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HW5-sol - CSE 341 Computer Organization Spring 2011...

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1 CSE 341: Computer Organization Spring 2011 Solution to HW #5 [Note: At the end, I have included the procedure to convert a decimal fraction to binary.]
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2 Notes: 1) In Problem a) above, you may have used the number as -1278 X 10^3. Always, convert the given number to binary, normalize and round it and test for overflows/underflows before going to the next step. 2) In Problem a) above, the sum is incorrect. When you add the two numbers, the G bit for the sum is 0 and R bit is 1. So, you round it down. The final answer is correct.
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3 Help with converting fractional decimal number to binary representation. This material is taken from: http://cs.furman.edu/digitaldomain/more/ch6/dec_frac_to_bin.htm . The source is being acknowledged for making this available to all. Converting Decimal Fractions to Binary In the text proper, we saw how to convert the decimal number 14.75 to a binary representation. In this instance, we "eyeballed" the fractional part of the binary expansion; 3/4 is obviously 1/2 + 1/4. While this worked for this particular example, we'll need a more systematic approach for less obvious cases. In fact, there is a simple, step-by-step method for computing the binary expansion on the right-hand side of the point. We will illustrate the method by converting the decimal value .625 to a binary representation..
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