A simple applet for visualizing floating-point configurations (with customizable exponent and mantissa bit sizes) and converting between decimal, binary, and hexadecimal floating point representations.

• Kotlin 1.7+
• Moulton Scalable Menus version 1.15

A pre-compiled jar file is also available for download.

Enter the desired value in binary, hexadecimal, or decimal. After deselection (hit enter for quick submission after editing), the contents of all four fields will be updated to represent the same value.

Below is a brief description of each field:

• Binary: The floating point value represented in binary. Each of the three sections (sign, exponent, mantissa) are automatically separated by spaces.
• Hexadecimal: The floating point value represented in hexadecimal. A space is automatically inserted after every two bytes for increased readability.
• Decimal: The exact value in decimal represented by the binary and hexadecimal fields. Floating point representation cannot always exactly represent the value entered in the Pretty field. In these cases, the decimal field shows the closest approximation used.
• Pretty: An exact value in decimal. Unlike the decimal field, this will not be modified if the value cannot be exactly represented. It is very useful when comparing approximations between precision configurations or when comparing error from the true result.

A floating point number has three component parts: a sign bit, some exponent bit(s), and some mantissa bit(s). For example, FP32 uses 32 bits in total: 1 sign bit, 8 exponent bits, and 23 mantissa bits. The exact number of bits to use for exponent and mantissa sections can be selected by entering that value in the corresponding text box at the top left and right, respectively, of the applet. For convenience, the number of bits for exponent or mantissa sections can also be increased or decreased by one by clicking the corresponding up or down button.

When a precision section is edited, the binary, hexadecimal, and decimal value fields will update to match the approximate the value in the Pretty field with the new configuration.

There are three types of shortcut buttons: precision shortcuts, value modifier shortcuts, and value definition shortcuts.

The precision shortcuts are green buttons towards the top-left of the applet. Precision shortcuts set exponent and mantissa section sizes. FP16 uses 5 exponent bits and 10 mantissa bits, FP32 (float) uses 8 exponent bits and 23 mantissa bits, and FP64 (double) uses 11 exponent bits and 52 mantissa bits.

The value definition shortcuts are orange buttons towards the top-right of the applet. They are used to set between several interesting float values. Each shortcut is described briefly below:

• inf: the float representation of positive infinity
• -inf: the float representation of negative infinity
• nan: NaN (not a number). Used to represent the result of illogical computations, such as inf*0, inf/inf, or nan+1
• 0: the value zero. Note that floats can represent -0, which is equivalent despite its distinct representation. To get -0, negate 0.
• max: the maximum value which the float can represent before rounding up to infinity. To get min, negate max.
• int: the upper limit for exact integer representation. For example, in FP16, this value is 2048 since 2049 is the smallest positive integer which cannot be exactly represented. If there are not enough exponent bits in the precision configuration, this value may exceed max, meaning that all integers in the range [max, min] are exactly representable.
• dec: the upper limit for fractional value representation. For example, in FP16, this value is 1024 since 1023.5 is the largest value with a fractional component which can be exactly represented. Similarly to int, if there are not enough exponent bits in the precision configuration, this value may exceed max, meaning that all exactly representable numbers in the range [max, min] may have a fractional component.
• low: the smallest representable positive (excluding 0) number

The value modifier shortcuts are pink buttons towards the top-left of the applet. Instead of setting to an interesting value, they modify the current value. Each of the three buttons is described below:

• -/+: negates the current value in Pretty
• +1: increments the float value by 1 unit of least precision
• -1: decrements the float value by 1 unit of least precision