IEEE Standard

IEEE - Institute of Electrical and Electronics Engineers

IEEE 754 Floating Point Standard

Also See Floating-Point Number System.

Two standards

1. IEEE Single Precision (32 bit)
2. IEEE Double Precision (64 bit)

From CS370: In implementation, the IEEE standards also reserve certain bit configurations for a few additional special numbers, including $0$, $\pm \infty$, and NaN (for Not a Number).

IEEE also slightly extends the range of available numbers near zero by allowing so-called denormalized or subnormal numbers.

CS370 does not consider these details in the course.

IEEE Floating-Point Standard

In the IEEE Floating-Point Standard, a numerical value is represented in three groups of bits:

1. sign (S)
2. exponent (E)
3. mantissa (M)

each (S, E, M) pattern uniquely identifies a numeric value according to the following formula: $Value=(-1{)}^S\ast 1.M\ast 2^{E-bias}$