1-M1-soln

# 1-M1-soln - Midterm 1 Solutions ECE 25 Fall 2010 Tuesday...

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Given X and Y below that are 5-bit numbers in 2’s complement form, ﬁll in the table of what S should be as a 5-bit number in 2’s complement 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 resu ltsinanoverﬂow , then just put an “x” under the S column). Also, in the last two columns, specify how the binary vector of X should be interpreted as an Octal number and a Hexadecimal number, respectively? (First two rows provide examples.) X Y S = X + Y S in 2’s X in X in 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? complement Octal Hexadecimal 11101 10001 01110 yes x 35 1D 00001 00111 01000 no 8 01 01 00111 01001 10000 yes x 07 07 00111 10111 11110 no -2 07 07 11001 10111 10000 no -16 31 19 11001 01001 00010 no 2 31 19 Note: X = 11001 is the same for the last two rows. Hence X in Octal should be the same for the last two rows as well. Same with X in Hexadecimal. 1

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F ( A, B, C, D )= ± m (0 , 1 , 5 , 6 , 7 , 8 , 12 , 13 , 15) d ( A, B, C, D ± m (3 , 10 , 11) ± ± ± [ ± ± ²² ²± ±± ±² &' ) ²² ²± \$% ± ± ± ± [ [ ±± ±² \$OO 3ULPHV ± ±
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1-M1-soln - Midterm 1 Solutions ECE 25 Fall 2010 Tuesday...

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