counter in hexadecimal base

Question

I have learned about counters from here. My question is, can I have a counter in other than 10 base, say hexadecimal one? How do I achieve that?

Answer 1

You can use expl3:

\documentclass{article}
\usepackage{geometry} % to see more pages
\geometry{paperwidth=5cm,paperheight=5cm,bottom=2cm}
\ExplSyntaxOn
\NewExpandableDocumentCommand{\hexa}{m}
 {
  \egreg_hexa:c { c@#1 }
 }
\cs_new:Npn \egreg_hexa:N #1 { \int_to_Hex:n { #1 } }
\cs_generate_variant:Nn \egreg_hexa:N { c }
\cs_set_eq:cN { @hexa } \egreg_hexa:N % for \pagenumbering
\ExplSyntaxOff
\newcounter{test}
\renewcommand{\thetest}{\hexa{test}}
\pagenumbering{hexa}
\begin{document}
\setcounter{page}{7}
\setcounter{test}{13}
\stepcounter{test}\thetest
\clearpage
\stepcounter{test}\thetest
\clearpage
\stepcounter{test}\thetest
\clearpage
\stepcounter{test}\thetest
\clearpage
\setcounter{test}{65566}\thetest
\end{document}

More generally, with any base up to 36

\documentclass{article}
\usepackage{geometry} % to see more pages
\geometry{paperwidth=5cm,paperheight=5cm,bottom=2cm}
\ExplSyntaxOn
\NewExpandableDocumentCommand{\cbase}{mm}
 {
  \egreg_cbase:nc { #1 } { c@#2 }
 }
\cs_new:Npn \egreg_cbase:nN #1 #2 { \int_to_Base:nn { #2 } { #1 } }
\cs_generate_variant:Nn \egreg_cbase:nN { nc }
\NewDocumentCommand{\newrepresentation}{mm}
 {% #1 = command name, #2 = base
  \cs_new:Npn #1 ##1 { \cbase{#2}{##1} }
  \cs_new:cpn { @\cs_to_str:N #1 } { \egreg_cbase:nN { #2 } }
 }
\newrepresentation{\basexxxvi}{36}
\ExplSyntaxOff
\newcounter{test}
\renewcommand{\thetest}{\cbase{20}{test}}
\pagenumbering{basexxxvi}
\begin{document}
\raggedright
\setcounter{page}{33}
\setcounter{test}{17}
\stepcounter{test}\thetest, should be~I \  page~X
\clearpage
\stepcounter{test}\thetest, should be~J \  page~Y
\clearpage
\stepcounter{test}\thetest, should be~10 \  page~Z
\clearpage
\stepcounter{test}\thetest, should be~11 \  page~10
\clearpage
\setcounter{test}{65566}\thetest, should be~83I6 \  page~11
\end{document}

Here test is represented in base 20, while the page is represented in base 36. For page numbering, \newrepresentation is needed.

If lowercase letters are preferred, replace \int_to_Base:nn with \int_to_base:nn.

Answer 2

I don't know if this is what you're after but:

\documentclass{article}
\usepackage{xparse}

\ExplSyntaxOn
\NewDocumentCommand{\tohex}{m}{\int_to_hex:n {#1}}
\ExplSyntaxOff

\begin{document}

\newcounter{mycounter}
\setcounter{mycounter}{43}

\tohex{\themycounter}

\end{document}

You could also convert to an arbitrary base (default 16) using

\documentclass{article}
\usepackage{xparse}

\ExplSyntaxOn
\NewDocumentCommand{\tobase}{O{16}m}{\int_to_base:nn {#2}{#1}}
\ExplSyntaxOff

\begin{document}

\newcounter{mycounter}
\setcounter{mycounter}{43}

\tobase[8]{\themycounter}


\end{document}