Find the largest power of 2 which is smaller than your number, e.g if you start with x = 10.0 then 23 = 8, so the exponent is 3. The exponent is biased by 127 so this means the exponent will be represented as 127 + 3 = 130. The mantissa is then 10.0/8 = 1.25. The 1 is implicit so we just need to represent 0.25, which is 010 0000 0000 0000 0000 0000 when expressed as a 23 bit unsigned fractional quantity. The sign bit is 0 for positive. So we have:
s | exp [130] | mantissa [(1).25] |
0 | 100 0001 0 | 010 0000 0000 0000 0000 0000 |
0x41200000
You can test the representation with a simple C program, e.g.
#include <stdio.h>
typedef union
{
int i;
float f;
} U;
int main(void)
{
U u;
u.f = 10.0;
printf("%g = %#x\n", u.f, u.i);
return 0;
}
VisibleEarth
h-schmidt.net โบ FloatConverter โบ IEEE754.html
IEEE-754 Floating Point Converter
This page allows you to convert between the decimal representation of a number (like "1.02") and the binary format used by all modern CPUs (a.k.a. "IEEE 754 floating point").
Numeral-systems
numeral-systems.com โบ ieee-754-converter
IEEE-754 floating point numbers converter
This calculator can be used to convert decimal numbers to a binary floating point number in IEEE-754 format or vice versa.
binary - How do I convert from a decimal number to IEEE 754 single-precision floating-point format? - Stack Overflow
How would I go about manually changing a decimal (base 10) number into IEEE 754 single-precision floating-point format? I understand that there is three parts to it, a sign, an exponent, and a mant... More on stackoverflow.com
How do you convert from IEEE 754 Floating Point to decimal without using a calculator?
There arent any decimals in the IEEE 754 standard so you'll have to clarify what you mean. More on reddit.com
5
1
May 1, 2019microcontroller - IEEE-754 Floating Point Converter - Electrical Engineering Stack Exchange
I have in hexadecimal representation a IEEE-754 Floating Point: uint32_t _u_IEEE_754 = 0x41100000; //9.0 The decimal representation is: 9.0 I am working in C under embedded system. I want to get the More on electronics.stackexchange.com
How to convert string to IEEE 754 floating point format?
Doing this correctly is rather difficult. This article gives an overview over the complexity of the task and this article describes the most common algorithm used. Best would be to find an existing implementation and adapt that for your use case. More on reddit.com
1
3
December 3, 2018Videos
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Decimal to IEEE 754 Floating Point Representation - YouTube
Baseconvert
baseconvert.com โบ ieee-754-floating-point
IEEE 754 Floating Point Converter - Base Convert
Online number base converter for binary, hexadecimal, octal, decimal, roman numerals, balanced ternary, negabinary, factorial, bijective, and any radix. Supports high precision and fractional values.
Top answer 1 of 3
28
Find the largest power of 2 which is smaller than your number, e.g if you start with x = 10.0 then 23 = 8, so the exponent is 3. The exponent is biased by 127 so this means the exponent will be represented as 127 + 3 = 130. The mantissa is then 10.0/8 = 1.25. The 1 is implicit so we just need to represent 0.25, which is 010 0000 0000 0000 0000 0000 when expressed as a 23 bit unsigned fractional quantity. The sign bit is 0 for positive. So we have:
s | exp [130] | mantissa [(1).25] |
0 | 100 0001 0 | 010 0000 0000 0000 0000 0000 |
0x41200000
You can test the representation with a simple C program, e.g.
#include <stdio.h>
typedef union
{
int i;
float f;
} U;
int main(void)
{
U u;
u.f = 10.0;
printf("%g = %#x\n", u.f, u.i);
return 0;
}
2 of 3
12
Take a number 172.625.This number is Base10 format.
Convert this format is in base2 format For this, first convert 172 in to binary format
128 64 32 16 8 4 2 1
1 0 1 0 1 1 0 0
172=10101100
Convert 0.625 in to binary format
0.625*2=1.250 1
0.250*2=.50 0
0.50*2=1.0 1
0.625=101
Binary format of 172.625=10101100.101. This is in base2 format 10101100*2
Shifting this binary number
1.0101100*2 **7 Normalized
1.0101100 is mantissa
2 **7 is exponent
add exponent 127 7+127=134
convert 134 in to binary format
134=10000110
The number is positive so sign of the number 0
0 |10000110 |01011001010000000000000
Explanation: The high order of bit is the sign of the number. number is stored in a sign magnitude format. The exponent is stored in 8 bit field format biased by 127 to the exponent The digit to the right of the binary point stored in the low order of 23 bit. NOTE---This format is IEEE 32 bit floating point format
Wikihow
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How to Convert a Number from Decimal to IEEE 754 Floating Point Representation
December 15, 2025 - For the example, you can convert the 133 that you found in the last step into 10000101.[6] X Research source ... Determine the mantissa. The mantissa aspect, or the third part of the IEEE 754 conversion, is the rest of the number after the decimal of the base 2 scientific notation.
Cornell University
cs.cornell.edu โบ ~tomf โบ notes โบ cps104 โบ floating
Floating Point
This document explains the IEEE 754 floating-point standard. It explains the binary representation of these numbers, how to convert to decimal from floating point, how to convert from floating point to decimal, discusses special cases in floating point, and finally ends with some C code to ...
