function [d,b]=digit(k)

% Given a positive integer k in decimal form, find vectors d, b,
% whose entries are the digits of the decimal or binary representation,
% respectively, of k. This function can be useful, for example, in
% building all kxk permutation matrices.
%   Caution: for integer >= 10^18 round-off errors occur!
 
k=abs(k); 
if k-fix(k)>0 'input is not an integer', break, end
if (k==0) d(1)=0; end

% create d(ecimal)
m=1; help=0; l=k;
while(help<l)
      d(m)=(l-10^m*fix(l/10^m))/10^(m-1);
      l=l-d(m)*10^(m-1); 
      help=d(m);
      m=m+1;
end
% reverse the order of the entries of d
d=d(max(size(d)):-1:1);


% create b(inary)

if (k<2) b(1)=k; break, end

m=1; r=0;
while (r-k)
       r=rem(k,2^m);
       if (r)
              b(m)=1;
       else
             b(m)=0; 
       end
       k=k-r; m=m+1;
end