Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 RealToHexString

Source Notebook

Get a string representing the hexadecimal form of a real number

Contributed by: Daniel Lichtblau

ResourceFunction["RealToHexString"][n,{e,h}]

gives the hexadecimal string corresponding to n, with an exponent field of e bits and a total length of h hex digits.

ResourceFunction["RealToHexString"][n]

gives the hexadecimal string for n, using the common IEEE double-precision values of 11 exponent bits and 64 bits total.

Details

ResourceFunction["RealToHexString"] uses rounding on arbitrary-precision inputs in order to get the final digit correct.

Examples

Basic Examples (1) 

Find the hexadecimal string for the decimal 1.1:

In[1]:=
ResourceFunction[ "RealToHexString", ResourceSystemBase -> "https://www.wolframcloud.com/obj/resourcesystem/api/1.0"][1.1]
Out[1]=

Scope (4) 

RealToHexString will handle arbitrary-precision reals:

In[2]:=
ResourceFunction[ "RealToHexString", ResourceSystemBase -> "https://www.wolframcloud.com/obj/resourcesystem/api/1.0"][N[11/10, 20]]
Out[2]=

RealToHexString can return a string with length exceeding the capacity of a machine double-precision value:

In[3]:=
ResourceFunction[ "RealToHexString", ResourceSystemBase -> "https://www.wolframcloud.com/obj/resourcesystem/api/1.0"][N[11/10, 20], {11, 20}]
Out[3]=

RealToHexString returns a string of all zeros for inputs that are numeric zeros:

In[4]:=
ResourceFunction[ "RealToHexString", ResourceSystemBase -> "https://www.wolframcloud.com/obj/resourcesystem/api/1.0"][0.]
Out[4]=
In[5]:=
ResourceFunction[ "RealToHexString", ResourceSystemBase -> "https://www.wolframcloud.com/obj/resourcesystem/api/1.0"][0.``20, {11, 24}]
Out[5]=

A small number:

In[6]:=
pi50 = N[10^(-4000)*Pi, 50]
Out[6]=

Convert it to a hex string with 20 hexadecimal digits and a mantissa of 16 bits:

In[7]:=
smallstr = ResourceFunction[ "RealToHexString", ResourceSystemBase -> "https://www.wolframcloud.com/obj/resourcesystem/api/1.0"][pi50, {16, 20}]
Out[7]=

Convert its reciprocal:

In[8]:=
bigstr = ResourceFunction[ "RealToHexString", ResourceSystemBase -> "https://www.wolframcloud.com/obj/resourcesystem/api/1.0"][1/pi50, {16, 20}]
Out[8]=

Check that they convert back and give the expected product:

In[9]:=
ResourceFunction["HexStringToReal"][smallstr, {16, 20}]* ResourceFunction["HexStringToReal"][bigstr, {16, 20}]
Out[9]=

Properties and Relations (2) 

Start with a number:

In[10]:=
n = N[11/10, 20]
Out[10]=

Use the resource function "HexStringToReal" to reverse the process, effectively round-tripping from RealToHexString:

In[11]:=
rhs = ResourceFunction[ "RealToHexString", ResourceSystemBase -> "https://www.wolframcloud.com/obj/resourcesystem/api/1.0"][N[11/10, 20]]; hsr = ResourceFunction["HexStringToReal"][rhs]
Out[12]=

Possible Issues (1) 

RealToHexString will pad with zeros if the number of hex digits to return makes it exceed the internal precision of the input:

In[13]:=
ResourceFunction[ "RealToHexString", ResourceSystemBase -> "https://www.wolframcloud.com/obj/resourcesystem/api/1.0"][N[11/10, 20], {11, 54}]
Out[13]=

Requirements

Wolfram Language 11.3 (March 2018) or above

Version History

  • 1.0.2 – 20 October 2025
  • 1.0.1 – 13 September 2024
  • 1.0.0 – 28 February 2019

Related Resources

License Information