https://codereview.stackexchange.com/a/126849/93659

FPxToFloatClass.java

import java.io.InputStream;
import java.io.ByteArrayOutputStream;
import java.io.IOException;


class FPxToFloatClass
{
	/**
	 * Converts a series of bytes in an FP*-like format to a native floating-
	 * point type.
	 *
	 * @param bytes  A byte array containing an FP*-encoded number
	 * @param offset  The offset of the first byte of the encoded number
	 * @param size  The total amount of bytes used to encode the number
	 * @param integerits  The length of the integral part of the encoded number
	 *   in bits (little-endian); the remaining bits represent the fractional
	 *   part.
	 * @return  A number representing the encoded number in a native floating-
	 *   point type
	 */
	public static double FPxToFloat( byte[] bytes, int offset, int size,
		int integerBits )
	{
		if (offset < 0 || offset >= bytes.length)
			throw new ArrayIndexOutOfBoundsException("offset");
		if (size < 0 || size > bytes.length - offset)
			throw new ArrayIndexOutOfBoundsException("size");
		if ((long) integerBits - (long) size * Byte.SIZE < Integer.MIN_VALUE)
			throw new ArithmeticException("integerBits");

		double result = 0;
		int exponent = integerBits - Byte.SIZE;
		for (; offset < size; offset++, exponent -= Byte.SIZE) {
			result += Math.scalb(bytes[offset] & 0xFF, exponent);
		}
		return result;
	}


	public static void main( String[] args ) throws IOException {
		int integerBits = Integer.parseInt(args[0]);
		byte[] data = readAll(System.in);
		double f = FPxToFloat(data, 0, data.length, integerBits);
		System.out.println(f);
	}

	private static byte[] readAll( InputStream s ) throws IOException {
		byte[] buf1 = new byte[4 << 10];
		ByteArrayOutputStream buf2 = new ByteArrayOutputStream();
		int count;
		while ((count = s.read(buf1)) >= 0)
			buf2.write(buf1, 0, count);
		return buf2.toByteArray();
	}
}