4-M1-soln

4-M1-soln - Midterm 1 ECE 25 Spring 2008 Tuesday April 29...

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Midterm 1 ECE 25, Spring 2008 Tuesday April 29 Name: PID: Problem Points Score 1 15 2 10 3 10 4 10 Total 45 a) Given X and Y below that are 4-bit numbers in 2’s complement form, ﬁll 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 (7) 0011 (3) 0100 No 4 1000 (-8) 0010 (2) x Yes -10(x) 1111 (-1) 1010 (-6) 0101 No 5 0110 (6) 1011 (-5) x 11(x) 0000 (0) 0001 (1) 1111 No -1 0101 (5) 0111 (7) 1110 No -2 “x” means number is not valid (because an overﬂow has occurred). b) For each binary vector below, what does it represent as an Octal number and a Hexadecimal number? Binary Octal Hexadecimal 000111 07 07 101001 51 29 100100 44 24 1

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Consider the following 16-bit adder design that adds the numbers F = X + Y + Z .A s sum e 1ns gate delay for all gates (i.e., 2-XOR, 2-AND, and 2-OR). D 16 D 15 X 15 Y 15 D 14 X 14 Y 14 D 1 X 1 Y 1 D 0 X 0 Y 0 D 2 E 16 E 15 F 15 Z 15 E 14 F 14 Z 14 E 1 F 1 Z 1 E 0 F 0 Z 0 E 2 Th elog i cfo rea chb i t s l i c e( r e c t -
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4-M1-soln - Midterm 1 ECE 25 Spring 2008 Tuesday April 29...

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