Z-domain transfer function to difference equation
$$\begin{align*}\dfrac{Y(z)}{X(z)} &amp;= \dfrac{1+z^{-1}}{2(1-z^{-1})}\\
\\
2(1-z^{-1})Y(z)&amp;=(1+z^{-1})X(z)\\
\\
Y(z) -Y(z)z^{-1}&amp;= \frac{1}{2}X(z) +\frac{1}{2}X(z)z^{-1}\\
\\
y[n]-y[n-1]&amp;=\frac{1}{2}x[n] + \frac{1}{2}x[n-1]\\
\\
y[n]&amp;=y[n-1]+\frac{1}{2}x[n] + \frac{1}{2}x[n-1]\\
\end{align*}$$

You'll need at least one register for the feedback of the output (the y[n-1] term).

You might as well call that register the accumulator, as this is essentially an integrator, integrating up the average of the two most recent input values.  Integrators are not stable, so you may want to clip the output at some point instead of letting it roll over.