IEEE 754 Data Representation Exam
Questions & Answers 2024/2025
Consider -54.625. How would you represent 54? Give the steps. - ANSWERSKeep dividing 54 by 2 until
you get to 0. write the remainders. In this case, it's 00110110. Remember to have 8 integers
Consider -54.625. How would you represent .625?Give the steps. - ANSWERSKeep multiplying the
decimal until you get to zero. Write down the 1 or the 0 on the left hand side of the decimal
Given you have the binary representation of an integer. i.e. 00110110.1010 How would you represent
this number in normalized form? - ANSWERSkeep moving the decimal point so that we have a 1 before
the decimal point. multiply how many time you moved the decimal point. if it was five times, you would
write "x 2^5"
Can zero be normalized? - ANSWERSno
What are the 3 components of normalized form? - ANSWERSFraction, exponent, and significand
Most CPU's conform to what standard? - ANSWERSIEEE Floating-Point Standard 754
What does IEEE Floating-Point Standard 754 allow? - ANSWERSthis standard allows single precision and
double precision formats
For single precision (32 bit) format, how many bits are used for the sign of the number, the exponent,
and for the fraction? - ANSWERS1 bit is used for the sign of the number. 8 bits are used for the exponent.
23 bits are used for the fraction
In single precision format, 23 bits are used for the fraction. Is the 1 before the binary point stored as
well? - ANSWERSNo. it is an implied 1.
Questions & Answers 2024/2025
Consider -54.625. How would you represent 54? Give the steps. - ANSWERSKeep dividing 54 by 2 until
you get to 0. write the remainders. In this case, it's 00110110. Remember to have 8 integers
Consider -54.625. How would you represent .625?Give the steps. - ANSWERSKeep multiplying the
decimal until you get to zero. Write down the 1 or the 0 on the left hand side of the decimal
Given you have the binary representation of an integer. i.e. 00110110.1010 How would you represent
this number in normalized form? - ANSWERSkeep moving the decimal point so that we have a 1 before
the decimal point. multiply how many time you moved the decimal point. if it was five times, you would
write "x 2^5"
Can zero be normalized? - ANSWERSno
What are the 3 components of normalized form? - ANSWERSFraction, exponent, and significand
Most CPU's conform to what standard? - ANSWERSIEEE Floating-Point Standard 754
What does IEEE Floating-Point Standard 754 allow? - ANSWERSthis standard allows single precision and
double precision formats
For single precision (32 bit) format, how many bits are used for the sign of the number, the exponent,
and for the fraction? - ANSWERS1 bit is used for the sign of the number. 8 bits are used for the exponent.
23 bits are used for the fraction
In single precision format, 23 bits are used for the fraction. Is the 1 before the binary point stored as
well? - ANSWERSNo. it is an implied 1.