SourceForge
sourceforge.net โบ projects โบ calc754
IEEE-754 converter download | SourceForge.net
February 26, 2016 - This little tool decodes: (1) single, double and extended precision floating point numbers from their binary representation (both Little and Big-Endian) into their decimal exponential representation; (2) 16-byte GUIDs from their binary ...
Binary Convert
binaryconvert.com โบ convert_float.html
Float (IEEE754 Single precision 32-bit) Converter
Online binary converter. Supports all types of variables, including single and double precision IEEE754 numbers
Iastate
class.ece.iastate.edu โบ arun โบ cpre305 โบ ieee754 โบ ie5.html
IEEE 754 tutorial: Converting to IEEE 754 Form
Convert the following single-precision IEEE 754 number into a floating-point decimal value.
Christophervickery
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IEEE-754 Floating-Point Conversion from Floating-Point to Hexadecimal
From Decimal Floating-Point To 32-bit and 64-bit Hexadecimal Representations Along with Their Binary Equivalents ยท [ Convert IEEE-754 32-bit Hexadecimal Representations to Decimal Floating-Point Numbers. ] [ Convert IEEE-754 64-bit Hexadecimal Representations to Decimal Floating-Point Numbers.
Weitz
weitz.de โบ ieee
IEEE 754 Calculator
This is a little calculator intended to help you understand the IEEE 754 standard for floating-point computation. It is implemented in JavaScript (using the amazing VanillaJS framework) and should work with recent desktop versions of Firefox and Chrome. I haven't tested with other browsers.
Wikipedia
en.wikipedia.org โบ wiki โบ IEEE_754
IEEE 754 - Wikipedia
5 days ago - The original IEEE 754-1985 standard also had the concept of extended formats, but without any mandatory relation between emin and emax. For example, the Motorola 68881 80-bit format, where emin = โ emax, was a conforming extended format, but it became non-conforming in the 2008 revision. Interchange formats are intended for the exchange of floating-point data using a bit string of fixed length for a given format.
Evanw
evanw.github.io โบ float-toy
Float Toy
Click on a cell below to toggle bit values, or edit the hex or decimal values directly. Use this to build intuition for the IEEE floating-point format.
Christophervickery
christophervickery.com โบ babbage โบ IEEE-754 โบ IEEE-754.old โบ 32bit.html
IEEE-754 Floating-Point Conversion from 32-bit Hexadecimal to Floating-Point
From 32-bit Hexadecimal Representation To Decimal Floating-Point Along with the Equivalent 64-bit Hexadecimal and Binary Patterns ยท [ Convert IEEE-754 64-bit Hexadecimal Representations to Decimal Floating-Point Numbers. ] [ Convert Decimal Floating-Point Numbers to IEEE-754 Hexadecimal Representations.
Exploring Binary
exploringbinary.com โบ home โบ decimal to floating-point converter
Decimal to Floating-Point Converter - Exploring Binary
June 1, 2018 - A decimal to IEEE 754 binary floating-point converter, which produces correctly rounded single-precision and double-precision conversions.
Omni Calculator
omnicalculator.com โบ other โบ floating-point
Floating-Point Calculator
August 7, 2025 - The floating-point calculator converts the binary representation of 32-bit floating-point numbers into real numbers and back again according to the IEEE754 standard. It has handy features like conversion to hexadecimal representations, calculation ...
Emory
cs.emory.edu โบ ~cheung โบ Courses โบ 170 โบ Syllabus โบ 04 โบ IEEE-float โบ IEEE754.html
IEEE-754 Floating Point Converter
This page allows you to convert between the decimal representation of numbers (like "1.02") and the binary format used by all modern CPUs (IEEE 754 floating point).
Reddit
reddit.com โบ r/askmath โบ how do you convert from ieee 754 floating point to decimal without using a calculator?
r/askmath on Reddit: How do you convert from IEEE 754 Floating Point to decimal without using a calculator?
May 1, 2019 -
We aren't allowed calculators in my upcoming exam, but are also required to convert IEEE 754 Floating Points with long mantissas into decimal.
The lecture slides only show examples where it's easy to work out, but I've gotten to a point where I need to convert 0.0000010011101 into decimal and this is simply impossible without a new approach.
Top answer 1 of 2
1
There arent any decimals in the IEEE 754 standard so you'll have to clarify what you mean.
2 of 2
1
It's just a matter of multiplying each digit by 2n where n is the position of the digit (with 0 being before the decimal place, and n decreasing to the right). 0 ร 20 . 0 ร 2-1 0 ร 2-2 0 ร 2-3 0 ร 2-4 0 ร 2-5 1 ร 2-6 0 ร 2-7 0 ร 2-8 1 ร 2-9 1 ร 2-10 1 ร 2-11 0 ร 2-12 1 ร 2-13 Add those up.
Zipcores
zipcores.com โบ floating-point-to-fixed-point-converter.html
Floating-point to Fixed-point Converter
Key Design Features - 32-bit floating-point input - Signed fixed-point or integer output - Configurable word width (up to 32-bits) - Configurable fraction width (up to 23-bits) - IEEE 754 compliant - High-speed fully pipelined architecture - Only 2 clock-cycles of latency - FPGA clock rates of 300MHz+ - Low area footprint Applications - Floating-point pipelines and arithmetic units - Floating-point processors - Interfacing between float/fixed number systems View datasheet