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# 2-M1 - Midterm 1 ECE 25 Fall 2009 Tuesday October 27 Name...

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1) Number representation (15 pts) a) For each binary vector below, what does it represent as an Octal number and a Hexadecimal number? Binary Octal Hexadecimal 10110011 01111100 11111111 b) Given X and Y below that are 5-bit numbers in 2’s complement form, fill in the table of what S should be bit-vector form ( even if the result causes an overﬂow ). Indicate whether or not there is an overﬂow and what S is as a number (if S results in an overﬂow, then just put an ”x” under the S column). (First two rows provide examples.) X Y S = X Y S as a x 4 x 3 x 2 x 1 x 0 y 4 y 3 y 2 y 1 y 0 s 4 s 3 s 2 s 1 s 0 Overﬂow? number 11101 00011 11010 no -6 00001 00111 11010 no -6 01000 10010 10111 10111 10111 01011 01100 00101 10101 10111 1

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2) 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

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