#1,087 – Representing Binary Floating Point Numbers Using Scientific Notation

We can represent decimal floating point numbers using scientific notation, using the form:

(where a and b are both decimal values).

We can also represent binary floating point numbers using scientific notation.  The basic form is:

(where a and b are both binary values).

Below is an example.  Assume that we have a binary floating point value of 101.101 (5.625 decimal).

If we have the binary value 1.01101, we need to shift the decimal point two places to the right to get our desired value of 101.101.  This is equivalent to multiplying by 4, or 2 raised to the power of 2.  We write the exponent in binary, so the power of 2 is written as “10”.