Assume the following representation for a floating point number 1 sign bit, 4 bi

Question

Assume the following representation for a floating point number 1 sign bit, 4 bits exponent, 4 bits for the significand, and a bias of 7 for the exponent (there is no implied 1 as in IEEE). a) What is the largest number (in binary) that can be stored? Estimate it in decimal. b) What is the smallest positive number( closest to 0) that can be stored in binary? Estimate it in decimal. c) Describe the steps for adding two floating point numbers. d) Describe the steps for multiplying two floating point numbers.

Explanation / Answer

a)

max exponent= 1111=15

in biased form =15-7=8

max significand=1111=(.9375)10

max value= 1.9375*28

b) min exp= 0000=0-7=-7(biased)

min value=1.0000*2(-7)

c) Addition : Suppose we want to add two floating point numbers, X and Y.

steps to add floating point numbers.

d) Multiplication :

Suppose you want to multiply two floating point numbers, X and Y.

steps to multiply floating point numbers.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.