A. Convert the decimal number 19557 to floating point. Use the format SEEMMMM. A

Question

A. Convert the decimal number 19557 to floating point. Use the format SEEMMMM. All digits are decimal. The exponent is stored excess-40 (not excess-50). The implied decimal point is at the beginning of the mantissa. The sign is 1 for a positive number, 7 for a negative number. Hint: Note carefully the number of digits in the mantissa! B. What is the range of numbers that can be stored in this format? C. What is the floatiing point representation for -19557? D. What is the six-digit 10's complement representation for -19557? E. What is the floating point representation for 0.0000019557? Please show your work and how you come up with the anwers I wil rate lifesaver

Explanation / Answer

a) To convert the number 19557 (ten) to the specified format requires the following step. i) Recognize that the number is positive, so the sign digit will be a 1 as specified. ii) Shift the decimal point in the number so that it matches the specified format. In the given problem, the decimal point is to be located to the left of all significant digits, making the number: .19557 x 10^5 iii) Since this number has a greater level of precision than the specified format allows, the number must be rounded to the allowed four significant digits. It will be assumed that a round-to-nearest method is being used: .1956 x 10^5 iv) To find the value of the exponent field using and N-excess format, you must add N to the value of the given exponent. Therefore, the exponent field for this 40-excess number will be: 40 + 5 = 45 v) Now that all fields have been calculated, the number can be expressed: 1451956 b) To find the range of this floating point system, both the largest and the smallest positive numbers must be found. The largest possible exponent field is 99, yielding a true exponent of 99 - 40 = 59, and the largest possible mantissa is 9999. This converts to the number .9999 x 10^59, or in scientific notation, 9.999 x 10^58. The smallest possible exponent field is 0, yielding a true exponent of 0 - 40 = -40, and the smallest nonzero mantissa is 0001. This converts to the number .0001 x 10^-40, or in scientific notation, 1 x 10^-44. Since this system supports both positive and negative values, the range is: +/- 1 x 10^-44 to +/- 9.999 x 10^58. c) The floating point representation of -19557 is the same as 19557 as calculated earlier, but with a negative sign digit. In this system, the negative sign digit is 7, giving the number: 7451956 d) To find the 10's complement of a decimal number, first you subtract each individual digit from 9, and then add 1 to the final result, as follows: 0 -> 9 - 0 = 9 0 -> 9 - 0 = 9 1 -> 9 - 1 = 8 9 -> 9 - 9 = 0 5 -> 9 - 5 = 4 7 -> 9 - 7 = 2 Adding 1 to this gives the final answer: 998043 e) To convert the number 0.0000019557 (ten) to the specified format requires the following step. i) Recognize that the number is positive, so the sign digit will be a 1 as specified. ii) Shift the decimal point in the number so that it matches the specified format. In the given problem, the decimal point is to be located to the left of all significant digits, making the number: .19557 x 10^-5 iii) Since this number has a greater level of precision than the specified format allows, the number must be rounded to the allowed four significant digits. It will be assumed that a round-to-nearest method is being used: .1956 x 10^-5 iv) To find the value of the exponent field using and N-excess format, you must add N to the value of the given exponent. Therefore, the exponent field for this 40-excess number will be: 40 + (-5) = 35 v) Now that all fields have been calculated, the number can be expressed: 1351956

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