Electronic – How to make 2 bit or more half adder circuit

The input of the circuit is a 2 bit number (max value = 3) and the hence the maximum value at output will be 27 (a 5 bit number). The truth table of the circuit is:

$$\begin{array}{cccccccl}&\mathbf{x} & &\mathbf{b} &\mathbf{a} & &\mathbf{Y_4} &\mathbf{Y_3} &\mathbf{Y_2} &\mathbf{Y_1} &\mathbf{Y_0} & &x^3\\ \hline &\style{color:red}{0} &\rightarrow &0 &0 & &0 &0 &0 &0 &0 &\rightarrow &\style{color:red}{0}\\ &\style{color:red}{1} &\rightarrow &0 &1 & &0 &0 &0 &0 &1 &\rightarrow &\style{color:red}{1}\\ &\style{color:red}{2} &\rightarrow &1 &0 & &0 &1 &0 &0 &0 &\rightarrow &\style{color:red}{8}\\ &\style{color:red}{3} &\rightarrow &1 &1 & &1 &1 &0 &1 &1 &\rightarrow &\style{color:red}{27}\\ \hline & & & & & &ab &b &0 &ab &a\\ \hline \end{array}$$

The 'carry out' of an half adder, with inputs a and b, will be \$ab\$. So circuit can be implemented as given below.

\$\mathtt{ba}\$ is the input and \$\mathtt{Y_4Y_3Y_2Y_1Y_0}\$ is the output (\$\mathtt{Y_0}\$ is the LSB).

It worked fine in the free online version. The only goofy thing was that I had to use these 3-to-1 outputs to get it to allow the output of one gate to go to multiple inputs of the next stage.