3. (a) A new binary finite precision floating point system is being developed. 100 bits (0...

 

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3. (a) A new binary finite precision floating point system is being developed. 100 bits (0 or 1) will be used. The sign will require 1 bit, the exponent 8 bits, and the mantissa 90 bits. The remaining bit will be used for special purposes, and the exponent range is -255 to +255. i. What is the smallest positive normalized floating point number? ii. What is the machine epsilon? (b) Explain whether or not 1+x> 1 in double precision floating point arithmetic, with Rounding to Nearest Rule, where (a) = 2-53, and (b) x = 2-53 +2-60 3. (a) A new binary finite precision floating point system is being developed. 100 bits (0 or 1) will be used. The sign will require 1 bit, the exponent 8 bits, and the mantissa 90 bits. The remaining bit will be used for special purposes, and the exponent range is -255 to +255. i. What is the smallest positive normalized floating point number? ii. What is the machine epsilon? (b) Explain whether or not 1+x> 1 in double precision floating point arithmetic, with Rounding to Nearest Rule, where (a) = 2-53, and (b) x = 2-53 +2-60