(1 - SRT(0.5))

using System.Numerics;

var w = BinaryIntegerFunctions.ComputeMagicConstant<ushort>();
Console.WriteLine($"{w} {Convert.ToString((long)w, 2)}");
var x = BinaryIntegerFunctions.ComputeMagicConstant<uint>();
Console.WriteLine($"{x} {Convert.ToString(x, 2)}");
var y = BinaryIntegerFunctions.ComputeMagicConstant<ulong>();
Console.WriteLine($"{y} {Convert.ToString((long)y, 2)}");
var z = BinaryIntegerFunctions.ComputeMagicConstant<UInt128>();
Console.WriteLine($"{z} {Convert.ToString((long)z, 2)}");

public static class BinaryIntegerConstants<T> where T : IBinaryInteger<T>
{
    public static T Size { get; }

    static BinaryIntegerConstants() {
        var size = T.PopCount(value: T.AllBitsSet);

        Size = size;
    }
}
public static class BinaryIntegerFunctions
{
    public static T ComputeMagicConstant<T>() where T : IBinaryInteger<T> {
        var @base = (T.One << 8);
        var limit = (T.One << 1);
        var power = T.Zero;
        var size = uint.CreateChecked(value: ((BinaryIntegerConstants<T>.Size >> 4) + T.One));
        var result = T.Zero;

        for (var i = 0U; (i < size); ++i) {
            limit *= @base.Exponentiate(exponent: (T.One << 1));
            power *= @base.Exponentiate(exponent: (T.One << 1));
            result *= @base;

            while ((power + (result << 1) + T.One) <= limit) {
                power += ((result << 1) + T.One);
                result += T.One;
            }
        }

        return (result / @base);
    }
    public static T Exponentiate<T>(this T value, T exponent) where T : IBinaryInteger<T> {
        var result = T.One;

        do {
            if (T.IsOddInteger(value: exponent)) {
                result *= value;
            }

            exponent >>= 1;
            value *= value;
        } while (T.Zero < exponent);

        return result;
    }
}

/*
    Expected output:

    255 11111111 <-- WRONG!
    19195 100101011111011
    1257966796 1001010111110110000110011001100
    5402926248376769403 100101011111011000011001100110000000110001000011001101101111011
 */