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copied!<p>You want to convert 32 bit floats to 16 bit integers with scaling. However, the example you give uses a decimal scaling and not a binary. I'm unsure if you want to keep working in the binary domain on a system without a floating point unit or if you actually want to convert to decimal representation of the number.</p> <p>Here I assume that your challenge is that you don't have access to floating point instructions. You haven't specified a programming language so I decided to code some stuff in C#. The language is easy to use but perhaps not the most suited for bit fiddling. You may find it easier and more efficient to implement this in say C or C++.</p> <p>As I'm going to keep using a binary representation the scale cannot be a number like 10 or 100 (an integral power of 10) but instead has to be an integral power of 2. Below is a class to take an IEEE 754 binary32 floating point number apart.</p> <pre><code>class Ieee754Binary32 { public Ieee754Binary32(Single value) { using (var memoryStream = new MemoryStream()) { var binaryWriter = new BinaryWriter(memoryStream); binaryWriter.Write(value); memoryStream.Seek(0, SeekOrigin.Begin); var binaryReader = new BinaryReader(memoryStream); var bits = binaryReader.ReadInt32(); Fraction = bits & 0x7FFFFF; Exponent = ((bits >> 23) & 0xFF) - 127; Sign = (bits & 80000000) == 1 ? -1 : 1; } } public Int32 Fraction { get; private set; } public Int32 Exponent { get; private set; } public Int32 Sign { get; private set; } public Int16 ToScaledInt16(Int32 scaling) { if (Exponent == -127 && Fraction == 0) return 0; var mantissa = 0x8000 | (Fraction >> 8); var unscaledInt32 = Exponent >= 0 ? mantissa << Exponent : mantissa >> -Exponent; var scaledInt16 = unscaledInt32 >> (15 - scaling); return (Int16) (Sign*scaledInt16); } } </code></pre> <p>The method <code>ToScaledInt16</code> is what you want to use. If you want to express numbers using fractions of 8 you should supply the value <code>3</code> for <code>scaling</code>. All number will be multiplied by <code>2^3 = 8</code>, e.g. 0.125 = 1/8 is converted to 1, 0.25 = 2/8 to 2 etc.</p> <p>The code does not handle more complex stuff like rounding, NaN or overflow but perhaps you can use it as a starting point?</p>

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