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P. Kornerup, D.W. Matula, "An Algorithm for Redundant Binary BitPipelined Rational Arithmetic," IEEE Transactions on Computers, vol. 39, no. 8, pp. 11061115, August, 1990.  
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@article{ 10.1109/12.57048, author = {P. Kornerup and D.W. Matula}, title = {An Algorithm for Redundant Binary BitPipelined Rational Arithmetic}, journal ={IEEE Transactions on Computers}, volume = {39}, number = {8}, issn = {00189340}, year = {1990}, pages = {11061115}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.57048}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  An Algorithm for Redundant Binary BitPipelined Rational Arithmetic IS  8 SN  00189340 SP1106 EP1115 EPD  11061115 A1  P. Kornerup, A1  D.W. Matula, PY  1990 KW  tree pipeline; Gosper; redundant binary bitpipelined rational arithmetic; redundant binary representation; sum; difference; product; quotient; rational operands; partial quotient arithmetic algorithm; online arithmetic unit; signed bit level; binary radix; binary rational representation; simulation; interconnection; parallel computation; online delays; digital arithmetic; number theory; redundancy. VL  39 JA  IEEE Transactions on Computers ER   
The authors introduce a redundant binary representation of the rationals and an associated algorithm for computing the sum, difference, product, quotient, and other useful functions of two rational operands, using this representation. The algorithm extends R.W. Gosper's (1972) partial quotient arithmetic algorithm and allows the design of an online arithmetic unit with computations granularized at the signed bit level. Each input or output port can be independently set to receive/produce operands/result in either binary radix or the binary rational representation. The authors investigate by simulation the interconnection of several such units for the parallel computation of more complicated expressions in a treepipelined manner, with particular regard to measuring individual and compounded online delays.
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