Event FinderDense and Cyclic Gray Codes
- Starts
- Ends
- Format
- In person
- Location
- School of Engineering, Technology and Aeronautics, 2500 North River Road, Manchester, NH 03106
About This Event
Abstract: The binary reflected Gray code, patented by Frank Gray in 1953, is a permutation of the sequence ⟨0, 1, …, n-1⟩, where n is a power of 2, with the property that the binary representation of each number in the sequence differs from that of the preceding number in exactly one bit. The binary reflected Gray code is also cyclic, in that the last and first numbers also differ in only one bit. What if n is not a power of 2? How can we create a dense Gray code: a permutation of ⟨0, 1, …, n-1⟩ with the Gray-code property for any integer n > 1? The answer turns out to be surprisingly simple, but not obvious at first why it should work. When can we create a dense Gray code with the cyclic Gray-code property, and how do we do it? The answer here is a bit more obvious—once you have already seen it. Because Gray codes apply to non-binary integer representations as well, I will also touch on Gray codes for radices other than 2 and for mixed radices.