Known Problem: if rounding produces a carry out of the mantissa bits, it fails to increment the exponent.

IEEE-754 Analysis

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Instructions

This page lets you examine the relationships among binary and decimal numbers and three number formats described by the IEEE-754-2008 floating-point standard. You can enter a numeric value in any one of five formats, and see all five corresponding values (Decimal, Normalized Binary, Binary32 (single precision), Binary64 (double precision), and Binary128 (quad precision), along with analyses of the binary structure of the floating-point formats.

You can create multiple analyzers so you can compare multiple values at the same time. Adding an analyzer will automatically hide these instructions. You can always toggle these instructions on/off using the Hide/Show Instructions button at the top of the page.

Input Formats

Keyboard Shortcuts

Keyboard shortcuts are under development. The following are available now:

The Esc key shows/hides these instructions. The Q key shows the FAQ. The Y key adds an analyzer.

Analyzer 1 supports the following keyboard shortcuts for selecting input elements.
Use the Ctrl key when typing:

Analyzer 1

Input Format
Rounding Mode
Value to analyze:

Syntax Entered: none

Decimal value: 0

Normalized binary value: 0

Binary32: --

Status Sign [1] Exponent [8] Significand [23]
--- - (-) -- (--) -- (--)

Binary64: --

Status Sign [1] Exponent [11] Significand [52]
--- - (-) -- (--) -- (--)

Binary128: --

Status Sign [1] Exponent [15] Significand [112]
--- - (-) -- (--) -- (--)