# 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.

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)