Haskell Parsec parser of Verilog-style number literals
Let's start with your imports. You should get rid of those you don't need, e.g. System.IO, import Data.Either.Extra (fromRight). Next, you shouldn't mix integral and floating point calculations, unless you're fine with imprecise results. For example, integerLog will give the wrong answer around 1024:

ghci&gt; integerLog (2^1023)
1023
ghci&gt; integerLog (2^1024)
179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137216


Next, record field names are functions:

data Number = Number {val::Integer, len:: BitSize} deriving Show


This gives you two functions,

val :: Number -&gt; Integer
len :: Number -&gt; Integer


Unless you're fine with those functions at global namespace, it's usually a better idea to either a)&nbsp;use a complete name, e.g. value, bitLength, or b) prefix/suffix them with the type's name, e.g. numberValue or lenNumber. The story slightly changes if you want to use lenses and Template Haskell, but that's for another post.

What follows afterwards are several top-level functions without type signature, which is considered bad style:

readBin = readInt 2 (`elem` "01") digitToInt

-- conversions String -&gt; Number
hexToInteger x = fst $ readHex x !! 0 :: Integer
octToInteger x = fst $ readOct x !! 0 :: Integer
binToInteger x = fst $ readBin x !! 0 :: Integer


All those functions are partial, e.g.

ghci&gt; hexToInteger "Hello"
*** Exception: Prelude.!!: index too large


Your use prevents this kind of error, since you're using ithexToInteger only on valid combinations, but you shouldn't export them either. That's not really an issue here since you've wrote a Main (main) module, but you should keep that in mind.

However, those functions would be a lot nicer with the appropriate type:

convertWith :: ReadS Integer -&gt; String -&gt; Maybe Integer
convertWith fn xs = case fn xs of
                      [(n,"")] -&gt; Just n
                      _        -&gt; Nothing

hexToInteger, octToInteger, binToInteger :: String -&gt; Maybe Integer
hexToInteger = convertWith readHex
octToInteger = convertWith readOct
binToInteger = convertWith (readInt 2 (`elem` "01") digitToInt)


In this case we've dumped the plumbing into convertWith, added type signatures and made the functions non-partial. Now, let's step back to your smart-constructor:

-- |makeNumber is a safe constructor of an Either String Number
makeNumber :: Integer -&gt; Integer -&gt; (Either String Number)
makeNumber v l
  | v &lt; 0     = Left "makeNumber: Negative values not allowed in Number"
  | size &gt; l  = Left $ "makeNumber: Value " ++ show v ++ " is " 
    ++ show size ++ " bits long, should be at most " ++ show l ++ " bits"
  | size &lt;= 0 = Left $ "makeNumber: Size can't be negative or zero"
  | otherwise = Right $ Number v l
  where size = numberSize v


While that's better than just a Maybe Number, it's still not optimal if you have an application that's creating those numbers. Since sum types aren't expensive to write, let's use one:

data NumberError = ENegative
                 | ENegativeSize
                 | EBitOverflow Integer Integer
 deriving (Show, Eq)


That way you can separate the formatting from the number handling:

makeNumber :: Integer -&gt; BitSize -&gt; (Either NumberError Number)
makeNumber v l
  | v &lt; 0     = Left $ ENegative
  | size &gt; l  = Left $ EBitOverflow v l
  | size &lt;= 0 = Left $ ENegativeSize
  | otherwise = Right $ Number v l
  where size = numberSize v


You could also provide some functions, e.g.

eNegative    :: Either NumberError a
eBitOverflow :: Integer -&gt; BitSize -&gt; Either NumberError a


to ease the use of those, but that's an overkill here.

Speaking of overkills, did you notice the BitSize above? Many of your functions use Integer -&gt; Integer -&gt; …. But what do those Integer's mean? Which one is the value? Which one is the bitsize? And is Integer as bitsize really a good idea?

