The question is missing many details that are important for defining a floating point format. I'm going to try to answer the first part of the question filling in the missing information by assuming that everything unspecified follows the common rules for binary interchange formats in IEEE Std 754-2008 IEEE Standard for Floating-Point Arithmetic.
The given parameters for Format A, in terms of Table 3.3 in the standard, are k=8 and p=5 (italic letters are parameters in the standard, not the question).
From that, and the formula in the standard, bias = emax = 2**(k - p - 1) - 1 = 3.
Taking example bits 0 001 0011
The fraction is, in binary, 0011/10000, decimal 3/16 = 0.1875. The exponent bits are non-zero so it is a normal value, with a non-stored leading one bit, so the significand is 1.1875.
The exponent is, in binary, 001-011, decimal 1-3 = -2.
Multiply the signficand by 2**(-2) = 1/4, giving absolute value 0.296875. Since the sign bit is zero, the absolute value is the final value.
Answer from Patricia Shanahan on Stack OverflowVisibleEarth
h-schmidt.net › FloatConverter › IEEE754.html
IEEE-754 Floating Point Converter
This webpage is a tool to understand IEEE-754 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-754. As an example, try "0.1". The conversion is limited to 32-bit ...
Is there a way to convert numbers to 8-bit and 12-bit floating point representation?
Is there a way to convert numbers to 8-bit and... Learn more about floating point More on mathworks.com
3
0
August 20, 2016Eight-bit floating point
"Those Who Do Not Learn History Are Doomed To Repeat It " https://en.wikipedia.org/wiki/G.711 An 8 bit logarithmic encoding with a 14 bit dynamic range. This was standardized in 1972 when every logic gate counted so the hardware implementation of encoding and decoding must be very efficient. No infinities, but the extremes might be used for that, if necessary. There are two zeros so one of them could be used as NaN. Almost every phone call in the world is encoded this way, with the exception of some mobile calls that are compressed end-to-end with some other codec. More on reddit.com
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April 15, 2018Floating point on 8 bit computer
Ben's computer is Turing-complete, so in principle you can do floating point operations (you can do anything). That would be very inefficient though, because you probably need at least 16 bits to store a FP value. If you want this to be faster, you need a hardware acceleration - FP ALU. Depending on how you want to store FP values it would have different architecture, but general idea is similar to classic ALU. More on reddit.com
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July 15, 2019A calculator that does addition and multiplication with 8-bit numbers
All the ugly stuff behind the wall just converts binary values to decimal. The calculator itself is at the left of the wall.
Workshop link: https://steamcommunity.com/sharedfiles/filedetails/?id=1913537301
More on reddit.com 13
166
November 15, 2019Videos
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Binary Representation of Floating-Point Values - Mini-float 8-bit ...
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Converting an IEEE-754 Float To Decimal (in Scientific Notation) ...
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8 Bit Floating Point Representation with examples - YouTube
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IEEE 754 Floating Point Representation to its Decimal Equivalent ...
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Decimal to IEEE 754 Floating Point Representation - YouTube
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Floating Point Number Representation - Conversion Example - YouTube
Observable
observablehq.com › @benaubin › floating-point
Floating Point Calculator / Ben Aubin | Observable
April 28, 2023 - Calculate IEEE-754 style floating point numbers with arbitrary precision (`p`) and range (`q`). Enter as decimal aproximation, hex, or click to modify the binary digits Deconstructed Representation bias/min/max implementation details
Weitz
weitz.de › ieee
IEEE 754 Calculator - Edmund Weitz
Note that this is the new version of this calculator that was released in August 2023. The battle-tested old version from 2016 can be found here. If you find any deviations, please let me know! If you enter a floating-point number in one of the three boxes on the left and press the Enter key, you will see the number's bit pattern on the right.
Mc
sandbox.mc.edu › ~bennet › cs110 › flt › dtof.html
Decimal to Floating-Point Conversions
Convert decimal 1.7 to our 8-bit floating point format.
Baseconvert
baseconvert.com
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.
Mc
sandbox.mc.edu › ~bennet › cs110 › flt › ftod.html
Float to Decimal Conversion
Convert the 8-bit floating point number d3 (in hex) to decimal.
