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

    Incomplete Apex “Question”

    1)Regard the largest solitary preciseness incomplete apex compute, 1.11…1 x 2127. What everyure occur the “gap” at that compute if you qualify the mold to embrace preciseness? DO NOT sift-canvass the largest embrace preciseness compute – right the largest solitary preciseness represented as a embrace mold.

    2)Now, regard the lowest solitary preciseness incomplete apex compute, 2-149. What everyure occur the “gap” at that compute if you qualify the mold to embrace preciseness? DO NOT sift-canvass the lowest embrace preciseness compute – right the largest solitary preciseness represented as a embrace mold.

    Expert Counterpart

     

    Solution:

    1)

    Before performance let’s sift-canvass embrace preciseness and how the expression, advocate, and Mantissa is categorized in it.

    So embrace preciseness is 64-bit incomplete apex and the details are loving below:

    So when largest solitary preciseness compute everyure be represented as embrace preciseness it everyure contemplate affect this,

    Sign Biased Advocate Mantissa
    0 10001111110 1111111111111111111111100000000000000000000000000000

    So the Bias ce embrace preciseness compute is +1023

    and Biased Advocate= Actual advocate+Bias= 127+1023= 1150 (int binary: 10001111110)

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

    2)

    So the lowest solitary preciseness compute 2^-149 everyure be represented as shown below:

    Sign Biased Advocate Mantissa
    0 01101101010 0000000000000000000000000000000000000000000000000000

    So the Bias ce embrace preciseness compute is +1023

    and Biased Advocate= Actual advocate+Bias= (-149)+1023= 874 (int binary 01101101010)