diff --git a/base/docs/helpdb/Base.jl b/base/docs/helpdb/Base.jl
index a3f2530e4fef3..97618d987910b 100644
--- a/base/docs/helpdb/Base.jl
+++ b/base/docs/helpdb/Base.jl
@@ -76,21 +76,6 @@ Subtraction operator.
 """
 -(x, y)
 
-"""
-    bits(n)
-
-A string giving the literal bit representation of a number.
-
-```jldoctest
-julia> bits(4)
-"0000000000000000000000000000000000000000000000000000000000000100"
-
-julia> bits(2.2)
-"0100000000000001100110011001100110011001100110011001100110011010"
-```
-"""
-bits
-
 """
     getindex(type[, elements...])
 
@@ -565,18 +550,6 @@ original string, otherwise they must be from distinct character ranges.
 """
 eachmatch
 
-"""
-    num2hex(f)
-
-Get a hexadecimal string of the binary representation of a floating point number.
-
-```jldoctest
-julia> num2hex(2.2)
-"400199999999999a"
-```
-"""
-num2hex
-
 """
     truncate(file,n)
 
@@ -1121,13 +1094,6 @@ julia> bin(bswap(1))
 """
 bswap
 
-"""
-    maxintfloat(T)
-
-The largest integer losslessly representable by the given floating-point DataType `T`.
-"""
-maxintfloat
-
 """
     delete!(collection, key)
 
@@ -1360,13 +1326,6 @@ false
 """
 isempty
 
-"""
-    hex2num(str)
-
-Convert a hexadecimal string to the floating point number it represents.
-"""
-hex2num
-
 """
     InexactError()
 
@@ -2165,14 +2124,6 @@ Values for `String` can be of that type, or `Vector{UInt8}`.
 """
 isvalid(T,value)
 
-"""
-    unsigned(x) -> Unsigned
-
-Convert a number to an unsigned integer. If the argument is signed, it is reinterpreted as
-unsigned without checking for negative values.
-"""
-unsigned
-
 """
     reverseind(v, i)
 
diff --git a/base/essentials.jl b/base/essentials.jl
index 6e06e23302d1d..11619fb49ff1c 100644
--- a/base/essentials.jl
+++ b/base/essentials.jl
@@ -138,6 +138,24 @@ convert(::Type{T}, x::T) where {T<:Tuple{Any,Vararg{Any}}} = x
 
 oftype(x,c) = convert(typeof(x),c)
 
+"""
+    unsigned(x) -> Unsigned
+
+Convert a number to an unsigned integer. If the argument is signed, it is reinterpreted as
+unsigned without checking for negative values.
+
+    unsigned(T::Type) -> UnsignedType
+
+Return the return-type of unsigned(x::T).
+
+```jldoctest
+julia> unsigned(12)
+0x000000000000000c
+
+julia> unsigned(Int)
+UInt64
+```
+"""
 unsigned(x::Int) = reinterpret(UInt, x)
 signed(x::UInt) = reinterpret(Int, x)
 
diff --git a/base/floatfuncs.jl b/base/floatfuncs.jl
index a5973c7d99986..9f8384835edcf 100644
--- a/base/floatfuncs.jl
+++ b/base/floatfuncs.jl
@@ -16,6 +16,11 @@ signbit(x::Float64) = signbit(bitcast(Int64, x))
 signbit(x::Float32) = signbit(bitcast(Int32, x))
 signbit(x::Float16) = signbit(bitcast(Int16, x))
 
+"""
+    maxintfloat(T)
+
+The largest integer losslessly representable by the given floating-point DataType `T`.
+"""
 maxintfloat(::Type{Float64}) = 9007199254740992.
 maxintfloat(::Type{Float32}) = Float32(16777216.)
 maxintfloat(::Type{Float16}) = Float16(2048f0)
@@ -24,18 +29,10 @@ maxintfloat() = maxintfloat(Float64)
 
 isinteger(x::AbstractFloat) = (x - trunc(x) == 0)
 
-num2hex(x::Float16) = hex(bitcast(UInt16, x), 4)
-num2hex(x::Float32) = hex(bitcast(UInt32, x), 8)
-num2hex(x::Float64) = hex(bitcast(UInt64, x), 16)
-
 function hex2num(s::AbstractString)
-    if length(s) <= 4
-        return bitcast(Float16, parse(UInt16, s, 16))
-    end
-    if length(s) <= 8
-        return bitcast(Float32, parse(UInt32, s, 16))
-    end
-    return bitcast(Float64, parse(UInt64, s, 16))
+    l = length(s)
+    l > 16 && throw(ArgumentError("the passed string must be of length <= 16, got $l"))
+    hex2num(l <= 4 ? Float16 : l <= 8 ? Float32 : Float64, s)
 end
 
 """
diff --git a/base/int.jl b/base/int.jl
index 19b65d5ea8f94..c568335b9f615 100644
--- a/base/int.jl
+++ b/base/int.jl
@@ -23,6 +23,14 @@ const BitInteger     = Union{BitInteger_types...}
 const BitSigned64T   = Union{Type{Int8}, Type{Int16}, Type{Int32}, Type{Int64}}
 const BitUnsigned64T = Union{Type{UInt8}, Type{UInt16}, Type{UInt32}, Type{UInt64}}
 
