Convert the following the hexadecimal representation of the IEEE double precisio
ID: 3919711 • Letter: C
Question
Convert the following the hexadecimal representation of the IEEE double precision format to a double number: 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 (either 0 or 1)
The biased exponent is a 11-bit binary number of . (Fill in exactly 11 binary bits. NO spaces!)
The fraction is a sequence of 52 binary bits xxxxxxxx0000 0000000000000000000000000000000000000000. What are the first 8 binary bits of the fraction? Answer (Fill in exactly 8 binary bits. NO spaces!)
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.
w = , x= , y = , and
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