Bitwise operation to get the weekday name
days_name? Shouldn't that rather be day_names? Actually, given its function it should probably be weekdays
Shouldn't "sar" be "sat" for Saturday? Never seen it abbreviated "sar"
The opposite of "all" is "none" - not "no"
Day names are capitalized in English, so "Mon", "Tue", "Wed", etc.
You rarely need to create an array and then push items to it. It's easier to simply filter a complete array. But if you do need to create an empty array, just use [] - no need for Array.new


Sticking close to your current code, I'd do this

def weekdays(hex)
  value = hex.to_i(16)
  case value
  when 127
    'All'
  when 0
    'None'
  else
    days = %w(Mon Tue Wed Thu Fri Sat Sun)
    days.each_with_index.select { |_, i| value &amp; 2**i &gt; 0 }.map(&amp;:first).join(" ")
  end
end


However, I'd probably prefer a method that simply returns an array of day names, rather than a string. Then let other code check and join the array as needed.

Something like this

def weekdays(hex)
  value = hex.to_i(16)
  days = %w(Mon Tue Wed Thu Fri Sat Sun)
  days.each_with_index.select { |_, i| value &amp; 2**i &gt; 0 }.map(&amp;:first)
end




Update: As tokland points out in the comments, it'd be cleaner to use map.with_index plus compact, rather than each_with_index.select plus map. I.e.

def weekdays(hex)
  value = hex.to_i(16)
  days = %w(Mon Tue Wed Thu Fri Sat Sun)
  days.map.with_index { |day, i| day if value &amp; 2**i &gt; 0 }.compact
end


or, for the first code block

def weekdays(hex)
  value = hex.to_i(16)
  case value
  when 127
    'All'
  when 0
    'None'
  else
    days = %w(Mon Tue Wed Thu Fri Sat Sun)
    days.map.with_index { |day, i| day if value &amp; 2**i &gt; 0 }.compact.join(" ")
  end
end




As mentioned in the comments, I happened to make a gem for weekday bitmasks a while back, which you might find useful. The major difference is that the gem expects Sunday to be zero, Monday to be 1 and so forth (like Date#wday and most other date APIs).