Floating Point Numbers
The most popular encoding format format for representing real numbers in a computer readable format is called floating point representation. Numbers with decimal points are referred to as floating point numbers in the computing world. The rules that guide the formating of these numbers are written in the IEEE Floating-Point Standard.
Since computers read only
0's at the lowest level (the circuit boards), computers need a way to represent numbers in a binary format (
0's). Floating point representation is a way to do this. Floating point representation adapts scientific notation to represent numbers in binary.
Here is an example of the number
150,000 in scientific notation:
1.5 x 105
While keeping the same form, floating point takes scientic notation and translates it to a binary form:
s × 10e *s = significand *e = exponent
In the example above,
s is the binary equivalent to the significand and
e is the binary equivalent of the exponent.
s can be a binary integer, fraction,
or mixed number and
e can be any binary integer.
To get that original scientific notation number into one long string of binary numbers, a certain format is required. The final binary number will have a single bit represent the sign of the number, a set number of bits to determine the significand, and a set number of bits to represent the exponent. The final result is one long string of
0's (a binary number).