Btw, a fun mathematics problem with many practical #FPGA / #DSP applications:

• does a useful non-unique binary representation of integers exist upon which hardware multiplication would be easier than on the unique binary representation?
• simpler version: easier in terms of logic gates needed
• harder version: easier in terms of the worst case timing

My intuition suggests, they probably exist, but using them may introduce an additional complexity of localised representational slack, and when multiplied repeatedly, they may require occasional re-fluffing to spread the slack around and improve the worst case timing. But I don't yet know in detail what these representations would look like, plus all the ones that I can vaguely see are complicated to convert to and from the conventional integer representation.