# Binary and hex calculator

This webpage is a tool to understand IEEE floating point numbers. This is the format in which almost all CPUs represent non-integer numbers. As this format is using base-2, there can be surprising differences in what numbers can be represented easily in decimal and which numbers can be represented in IEEE As an example, try "0.

The conversion is limited to bit single precision numbers, while the IEEEStandard contains formats with increased precision. You can either convert a number by choosing its binary representation in the button-bar, the other fields will be updated immediately. Or you can enter a binary number, a hexnumber or the decimal representation into the corresponding textfield and press return to update the other fields. To make it easier to spot eventual rounding errors, the selected float number is displayed after conversion to double precision.

Please note there are two kinds of zero: The sign is stored in bit The exponent can be computed from bits by subtracting The mantissa also known as significand or fraction is stored in bits An invisible leading bit i.

As a result, the mantissa has a value between 1. If the exponent reaches binary , the leading 1 is no longer used to enable gradual underflow. The below steps may useful to know how to perform hex to binary number conversion. Separate the digits of the given hexadecimal, if more than 1 digit. Find the equivalent binary number for each digit of hex number, add 0's to the left if any of the binary equivalent is shorter than 4 bits. Write the all groups binary numbers together, maintaining the same group order provides the equivalent binary for the given hexadecimal.

Solved Example Problem The below solved example problem may useful to understand how to perform hex to binary number conversion.

Problem Convert the hexadecimal 9DB. A5 16 to its binary equivalent. Numbers Conversion Table Decimal Binary Octal Hex 0 0 0 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 10 8 9 11 9 10 12 A 11 13 B 12 14 C 13 15 D 14 16 E 15 17 F. Don't confuse this with true hexadecimal floating point values in the style of 0xab.

This source code for this converter doesn't contain any low level conversion routines. The conversion between a floating point number i. The conversion between a string containing the textual form of a floating point number e.

If you need to write such a routine yourself, you should have a look at the sourecode of a standard C library e. GNU libc, uclibc or the FreeBSD C library - please have a look at the licenses before copying the code - be aware, these conversions can be complicated.

This page relies on existing conversion routines, so formats not usually supported in standard libraries cannot be supported with reasonable effort. Double-precision bit floats would work, but this too is some work to support alongside single precision floats.

As the primary purpose of this site is to support people learning about these formats, supporting other formats is not really a priority. Your converter is wrong! The conversion routines are pretty accurate see above. Until now, checking the results always proved the other conversion less accurate. First, consider what "correct" means in this context - unless the conversion has no rounding error, there are two reasonable results, one slightly smaller the entered value and one slightly bigger.

The best result is usually the one closer to the value that was entered, so you should check for that. Please check the actual represented value second text line and compare the difference to the expected decimal value while toggling the last bits.