Suppose there is a computer that stores real numbers in only 12 bits; the first

Question

Suppose there is a computer that stores real numbers in only 12 bits; the first bit is the sign bit, the next four bits are the exponent (with a bias of 7), and the remaining 7 bits are used for the mantissa (fractional part). Assume the fraction is normalized so that it is always between 0.5 and 1. a. What is the largest positive real number (base 10) which can be represented by this scheme? b. What is the expected round-off error in storing a number? c. How many digits of precision (base 10) would be expected? d. What is the purpose of the bias? e. What would the following real number be?

Explanation / Answer

a) Largest no. which can be represented by this scheme: 0 1111 1111111

Decimal value: 0.127*1015

b) 0.25 is the expected error.

c) 10 digits of precision.

d) Purpose of bias is to give an exponent power of 10.

e) 011001110100 = 0.116 * 1012

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