Therefore, try to add some documentation at the type level, even if it isn't a new type:

type BitSize = Int


Now, let's have a look at the parser:

-- |parse Verilog-style numbers &lt;size&gt;'&lt;radix&gt;value
parseNumber :: Parser Number
parseNumber = do
  size &lt;- option "32" (many1 digit)
  char '\''
  radix &lt;- option 'd' $ oneOf "hH" &lt;|&gt; oneOf "dD" &lt;|&gt; oneOf "oO" &lt;|&gt; oneOf "bB"
  let (thisDigit, convert_digits) =
        case toLower radix of
          'h' -&gt; (hexDigit, hexToInteger)
          'o' -&gt; (octDigit, octToInteger)
          'd' -&gt; (digit   , read)
          'b' -&gt; (binDigit, binToInteger)
          _  -&gt;  error "parseNumber: Internal error"
  val &lt;- many1 thisDigit
  let size' = read size :: Integer
      val' = convert_digits val :: Integer
      num = makeNumber val' size'
    in
    either fail return num


This is well done, except for two minor quirks: you can collect all oneOf &lt;prefix&gt; parsers into a single one:

oneOf "hHdDoObB"


and your use of error, which makes this parser partial again. Instead, you could have used 

  (thisDigit, convert_digits) &lt;-
        case toLower radix of
          'h' -&gt; return (hexDigit, hexToInteger)
          'o' -&gt; return (octDigit, octToInteger)
          'd' -&gt; return (digit   , read)
          'b' -&gt; return (binDigit, binToInteger)
          _  -&gt;  fail "parseNumber: Internal error"


Note that parseNumber slightly changes if you use String -&gt; Maybe Integer from above (you should use readMaybe instead of read in this case). Also note that parseNumber isn't a good name in this case, it indicates that you're parsing, but you only define a parser. numberParser is usually slightly better.

Also, make sure that your variables follow the same naming convention. convert_digits kind of falls of the rest of your names.

Last but not least, it's strange that you get your numbers as arguments, e.g.

$ ./MyApplication 32\'b100101001


Usually, you take those values from stdin and print them to stdout. The interact function will come in handy.

Bonus content: Separated concerns and an applicative Parser

So, now that we had a look at your code, how would I write it? I would probably introduce a function that takes the bitsize, the prefix, and the rest:

type BitSize      = Word
data NumberFormat = Bin | Oct | Dec | Hex

makeNumber :: BitSize -&gt; NumberFormat -&gt; String -&gt; Either NumberError Number
makeNumber l d xs = do
  num &lt;- readWith d xs
  case num of
   _ | num  &lt; 0 -&gt; eNegative
   _ | bits &gt; l -&gt; eBitOverflow num l
   _            -&gt; return $ Number num l
  where num  = readWith d xs
        bits = fromIntegral $ numberSize num

readWith :: NumberFormat -&gt; String -&gt; Either NumberError Number
readWith d xs = maybeToEither $ case d of
                   Bin -&gt; binToInteger xs
                   Oct -&gt; octToInteger xs
                   Dec -&gt; readMaybe    xs
                   Hex -&gt; hexToInteger xs


Essentially that's still your code, only put into two functions and using the NumberError above. This makes it possible to later test the parts of your previously large parseNumber. Note that all those functions are rather small, and do only one thing (and one thing well).

Now what's left is the Parser. Instead of the previous Monad one, we can now easily use an Applicative one. For this, we provide three additional parsers that parse the sub-expressions &lt;bits&gt;'&lt;format&gt;&lt;digits&gt;:

bitSizeParser :: Parser BitSize
bitSizeParser = option 32 $ fmap read $ many1 digits
-- read is fine here, since we use only digits

numberFormatParser :: Parser NumberFormat
numberFormatParser = option Dec $ fmap toFormat $ oneOf "hHoOdDbB"
  where toFormat c = case toLower c of
          'h' -&gt; Hex
          'b' -&gt; Bin
          'd' -&gt; Dec
          'o' -&gt; Oct

digitsParser :: Parser String
digitsParser = many1 $ oneOf "0123456789abcdef"


Now what's left is using those three parsers together and feeding them into makeNumber:

 import Control.Applicative ((&lt;$&gt;), (&lt;*&gt;)) -- not needed in GHC 7.10 or higher

numberParser' :: Parser (Either NumberError Number)
numberParser' = 
  makeNumber &lt;$&gt; bitSizeParser &lt;*&gt; numberFormatParser &lt;*&gt; digitsParser

numberParser :: Parser Number
numberParser = numberParser' &gt;&gt;= either fail return


Note that the parts of our parser are now reasonably dumb. They only get things, i.e. &lt;bits&gt;'&lt;format&gt;&lt;digits&gt;. The logic is now in makeNumber, which can be used without actually parsing, which might be handy if you want to check values from a database or similar.