Exploring Binary
exploringbinary.com › home › decimal to floating-point converter
Decimal to Floating-Point Converter - Exploring Binary
June 1, 2018 - Essentially, you can enter what ... as a floating-point literal, except without any suffix (like ‘f’). Check the boxes for the IEEE precision you want; choose Double, Single, or both. (Double is the default.) Double means a 53-bit significand (less if subnormal) with an 11-bit exponent; Single means a 24-bit significand (less if subnormal) with an 8-bit ...
Evanw
evanw.github.io › 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.
Numeral-systems
numeral-systems.com › 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. Floating point numbers in the IEEE-754 representation have a fixed number of bits (usually 32 or 64).
Keepcalculator
keepcalculator.com › Convert-Number-to-Floating-Point-Calculator-8-Bit.php
Convert Number to Floating Point Calculator 8 Bit
Tips: Enter any decimal number to see its 8-bit floating point representation. The calculator will show the sign, exponent, and mantissa components, the binary representation, and the reconstructed value showing the precision loss.
Omni Calculator
omnicalculator.com › other › floating-point
Floating-Point Calculator
August 7, 2025 - If you want to convert the binary encoding of a floating-point number to the decimal number it represents, select floating-point to number at the top of the calculator. Then: Select the precision used. This determines how your binary representation will be interpreted. Enter the floating-point number's binary digits. You can enter the sign, exponent, and fraction separately, or you can enter the entire bit-string in one go — select your preference in the Bit input method dropdown menu.
Wikipedia
en.wikipedia.org › wiki › Minifloat
Minifloat - Wikipedia
2 days ago - To fix this problem, the machine learning industry has invented "microscaling formats" (MX), a kind of block floating-point. In a MX format, a group of 32 minifloats share an additional scaling factor represented by an "E8M0" minifloat (which is able to represent powers of 2 between 2−127 and 2127). MX has been defined for FP8-E5M2, FP8-E4M3, FP6-E3M2 (1.3.2), FP6-E2M3 (1.2.3), and FP4-E2M1. A minifloat in 1 byte (8 bits) with 1 sign bit, 4 exponent bits and 3 significand bits (1.4.3) is demonstrated here.
Ultimate Solver
ultimatesolver.com › en › ieee-754
Decimal number ↔ IEEE 754
With this converter you can convert a decimal number into a floating point number (IEEE) and vice versa.
Calculator Academy
calculator.academy › home › decimal to floating point calculator
Decimal To Floating Point Calculator - Calculator Academy
January 15, 2026 - Where F is the floating point number · s is the sign bit (0 for positive, 1 for negative) E is the exponent (8-bit binary with a bias of 127) M is the mantissa (23-bit binary value) To convert a decimal to floating point, the calculator computes the sign bit, exponent, and mantissa of the number.
Mason
mason.cc › float
IEEE-754 Floating Point Calculator - mason.cc
February 15, 2024 - IEEE-754 Float Converter/Calculator v2 · Built by Mason Hieb · Unlike many others online, this converter does not use any built-in programming language functions to produce its answer. Behind the scenes it recreates the pencil-and-paper method. Fixed and updated on February 15, 2024 · Additional thanks to Waltibaba for bug reporting! Big Endian Little Endian · 32-Bit (Single Precision) 64-Bit (Double Precision) Fractional Part Calculation
Cburch
cburch.com › books › float
Floating-point representation
Into the mantissa bits we place the bits following the decimal point of the scientific notation, 011. This gives us 0 1001 011 as the 8-bit representation of 5.5(10). We call this floating-point representation because the values of the mantissa bits “float” along with the decimal point, ...
Oletus
oletus.github.io › float16-simulator.js
Calculator that simulates floating-point numbers at the specified precision
This page implements a crude simulation of how floating-point calculations could be performed on a chip implementing n-bit floating point arithmetic. It does not model any specific chip, but rather just tries to comply to the OpenGL ES shading language spec.
Reddit
reddit.com › r/programming › eight-bit floating point
r/programming on Reddit: Eight-bit floating point
April 15, 2018 - At the 8-bit level I doubt you would bother with floating point calculations at all, just do all the math with 16 bit lookup tables.