Base convertion without dec2base and base2dec

Good day! I need to create a programm which converts numbers from any base to decimal and from decimal to any base.Without using dec2base,base2dec,dec2bin ,etc.They're working but there is a question. How can I add letters A,B,C,D,E,F there? From decimal:

a=input('number');
  b=input('base1');
  c=input('base2');
  if b==10
  i = 1;
  q = floor(a/c);
  r = rem(a, c);
  u(i) = num2str(r(i));
  while c <= q
      a = q;
      i = i + 1;
      q = floor(a/c);
      r = rem(a, c);
      u(i) = num2str(r);
  end
  u(i + 1) = num2str(q);
  u = fliplr(u)
  end
  u

To decimal:

else
u=0; 
for i=1:length(a) 
    u=u+str2num(a(i))*b^(length(a)-i);
end

[Stephen23]

There is no need to use loops and the slow num2str or str2num to solve this. Read Andrei Bobrov's solution and see a good example of how to write vectorized code in MATLAB.

Answer 1

[Andrei Bobrov]

function bs = dec2base_mtx(d,base,l)
%input: d - array, 'base' - base, l -> 'length' numbers in row
ll = ceil(log(max(d(:)))/log(base));
if nargin == 3
    ll = max(ll,l);
end
bs = rem(floor(d(:)*base.^(1-ll:0)),base);

function x = base2dec_mtx(bs,base)
% input bs -> array base; 
x = bs * base.^(size(bs,2)-1:-1:0).';

example of using

d= [4000; 13; 56000];
base = 16;
bs = dec2base_mtx(d,base);
z = ['0':'9','a':'f'];
bs16 = z(bs+1);

inverse transformation:

z = ['0':'9','a':'f'];
[~,jj] = ismember(bs16,z);
x = base2dec_mtx(jj-1,16);

Answer 2

[Walter Roberson]

digitcodes = ['0123456789ABCD'};

then, everywhere you have num2str() of a value that is intended to be a separate digit, use digitcodes(value+1) to get the character version of the digit.