QUESTION 6 Convert the following the hexadecimal representation of the IEEE sing

Question

QUESTION 6

Convert the following the hexadecimal representation of the IEEE single precision format to a floating number: 0x42720000

First of all, convert 0x42720000 to a 32-bit binary number. 0100 0010 0111  0010 0000 0000 0000 0000.

The sign bit is   . (Either 0 or 1).

The biased exponent is a 8-bit binary number of  . (Fill in exactly 8 binary bits. NO spaces!)

The fraction is a sequence of 23 binary bits  xxxxxxxx000000000000000. What are the first 8 binary bits of the fraction? Answer

Based on your answers above, we can find out that  0x42720000 represents the (decimal) floating points number xy.z, where x, y and z are three decimal digits.

x= , y = , and z=

Explanation / Answer

0xC029800000000000

First of all, convert 0xC029800000000000 to a 64-bit binary number. 1100 0000 0010 1001 1000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000

The sign bit is 1

The biased exponent is a 11-bit binary number of 10000000010

The fraction is a sequence of 52 binary bits xxxxxxxx00000000000000000000000000000000000000000000. What are the first 8 binary bits of the fraction? Answer 10011000

Based on your answers above, we can find out that 0xC029800000000000 represents the (decimal) floating point number -wx.yz where w,x, y and z are decimal digits.

-1 2^(1026 - 1023) 1.1001100000000000000000000000000000000000000000000000

=> -1 2^(3) 1.1001100000000000000000000000000000000000000000000000

=> -12.75

w = 1, x= 2, y = 7, and z=5

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