diff --git a/README.md b/README.md
index d5cdd0b..abfb633 100644
--- a/README.md
+++ b/README.md
@@ -5,22 +5,16 @@
 This library implements the [RFC7049: Concise Binary Object Representation (CBOR)][rfc]
 in Crystal.
 
+**WARNING:** This library is still a work in progress.
+
 ## Features
 
 - Full support for diagnostic notation
 - Assign a field to a type base on the CBOR tag
-- Support for a wide range of IANA CBOR Tags
+- Support for a wide range of IANA CBOR Tags (see below)
 
 ## Limitations
 
-### Half-precision floating point is not supported
-
-Crystal doesn't have a `Float16` type, so half-precision floating point numbers
-are not supported for the time being.
-
-If you know of a way to solve handle half-precision float, a contribution would
-be really appreciated.
-
 ### Maximum Array/String array/Bytes array length
 
 The spec allows for the maximum length of arrays, string arrays and bytes array
@@ -49,6 +43,15 @@ require "cbor"
 
 TODO: Write usage instructions here
 
+## Supported tags
+
+All the tags specified in [section 2.4 of RFC 7049][rfc-tags] are supported
+and the values are encoded in the respective Crystal types:
+
+- `Time`
+- `BigInt`
+- `BigFloat`
+
 ## Development
 
 TODO: Write development instructions here
@@ -66,3 +69,4 @@ TODO: Write development instructions here
 - [Alberto Restifo](https://github.com/your-github-user) - creator and maintainer
 
 [rfc]: https://tools.ietf.org/html/rfc7049
+[rfc-tags]: https://tools.ietf.org/html/rfc7049#section-2.4
diff --git a/spec/rfc_spec.cr b/spec/rfc_spec.cr
index 6eaace6..c052b25 100644
--- a/spec/rfc_spec.cr
+++ b/spec/rfc_spec.cr
@@ -3,19 +3,17 @@ require "./spec_helper"
 # All those tests have been exported from the RFC7049 appendix A.
 
 tests = [
-  # Disabled as half-precision floats are not supported:
   { %(0.0), "f9 00 00" },
   { %(-0.0), "f9 80 00" },
   { %(1.0), "f9 3c 00" },
   { %(1.5), "f9 3e 00" },
   { %(65504.0), "f9 7b ff" },
-  # { %(0.00006103515625), "f9 04 00" }, TODO: Something about the presentation
+  { %(6.1035156e-5), "f9 04 00" },
   { %(-4.0), "f9 c4 00" },
-  # { %(5.960464477539063e-8), "f9 00 01" },
-  # { %(Infinity), "f9 7c 00" },
-  # { %(NaN), "f9 7e 00" },
-  # { %(-Infinity), "f9 fc 00" },
-
+  { %(5.9604645e-8), "f9 00 01" },
+  { %(Infinity), "f9 7c 00" },
+  { %(NaN), "f9 7e 00" },
+  { %(-Infinity), "f9 fc 00" },
   { %(0), "00" },
   { %(1), "01" },
   { %(10), "0a" },
@@ -36,7 +34,7 @@ tests = [
   { %(-1000), "39 03 e7" },
   { %(1.1), "fb 3f f1 99 99 99 99 99 9a" },
   { %(100000.0), "fa 47 c3 50 00" },
-  # { %(3.4028234663852886e+38), "fa 7f 7f ff ff" }, TODO: Not precise enough?
+  { %(3.4028235e+38), "fa 7f 7f ff ff" },
   { %(1.0e+300), "fb 7e 37 e4 3c 88 00 75 9c" },
   { %(-4.1), "fb c0 10 66 66 66 66 66 66" },
   { %(Infinity), "fa 7f 80 00 00" },
diff --git a/src/cbor/type/float_16.cr b/src/cbor/type/float_16.cr
index fa383e9..f81e26d 100644
--- a/src/cbor/type/float_16.cr
+++ b/src/cbor/type/float_16.cr
@@ -1,30 +1,29 @@
-# Returns a Float32 by reading the 16 bit as a IEEE 754 half-precision floating
-# point (Float16).
+# Reads the `UInt16` as a half-point floating point number
 def Float32.new(i : UInt16)
   # Check for signed zero
-  if i & 0x7FFF_u16 == 0
+  if i & 0x7FFF == 0
     return (i.unsafe_as(UInt32) << 16).unsafe_as(Float32)
   end
 
-  half_sign = (i & 0x8000_u16).unsafe_as(UInt32)
-  half_exp = (i & 0x7C00_u16).unsafe_as(UInt32)
-  half_man = (i & 0x03FF_u16).unsafe_as(UInt32)
+  half_sign = (i & 0x8000).to_u32
+  half_exp = (i & 0x7C00).to_u32
+  half_man = (i & 0x03FF).to_u32
 
   # Check for an infinity or NaN when all exponent bits set
-  if half_exp == 0x7C00_u32
+  if (i & 0x7C00) == 0x7C00
     # Check for signed infinity if mantissa is zero
     if half_man == 0
-      return ((half_sign << 16) | 0x7F80_0000_u32).unsafe_as(Float32)
+      return ((half_sign << 16) | 0x7F80_0000).unsafe_as(Float32)
     else
       # NaN, keep current mantissa but also set most significiant mantissa bit
-      return ((half_sign << 16) | 0x7FC0_0000_u32 | (half_man << 13)).unsafe_as(Float32)
+      return ((half_sign << 16) | 0x7FC0_0000 | (half_man << 13)).unsafe_as(Float32)
     end
   end
 
   # Calculate single-precision components with adjusted exponent
   sign = half_sign << 16
   # Unbias exponent
-  unbiased_exp = ((half_exp.unsafe_as(Int32)) >> 10) - 15
+  unbiased_exp = (half_exp.unsafe_as(Int32) >> 10) - 15
 
   # Check for subnormals, which will be normalized by adjusting exponent
   if half_exp == 0
@@ -33,12 +32,12 @@ def Float32.new(i : UInt16)
 
     # Rebias and adjust exponent
     exp = (127 - 15 - e) << 23
-    man = (half_man << (14 + e)) & 0x7F_FF_FF_u32
+    man = (half_man << (14 + e)) & 0x7F_FF_FF
     return (sign | exp | man).unsafe_as(Float32)
   end
 
   # Rebias exponent for a normalized normal
   exp = (unbiased_exp + 127).unsafe_as(UInt32) << 23
-  man = (half_man & 0x03FF_u32) << 13
+  man = (half_man & 0x03FF) << 13
   (sign | exp | man).unsafe_as(Float32)
 end