foreachprogrammingtables
Is there a way to get a binary string of an integer calculated by e.g., \pgfmathparse{pow(2,3)} \pgfmathresult such that later on I can use the string digits in a foreach loop like .. if it is '1' do this or if the digit is '0' do that?
I don't need to use the tikz or pgf packages; if there is any other math engine with programming language features, that would be fine, too. My goal is to generate a table atuomatically.
This is the relevant part from etex.ch:
5247 @ The function |quotient(n,d)| computes the rounded quotient
5248 $q=\lfloor n/d+{1\over2}\rfloor$, when $n$ and $d$ are positive.
5249
5250 @<Declare subprocedures for |scan_expr|@>=
5251 function quotient(@!n,@!d:integer):integer;
5252 var negative:boolean; {should the answer be negated?}
5253 @!a:integer; {the answer}
5254 begin if d=0 then num_error(a)
5255 else begin if d>0 then negative:=false
5256 else begin negate(d); negative:=true;
5257 end;
5258 if n<0 then
5259 begin negate(n); negative:=not negative;
5260 end;
5261 a:=n div d; n:=n-a*d; d:=n-d; {avoid certain compiler optimizations!}
5262 if d+n>=0 then incr(a);
5263 if negative then negate(a);
5264 end;
5265 quotient:=a;
5266 end;
5267
5268 @ Here the term |t| is multiplied by the quotient $n/f$.
5269
5270 @d expr_s(#)==#:=fract(#,n,f,max_dimen)
5271
5272 @<Cases for evaluation of the current term@>=
5273 expr_scale: if l=int_val then t:=fract(t,n,f,infinity)
5274 else if l=dimen_val then expr_s(t)
5275 else begin expr_s(width(t)); expr_s(stretch(t)); expr_s(shrink(t));
5276 end;
5277
5278 @ Finally, the function |fract(x,n,d,max_answer)| computes the integer
5279 $q=\lfloor xn/d+{1\over2}\rfloor$, when $x$, $n$, and $d$ are positive
5280 and the result does not exceed |max_answer|. We can't use floating
5281 point arithmetic since the routine must produce identical results in all
5282 cases; and it would be too dangerous to multiply by~|n| and then divide
5283 by~|d|, in separate operations, since overflow might well occur. Hence
5284 this subroutine simulates double precision arithmetic, somewhat
5285 analogous to \MF's |make_fraction| and |take_fraction| routines.
5286
5287 @d too_big=88 {go here when the result is too big}
Why Peter Breitenlohner decided to round rather than truncate is not explained. There may have been discussion on the matter in the NTS group. It surely is a nuisance having similar operations that can give different results.
In any case the behavior is clearly documented in etex_man.tex:
454 The arithmetic performed by \eTeX's expressions does not do much that could
455 not be done by \TeX's arithmetic operations \|\advance|, \|\multiply|, and
456 \|\divide|, although there are some notable differences: Each factor is
457 checked to be in the allowed range, numbers must be less than $2^{31}$ in
458 absolute value, dimensions or glue components must be less than
459 $2^{14}$\[pt], \[mu], \[fil], etc.\ respectively. The arithmetic operations
460 are performed individually, except for `scaling' operations (a
461 multiplication immediately followed by a division) which are performed as
462 one combined operation with a 64-bit product as intermediate value. The
463 result of each operation is again checked to be in the allowed range.
464 Finally the results of divisions and scalings are rounded, whereas \TeX's
465 \|\divide| truncates.
In expl3 there are
\int_div_round:nn
\int_div_truncate:nn
so that one always knows what's the used division.
This can be done using the package xstring. The code also uses \foreach, which is part of tikz but can be loaded with pgffor if your document doesn't use tikz.
\documentclass{article}
\usepackage[T1]{fontenc} % to use accented characters and others
\usepackage{xstring}
\usepackage{pgffor} % in case you're not using tikz
\newcommand{\markletters}[1]{\StrLen{#1}[\strlen]\foreach \chr in {1,...,\strlen}{$<$\StrChar{#1}{\chr}$>$}}
\begin{document}
\markletters{Hello World!}
\markletters{äöü ÄÖÜ // ß}
\end{document}
Best Answer
To store the binary representation of an integer in a macro you can use PGF/TikZ
\pgfmathdectobase:In order to use this in a
\foreachloop you would still need add commas between the bits.