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4-F-soln

# 4-F-soln - Final Exam Guide ECE 25 Spring 2008 Thursday...

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a) For each binary vector below, what does it represent as an Octal number and a Hexadecimal number? Binary Octal Hexadecimal 11010001 321 D1 00110011 063 (63 OK) 33 b) Given X and Y below that are 4-bit numbers in 2’s complement form, ±ll in the table of what S should be bit-vector form, whether or not there is an overﬂow ,andwhat S is as a number. (First row provides an example.) X Y S = X Y S as a x 3 x 2 x 1 x 0 y 3 y 2 y 1 y 0 s 3 s 2 s 1 s 0 Overﬂow? number 0111 0011 0100 No 4 0110 1110 1000(x) Yes 10(x) 0000 1111 0001 No 1 0111 0000 0111 No 7 1000 1100 1100 No -4 “x” means number is not valid (because an overﬂow has occurred), so doesn’t matter what they write down, just as long as they got the “overﬂow” part correct. 1

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Consider the logic diagram shown below. X XOR AND Y A B AND C D AND AND OR F a) The second block F ( A, B, C, D ) is a function of A , B , C ,and D . Please Fll out the following K-map by taking into consideration combinations of A and B that cannot occur as don’t cares because A and B are themselves functions of X and Y . 1 1 1 1 00 01 11 10 CD F 00 01 AB x x 1 x x 1 1 11 10 b) ±or the K-map derived in part (a) for F , specify all the primes and essential primes. Prime Essential --11 CD X --00 ¯ C ¯ D X 1100 AB 1-1- AC 1--0 A ¯ D c) ±ind the minimum two-level logic implementation for F . F = + ¯ C ¯ D + AC OR = + ¯ C ¯ D + A ¯ D 2
Consider the following Mealy state machine with A as the initial state. A B C 1/0 0/1 0/1 1/0 1/1 0/0 Figure 1: Mealy machine. If the input sequence is 011, then the corresponding output sequence, A 0 / 1 −→ B 1 / 0 C 1 / 1 A ,wou ld be 101 . a) What would be output sequence if the input sequence is 100? 011 , A A B A also OK.

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4-F-soln - Final Exam Guide ECE 25 Spring 2008 Thursday...

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