IEEE Floating-Point Standard

In essence, computers are integer machines and are capable of representing real numbers only by using complex codes. The most popular code for representing real numbers is called the IEEE Floating-Point Standard.

Here is a link to an IEEE 754 converter

IEEE 754 Standard

Sign, significand, exponent

More bits for significand gives more accuracy

More bits for exponent increases range

IEEE 754 floating point standard

Exponent is biased - Biased-127 for single precision and 1023 for double precision

All 0s is the smallest exponent; all 1s is largest

True exponent = biased-exponent – bias

Leading 1 bit of significand is implicit

Significand in the representation is the true significand without leftmost 1 (hidden bit)