Please review Number Representation before proceeding if you aren't comfortable with the various binary and hexadecimal ways of representing numbers.

For straight binary, unipolar coding, the R/2R network described in Ladder Networks is all that is needed. What about other representations of binary numbers?

For offset binary, an offset potential can be summed with the potential coming out of the R/2R ladder. Suppose the reference potential is -V_{0}, so that the output for an N-bit coding would be from -V_{0} (binary code 0) to 0 (binary code 2^{N-1}) to (2^{N-1}-1)/(2^{N-1})V_{0}. From input codes of 0 to 2^{N-1}-1, output should follow exactly the pattern already given for straight binary, but offset by V_{0}. From 2^{N-1} to 2^{N}-1, the output is the same as for a straight binary network, ignoring the most significant bit. Another way to say that is that offset binary for N bits goes through straight binary encoding for N-1 bits twice, once with a -V_{0} offset, and once without. You can show (or, at least, it can be shown) that the output of the following circuit is V_{1} - V_{2}:

If the output of the straight binary ladder network goes into V_{2}, then we need only apply -V_{0} to V_{1} for inputs of binary 0 to 2^{N-1}-1, and apply 0 to V_{1} for the other codes. It's just one more switch, and that switch can be directly controlled in the same way as the switches in the ladder network.