Let x 45 In the double precision IEEE representation what a

Let x = 4/5. In the double precision IEEE representation, what are the two nearest machine numbers to x? What are the exact relative errors of each of these two nearest machine numbers?

Solution

3.x =4/5 = 0.8

3.1

x= 0.8 in double precision IEEE representation is

sign 1bit

Exponent 11 bits

fraction 52 bits..

S         Exponent                     Fraction

0 0111111 1110          1001 10011001 10011001 10011001 10011001 10011001 10011010

The nearest machine can be ubtained by changing the list significant bit...

1)

S         Exponent                     Fraction

0 0111111 1110          1001 10011001 10011001 10011001 10011001 10011001 10011001

2)

S         Exponent                     Fraction

0 0111111 1110          1001 10011001 10011001 10011001 10011001 10011001 10011011

3.2

the relative error between original number and first nearest number is last two significant bits...

second number and original number is last significant bit..