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A new breed of engineer is developing in our contemporary society. These engineers are concerned with communications and computers, economics and regulation. These new engineers apply themselves to data-to its pack? aging, transmission, and protection. They are data engineers. Formal curricula do not yet exist for their dedicated development. Rather they learn most of their tools on the job and their roots are in computer engineering, communications engineering, and applied mathe? matics. There is a need to draw relevant material together and present it so that those who wish to become data engineers can do so, for the betterment of themselves, their employer, their country, and, ultimately, the world-for we share the belief that the most effective tool for world peace and stability is neither politics nor armaments, but rather the open and timely exchange of information. This book has been written with that goal in mind. Today numerous signs encourage us to expect broader information exchange in the years to come. The movement toward a true Integrated Services Digital Network (ISDN) is perhaps the clearest of these. Also, the development offormal protocol layers reflects both a great deal of brilliance and compromise and also the desire for a common language among data engineers.1. DataIts Representation and Manipulation.- 1.1. Introduction.- 1.2. Number Systems.- 1.3. Negabinary Numbers.- 1.4. The Factorial Number System.- 1.5. The Gray Code.- 1.6. A Look at Boolean Functions.- References.- 2. Counting and Probability.- 2.1. Counting.- 2.2. Generating Functions.- 2.3. Permutations.- 2.4. Combinations.- 2.5. Recurrence Relations/Difference Equations.- 2.6. Probability.- 2.7. Generating Functions in Probability Theory.- 2.8. The Bernoulli Source.- 2.9. Some Important and Famous Problems.- 2.10. Random Mappings.- 2.11. Redundancy and the Perfect Voter.- 2.12. Bias.- 2.13. Maximum Likelihood Estimation.- References.- 3. The Natural Numbers and Their Primes.- 3.1. Il³Û