Convert the binary number to scientific notation. This works the same way as converting a whole number, except, instead of a 10-based system, you are using a 2-based system. Example: the binary number 11001101 converts to 1.1001101 X 2 to the 7th.
Assign the single bit into the sign field. A "0" indicates the number is positive, and a "1" indicates a negative number. For the example, you will place a "0" in the sign field, because it is a positive number.
Add the binary number to represent the exponent in the exponent field. A value is added to the exponent to cover the full range of negative and positive numbers. A single precision floating point requires the addition of the number 127 to the exponent, while a double precision will add 1,023. In the example, the number to convert to binary is 127 + 7 = 134 for single, or 1,023 + 7 = 1,030 for double precision points. So, the binary number for a single precision point is 10000110, and for a double precision point is 10000000110.
Add the actual binary number into the mantissa field. There is one thing different about binary than any other number system: the first number is always a "1." No exception to this rule. So, the "1" at the beginning of the number is not added to the mantissa field; it is an already known value, without exception. You will add 10011010000000000000000 to the single precision floating point, and 1001101000000000000000000000000000000000000000000000 for a double precision. You add your number and add zeroes for the remaining number of bits in the mantissa field.
Place the numbers from the three fields together to create the floating point.
Single: 0 10000110 10011010000000000000000
Double: 0 10000000110 1001101000000000000000000000000000000000000000000000