Yes, but you'll need many 3-to-8 decoders if you build it this way! The question asked for the minimal number of decoders, so I had to know the actual requirements.

Yes I can do it with just two 3-to-8 decoders plus three 2-input OR gates. I've been a bit reluctant to contribute to this thread or post a complete solution becasue it certainly looks a bit like homework.

Xodox, tell us what you already know or have done. Do you know what a "min-term" is? Do you know how to construct a boolean function as a sum of min-terms? Have you learnt that a decoder can be considered as a "min-term generator"?

Hi CRGreathouse, I think I know where you needed more OR gates. The A’CD + AC’D’ part is easy right, just two min terms of (A,C,D); but the A’B + AB’ may require more min terms and hence more OR gates depending on how you approach it.

You can however easily make A’B + AB’ with only two min terms of (A,B,X) if you make an appropriate choice for "X". Hint: think about boolean constants rather than only variables. :)