Question

3. IEEE Floating Point Representation

What decimal number does the 32-bit IEEE floating point number 0xC27F0000 represent? Fill in the requested information in the blanks below. What is the sign of the number (say positive or negative): What is the exponent in decimal format: What is the significand in binary: What is the value of the stored decimal number in decimal (final answer): Credit will be given for your final answer in the blanks and the work shown below.

Answer 1

The 32 bit IEEE floating point number can be divided as follows

After converting the floating point to binary,the below division is performed.

The binary conversion of 0xC27F0000 is 11000010011111110000000000000000.

1. First bit represents the sign - 0 means positive and 1 means negative. here it is 1 so its negative
2. The next 8 bits are the exponent - 10000100 -  The exponent can be computed from bits 24-31 by subtracting 127. 10000100 - 132. So 132 - 127 = 5. So it will be 2^5
3. 11111110000000000000000 - This is called the Mantissa. An invisible leading bit (i.e. it is not actually stored) with value 1.0 is placed in front, then bit 23 has a value of 1/2, bit 22 has value 1/4 etc. As a result, the mantissa has a value between 1.0 and 2. So that means it will be 1.0 + 0.5 + .25 + .125 + .0625 + .03125 + .015625 + .0078125 = 1.9921875

So the Decimal number will be 1.9921875 * 2 ^ 5 = 63.75. Since the sign bit is -ve the final decimal number is -63.75.