1-F-soln

# 1-F-soln - 1) Number representation (10 pts) a) Convert the...

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a) Convert the following binary numbers to unsigned decimal numbers (e.g., “1000” = 8): 100 4 0000000000000001 1 111111 63 101010 42 b) Convert the following numbers to a 5-bit 2’s complement binary representation (e.g. 3 = “00011” and 3 = “11101”): 9 01001 15 01111 16 10000 5 11011 c) Convert the following hexidecimal numbers to binary and octal (e.g. AA = “1010 1010” in binary or “252” in octal): hexidecimal binary octal FF 1111 1111 377 F0A2 1111 0000 1010 0010 170242 0F100 0000 1111 0001 0000 0000 0170400 100 0001 0000 0000 0400 For part c), leading 0’s can be omitted for binary (e.g. “1111 0001 0000 0000” instead of ‘0000 1111 0001 0000 0000” is ±ne) or octal (e.g. “170400” instead of “0170400” is ±ne). 2

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F ( A,B,C,D )= X m (0 , 3 , 6 , 8 , 9) d ( X m (11 , 12 , 15) 1 0 0 0 1 0 0 1 00 01 11 10 CD 00 01 AB x 0 1 1 x 0 x 0 11 10 All Primes 1 0 0 0 1 0 0 1 00 01 11 10 CD 00 01 AB x 0 1 1 x 0 x 0 10 Minimal Solution 1 1 0 0 0 1 0 0 1 00 01 11 10 CD 00 01 AB x 0 1 1 x 0 x 0 10 Minimal Solution 2 a) Identify all the prime and essential prime implicants. Prime Essential 1-00 A ¯ C ¯ D -000 ¯ B ¯ C ¯ D ¯ B ¯ C ¯ D 100- A ¯ B ¯ C 10-1 A ¯ BD 1-11 ACD -011 ¯ BCD ¯ 0110 ¯ ABC ¯ D ¯ ABC ¯ D b) Find the minimum two-level logic implementation. F = ¯ B ¯ C ¯ D + ¯ + ¯ ABC ¯ D + A ¯ B ¯ C OR = ¯ B ¯ C ¯ D + ¯ + ¯ ABC ¯ D + A ¯ 3
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.

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## This note was uploaded on 01/09/2012 for the course CSE 140 taught by Professor Rosing during the Spring '06 term at UCSD.

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1-F-soln - 1) Number representation (10 pts) a) Convert the...

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