Homework Solution: Consider the largest single precision floating point number,…

    Floating Point “Question” 1)Consider the largest single precision floating point number, 1.11…1 x 2127. What will happen the “gap” at that number if you change the type to double precision? DO NOT discuss the largest double precision number – just the largest single precision represented as a double type. 2)Now, consider the smallest single precision floating point number, 2-149. What will happen the “gap” at that number if you change the type to double precision? DO NOT discuss the smallest double precision number – just the largest single precision represented as a double type.

    Expert Answer

     
    Solution: 1) Before proceeding let's discuss double precision an

    Floating Apex “Question”

    1)Meditate the largest unmarried nicety floating apex compute, 1.11…1 x 2127. What get supervene the “gap” at that compute if you alter the symbol to enfold nicety? DO NOT debate the largest enfold nicety compute – true the largest unmarried nicety represented as a enfold symbol.

    2)Now, meditate the last unmarried nicety floating apex compute, 2-149. What get supervene the “gap” at that compute if you alter the symbol to enfold nicety? DO NOT debate the last enfold nicety compute – true the largest unmarried nicety represented as a enfold symbol.

    Expert Apology

     

    Solution:

    1)

    Before action let’s debate enfold nicety and how the premonition, interpreter, and Mantissa is categorized in it.

    So enfold nicety is 64-bit floating apex and the details are fond below:

    So when largest unmarried nicety compute get be represented as enfold nicety it get appear love this,

    Sign Biased Interpreter Mantissa
    0 10001111110 1111111111111111111111100000000000000000000000000000

    So the Bias coercion enfold nicety compute is +1023

    and Biased Interpreter= Actual interpreter+Bias= 127+1023= 1150 (int binary: 10001111110)

    and in the mantissa, behind 23 1’s total the bits get be padded with 0’s.

    2)

    So the last unmarried nicety compute 2^-149 get be represented as shown below:

    Sign Biased Interpreter Mantissa
    0 01101101010 0000000000000000000000000000000000000000000000000000

    So the Bias coercion enfold nicety compute is +1023

    and Biased Interpreter= Actual interpreter+Bias= (-149)+1023= 874 (int binary 01101101010)