hw1_soln_w2011

hw1_soln_w2011 - Homework #1Solutions ECE 15a Winter 2011...

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Homework #1Solutions ECE 15a Winter 2011 1. Do the following conversion problems: (5p) (a) Convert decimal 35.4377 to binary Soln: 35/2 = 17 + 1 17/2 = 8 + 1 8/2 = 4 + 0 4/2 = 2 + 0 2/2 = 1 + 0 1/2 = 0 + 1 (35) 10 = (100011) 2 .4377 x 2 = 0 + .8754 .8754 x 2 = 1 + .7508 .7508 x 2 = 1 + .5016 .5016 x 2 = 1 + .0032 .0032 x 2 = 0 + .0064 .0064 x 2 = 0 + .0128 .0128 x 2 = 0 + .0256 .0256 x 2 = 0 + .0512 (.4377) 10 = (.01110000) 2
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(35.4377) 10 = (100011.01110000) 2 (5p) (b) Calculate the binary equivalent of 1/3 out to 8 places. Then convert from binary to decimal. How close is the result to 1/3? 1/3 = 0.333 0.333 x 2 = 0 + 0.666 .666 x 2 = 1 + .332 .332 x 2 = 0 + .664 .664 x 2 = 1 + .328 .328 x 2 = 0 + .656 .656 x 2 = 1 + .312 .312 x 2 = 0 + .614 .614 x 2 = 1 + .228 Binary equivalent of (1/3) 10 = (0.01010101) 2 Binary to decimal: (0.01010101) 2 = (1/4 + 1/16 + 1/64 + 1/256) 10 = 85/256 = (0.33203125) 10 2. A computer has a word length of 8 bits, including sign. Obtain 1’s and 2’s complement of the following binary numbers. This problem may be interpreted in several ways: (1) The given numbers are in sign and magnitude representation, and (2) they are in 1’s or (3) in 2’s complement representation. (1) The given binary numbers are in sign and magnitude representation: 8 bit word (including sign) Base integer 1s Complement 2s Complement 1 1101010= -1101010 0 1101010 10010101 10010110 0 1111110= +1111110 0 1111110 01111110 01111110 0 0000001= +0000001 0 0000001 00000001 00000001 1 0000000= -0000000 0 0000000 11111111 00000000 0 0000000= +0000000 0 0000000 00000000 00000000 - Base integer is obtained by replacing the sign bit by 0
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- 1s complement is obtained by replacing the 0s to 1s and 1s to 0s in base integer if the sign bit of the 8 bit word is 1 - 2s complement is obtained by adding 1 to 1s complement if the sign bit of the 8 bit word is 1 (2) The given binary numbers are in 1’s complement representation: 8 bit word A (including sign) 1s complement Taking 1s complement of A allows us to 1
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hw1_soln_w2011 - Homework #1Solutions ECE 15a Winter 2011...

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