As a practical matter the first flag should have a value of one and not zero. The idea of a bit map is to have each value map to a unique bit. Since zero and one use the same bit (2^0) starting with zero will prevent both values from being represented at the same time. The enum shown below will allow all values to be represented when DayOfTheWeek value of 127.
[Flags]
public enum DayOfTheWeek
{
Sunday = 1,
Monday = 2,
Tuesday = 4,
Wednesday = 8,
Thursday = 16,
Friday = 32,
Saturday = 64
}
for( int val = 0; val <= 127; val++ )
Console.WriteLine( "{0,3} - {1}",
val, ( (DayOfTheWeek)val ).ToString( ) );