diff --git a/src/fixed.jl b/src/fixed.jl
index a989d890..df747140 100644
--- a/src/fixed.jl
+++ b/src/fixed.jl
@@ -85,10 +85,10 @@ rem(x::Integer, ::Type{Fixed{T,f}}) where {T,f} = Fixed{T,f}(rem(x,T)<<f,0)
 rem(x::Real,    ::Type{Fixed{T,f}}) where {T,f} = Fixed{T,f}(rem(Integer(trunc(x)),T)<<f + rem(Integer(round(rem(x,1)*(one(widen1(T))<<f))),T),0)
 
 
-Base.BigFloat(x::Fixed{T,f}) where {T,f} =
-    BigFloat(x.i>>f) + BigFloat(x.i&(one(widen1(T))<<f - 1))/BigFloat(one(widen1(T))<<f)
-(::Type{TF})(x::Fixed{T,f}) where {TF <: AbstractFloat,T,f} =
-    TF(x.i>>f) + TF(x.i&(one(widen1(T))<<f - 1))/TF(one(widen1(T))<<f)
+(::Type{Tf})(x::Fixed{T,f}) where {Tf <: AbstractFloat, T, f} = Tf(Tf(x.i) * Tf(@exp2(-f)))
+Base.Float16(x::Fixed{T,f}) where {T, f} = Float16(Float32(x))
+Base.Float32(x::Fixed{T,f}) where {T, f} = Float32(x.i) * Float32(@exp2(-f))
+Base.Float64(x::Fixed{T,f}) where {T, f} = Float64(x.i) * @exp2(-f)
 
 function Base.Rational(x::Fixed{T,f}) where {T, f}
     f < bitwidth(T)-1 ? x.i//rawone(x) : x.i//(one(widen1(T))<<f)
diff --git a/test/fixed.jl b/test/fixed.jl
index b3da7e59..4ad1ebc3 100644
--- a/test/fixed.jl
+++ b/test/fixed.jl
@@ -270,6 +270,43 @@ end
     @test isa(float(one(Fixed{Int32,25})), Float64)
 end
 
+@testset "conversions to float" begin
+    for T in (Float16, Float32, Float64, BigFloat)
+        @test isa(convert(T, Q0f7(0.3)), T)
+    end
+
+    for Tf in (Float16, Float32, Float64)
+        @testset "$Tf(::Fixed{$T})" for T in (Int8, Int16)
+            @testset "$Tf(::Fixed{$T,$f})" for f = 0:bitwidth(T)-1
+                F = Fixed{T,f}
+                float_err = 0.0
+                for i = typemin(T):typemax(T)
+                    f_expected = Tf(i * BigFloat(2)^-f)
+                    f_actual = Tf(reinterpret(F, i))
+                    float_err += abs(f_actual - f_expected)
+                end
+                @test float_err == 0.0
+            end
+        end
+        @testset "$Tf(::Fixed{$T})" for T in (Int32, Int64, Int128)
+            @testset "$Tf(::Fixed{$T,$f})" for f = 0:bitwidth(T)-1
+                F = Fixed{T,f}
+                error_count = 0
+                for i in vcat(typemin(T):(typemin(T)+0xFF),
+                              -T(0xFF):T(0xFF),
+                              (typemax(T)-0xFF):typemax(T))
+                    f_expected = Tf(i * BigFloat(2)^-f)
+                    isinf(f_expected) && break # for Float16() and Float32()
+                    f_actual = Tf(reinterpret(F, i))
+                    f_actual == f_expected && continue
+                    error_count += 1
+                end
+                @test error_count == 0
+            end
+        end
+    end
+end
+
 @testset "predicates" begin
     @test isfinite(1Q7f8)
     @test !isnan(1Q7f8)