function [vo] = DAC_out(Vc, ZL, r, a)

% Vc voltage for "1", for example 3.3V
% ZL load resistance
% r = [r_0 r_1 r_2 r_3 ... r_{N-1}] DAC resistors
% a = [a_0 a_1 ... a_{N-1} a_{N-2}] binary code to convert in analog voltage

N = length(r);
if N ~= length(a)
    error('r and a vectors must have the same lenght');
end

req = zeros(1, N);
out = zeros(1, N);

% Calculate de equivalent resistor of the all resistors in parelell except the current resistor
% for example, for a_0 is 
% req(1) = r_1*r_2*...*r_{N-1}*ZL / (r_2*r_3...*r_{N-1}*ZL + r_1*r_3*r_4...*r_{N-1}*ZL + ... + 
% r_1*r_2*...*r_{N-2}*ZL + r_1*r_2*...*r_{N-1})

for i=1:N
    rt    = [r ZL];
    rt(i) = [];
    
    req(i) = prod(rt)/sumprod(rt);
    out(i) = Vc * req(i)/(req(i) + r(i));
end

% The network is linear
vo = 0;
for i=1:N
    if a(i) == 1
        vo = vo + out(i);
    end
end


function [a] = sumprod(r) 
% Calculates the sum of products of the elements of r excludinf j-th
% element of r in each iteration. j = 1, 2, ... N


a = 0;
for j=1:length(r)

    p = 1;
    for i=1:length(r)
        if i ~= j
            p = p * r(i);
        end
    end

    a = a + p;
end