Definition:Floating-Point Representation/Normalized

Definition

Let $x$ be a real number implemented in floating-point representation as:

$x = f \times \beta^e$

such that:

$x = \pm \sqbrk {0.f_1 f_2 \ldots f_t} \times \beta^e$

This representation is said to be normalized if and only if $f_1 \ne 0$.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): floating-point representation
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): normalized number
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): floating-point representation
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): normalized number