High-Speed VLSI Multiplication Algorithm with a Redundant Binary Addition Tree
IEEE Transactions on Computers
IEEE Transactions on Information Theory
Generating functionology
Bus-invert coding for low-power I/O
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Potential benefits of delta encoding and data compression for HTTP
SIGCOMM '97 Proceedings of the ACM SIGCOMM '97 conference on Applications, technologies, architectures, and protocols for computer communication
Exploiting the locality of memory references to reduce the address bus energy
ISLPED '97 Proceedings of the 1997 international symposium on Low power electronics and design
A coding framework for low-power address and data busses
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Narrow bus encoding for low-power DSP systems
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Odd/even bus invert with two-phase transfer for buses with coupling
Proceedings of the 2002 international symposium on Low power electronics and design
GLS '97 Proceedings of the 7th Great Lakes Symposium on VLSI
Modeling Delta Encoding of Compressed Files
DCC '06 Proceedings of the Data Compression Conference
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
A Bus-Encoding Scheme for Crosstalk Elimination in High-Performance Processor Design
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
On success runs of a fixed length in Bernoulli sequences: Exact and asymptotic results
Computers & Mathematics with Applications
On the mean and extreme distances between failures in Markovian binary sequences
Journal of Computational and Applied Mathematics
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In this paper, we derive the number of binary strings which contain, for a given i"k, exactly i"k runs of 1's of length k in all possible binary strings of length n, 1@?k@?n. Such a knowledge about the distribution pattern of runs of 1's in binary strings is useful in many engineering applications - for example, data compression, bus encoding techniques to reduce crosstalk in VLSI chip design, computer arithmetic using redundant binary number system and design of energy-efficient communication schemes in wireless sensor networks by transformation of runs of 1's into compressed information patterns, among others. We present, here, a generating function based approach to derive a solution to this counting problem. Our experimental results demonstrate that, for most commonly used file formats, the observed distributions of exactly i"k runs of length k, 1@?k@?n, closely follow the theoretically derived distributions, for a given n. For n=8, we find that the experimentally obtained values for most file formats agree within +/-5% of the theoretically obtained values for all i"k runs of length k, 1@?k@?n. Also, the root mean square (RMS) values of these deviations across all file types studied in this paper are less than 5% for n=8. In view of these facts, the results presented in this paper could be useful in various application domains, like the ones mentioned above.