Convert the following number to IEEE single precision float

Convert the following number to IEEE single precision float point number. -8.546 E-7

Solution

The IEEE 754 single precision format is 32 bits, which are (from left to right):

    One bit for the sign;

  8 bits for the exponent and     23 bits for the mantissa/significand.

Converting the given number to decimal results -0.0000008546

Step 1: convert decimal number to binary by separating decimal point and fractional part

0.0000008546 = 0.11001010110011110101010 * 2^-21

Step 2: normalize binary

Step 3: exponent -21 + 127 = 106 = binary 1101010

Step 4: remove hidden digit from 0.11001010110011110101010 which is 11001010110011110101010

Step 5: Write down the 1+8+23 = 32 bits.

    -1 is negative - the sign bit is one:        1

    The next eight bits are the exponent:        01101010

    The next 23 bits are the mantissa:           11001010110011110101010

    Binary result (32 bits): 10110101011001010110011110101010

Step 6: 1011 0101 0110 0101 0110 0111 1010 1010

               B 5 6      5 6 7       A       A

Answer: -8.546E^-7 is 0xB56567AA in IEEE 754 single-precision format.