G ) = X ( Y + G ) Q = ABC ¯ D + ABC ¯ E + ABC ¯ F + ¯ ADEF + ¯ BDEF + ¯ CDEF = ABC ( ¯ D + ¯ E + ¯ F )+ ( ¯ A + ¯ B + ¯ C ) = X ¯ Y + ¯ XY R = AEF G + ¯ E + ¯ F = AG + ¯ E + ¯ F 17 literals 3
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a) Represent these numbers in 7-bit signed 2’s complement form or indicate that it is not possible.
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3-F-soln - 1) Two-level logic minimization (10 pts) Suppose...

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