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Dale - Computer Science Illuminated 109

Dale - Computer Science Illuminated 109 - the number a...

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82 Chapter 3 Data Representation a. How many positive integers can be represented? b. How many negative integers can be represented? c. Draw the number line showing the three smallest and largest positive numbers, the three smallest and largest negative numbers, and zero. 11. Use the number line on page 58 to calculate the following expressions, where A is 499999 and B is 3. a. A + B b. A B c. B + A d. B A 12. Use the formula for the ten’s complement to calculate the following numbers in the scheme described in on page 59. a. 35768 b. 35768 c. 4455 d. 12345 13. In calculating the ten’s complement in Exercise 12, did you have trouble borrowing from so many zeros? Such calculations are error prone. There is a trick that you can use that makes the calculation easier and thus less prone to errors: Subtract from all 9’s and then add 1. A number subtracted from all 9’s is called the nine’s complement of
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Unformatted text preview: the number. a. Prove that the nine’s complement of a number plus 1 is equal to the ten’s complement of the same number. b. Use the nine’s complement plus one to calculate the values in Exer-cise 12 b, c, and d. c. Which did you find easier to use, the direct calculation of the ten’s complement or the nine’s complement plus 1? Justify your answer. 14. Evaluate the following expressions, where A is 00110011 and B is 01010101 a. A + B b. A ± B c. B ± A d. ± B e. ± ( ± A) 15. Is the two’s complement of a number always a negative number? Explain. 16. The one’s complement of a number is analogous to the nine’s comple-ment of a decimal number. Use the scheme outlined in Exercise 13 to calculate the results of Exercise 14, using the one’s complement rather than the two’s complement....
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