+const BitFloat_types = (Float16, Float32, Float64)
+const BitFloat       = Union{BitFloat_types...}
+const BitReal_types  = (BitInteger_types..., BitFloat_types...)
+const BitReal        = Union{BitReal_types...}
+
+reinterpret(::Type{Unsigned}, x::BitInteger) = unsigned(x)
+
+
 ## integer comparisons ##
 
 (<)(x::T, y::T) where {T<:BitSigned}  = slt_int(x, y)
diff --git a/base/intfuncs.jl b/base/intfuncs.jl
index 50bb11bd47f59..7fd538a9d9986 100644
--- a/base/intfuncs.jl
+++ b/base/intfuncs.jl
@@ -483,7 +483,48 @@ function hex(x::Unsigned, pad::Int, neg::Bool)
     String(a)
 end
 
-num2hex(n::Integer) = hex(n, sizeof(n)*2)
+"""
+    num2hex(f)
+
+An hexadecimal string of the binary representation of a number.
+See also the [`bits`](@ref) function, which is similar but gives
+a binary string.
+
+```jldoctest
+julia> num2hex(Int64(4))
+"0000000000000004"
+
+julia> num2hex(2.2)
+"400199999999999a"
+
+```
+"""
+num2hex(n::BitReal) = hex(reinterpret(Unsigned, n), sizeof(n)*2)
+num2hex(n::Bool) = hex(n)
+
+"""
+    hex2num(T::Type, str)
+
+Interprets a hexadecimal string as the bit representation of a
+number of type `T`. See also [`num2hex`](@ref).
+
+```jldoctest
+julia> hex2num(Float64, "400199999999999a")
+2.2
+
+julia> hex2num(Int32, "fffffffe")
+-2
+```
+
+    hex2num(str)
+
+Convert a hexadecimal string to the floating point number it represents.
+This function, which is inherently type-unstable, returns a `Float16`,
+a `Float32`, or a `Float64` depending on the length of the string `str`
+(note that this length must hence be no greater than 16).
+"""
+hex2num(::Type{T}, s::AbstractString) where {T<:BitReal} =
+    reinterpret(T, parse(unsigned(T), s, 16))
 
 const base36digits = ['0':'9';'a':'z']
 const base62digits = ['0':'9';'A':'Z';'a':'z']
@@ -573,6 +614,21 @@ Convert an integer to a decimal string, optionally specifying a number of digits
 """
 dec
 
+"""
+    bits(n)
+
+A string giving the literal bit representation of a number.
+See also the [`num2hex`](@ref) function, which is similar but
+gives an hexadecimal string.
+
+```jldoctest
+julia> bits(4)
+"0000000000000000000000000000000000000000000000000000000000000100"
+
+julia> bits(2.2)
+"0100000000000001100110011001100110011001100110011001100110011010"
+```
+"""
 bits(x::Union{Bool,Int8,UInt8})           = bin(reinterpret(UInt8,x),8)
 bits(x::Union{Int16,UInt16,Float16})      = bin(reinterpret(UInt16,x),16)
 bits(x::Union{Char,Int32,UInt32,Float32}) = bin(reinterpret(UInt32,x),32)
diff --git a/base/multinverses.jl b/base/multinverses.jl
index 5b60e76e40a29..be34348a1a17e 100644
--- a/base/multinverses.jl
+++ b/base/multinverses.jl
@@ -11,7 +11,10 @@ unsigned(::Type{Int16}) = UInt16
 unsigned(::Type{Int32}) = UInt32
 unsigned(::Type{Int64}) = UInt64
 unsigned(::Type{Int128}) = UInt128
-unsigned{T<:Unsigned}(::Type{T}) = T
+unsigned(::Type{T}) where {T<:Unsigned} = T
+unsigned(::Type{Float16}) = UInt16
+unsigned(::Type{Float32}) = UInt32
+unsigned(::Type{Float64}) = UInt64
 
 abstract type  MultiplicativeInverse{T} end
 
diff --git a/test/floatfuncs.jl b/test/floatfuncs.jl
index e246e8df5cac6..96ae477f0fdbd 100644
--- a/test/floatfuncs.jl
+++ b/test/floatfuncs.jl
@@ -39,7 +39,9 @@ end
 for elty in (Float16,Float32,Float64), _ = 1:10
     x = rand(elty)
     @test hex2num(num2hex(x)) ≈ x
+    @test hex2num(elty, num2hex(x)) ≈ x
 end
+@test_throws ArgumentError hex2num(String(rand('a':'f', rand(17:100))))
 
 # round
 for elty in (Float32,Float64)
diff --git a/test/intfuncs.jl b/test/intfuncs.jl
index 0c6fc028a11c8..175c0fe5dbbf5 100644
--- a/test/intfuncs.jl
+++ b/test/intfuncs.jl
@@ -124,6 +124,14 @@ end
 @test hex(12) == "c"
 @test hex(-12, 3) == "-00c"
 @test num2hex(1243) == (Int == Int32 ? "000004db" : "00000000000004db")
+@test num2hex(-1243) == (Int == Int32 ? "fffffb25" : "fffffffffffffb25")
+@test num2hex(true) == "1"
+@test num2hex(false) == "0"
+
+for elty in Base.BitInteger_types, _ = 1:10
+    x = rand(elty)
+    @test hex2num(elty, num2hex(x)) == x
+end
 
 @test base(2, 5, 7) == "0000101"