The value -20.75 is to be stored in the IEEE 754 single precision format. Answer

Question

The value -20.75 is to be stored in the IEEE 754 single precision format. Answer the following questions about the conversion.

a. What is the value of the sign bit? ---------------------

b. What is the value of the exponent before biasing? Give your answer in the correct number of bits?. ----------------

c. What is the value of the exponent after biasing? Give your answer in the correct number of bits. ---------------------

d. What is the value of the significand? Give your answer in the fewest number of bits. ------------------------

e. What is the value of the fraction? Give your answer in the fewest number of bits and no leading 0 or binary point. ----------------------------

Explanation / Answer

a) 1

sign bit is MSB it is 0 if sign is positive it is 1 if neagitive

b) 00000100

before baising the exponent is 4=100 because exponent is 24

c) 10000011

after baising 4+127=131=10000011

d) 2490368 1001100000000000000000

significard or matinssa is 2490368 just refer the point "The mantissa (also known as significand or fraction) is stored in bits 1-23. An invisible leading bit (i.e. it is not actually stored) with value 1.0 is placed in front, then bit 23 has a value of 1/2, bit 22 has value 1/4 etc. As a result, the mantissa has a value between 1.0 and 2. If the exponent reaches -127 (binary 00000000), the leading 1 is no longer used to enable gradual underflow."

e) 296875 1001000011110101011

fraction part is remaining value after the exponent i.e 1.296875 it can be writtenby removing 1.0 as 1001000011110101011

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