The Area-Time Complexity of Binary Multiplication

The problem of performing multtphcaUon of n-bit binary numbers on a chip is considered Let A denote the ch~p area and T the time reqmred to perform mult~phcation. By using a model of computation which is a realistic approx~mauon to current and anucipated LSI or VLSI technology, ~t is shown that A T 2.

[1]  C. Thomborson,et al.  Area-time complexity for VLSI , 1979, STOC.

[2]  H. T. Kung,et al.  A Regular Layout for Parallel Adders , 1982, IEEE Transactions on Computers.

[3]  S. Wagstaff.  Greatest of the least primes in arithmetic progressions having a given modulus , 1979 .

[4]  R. J. Bonneau.  A CLASS OF FINITE COMPUTATION STRUCTURES SUPPORTING THE FAST FOURIER TRANSFORM , 1973 .

[5]  J. Rosser,et al.  Approximate formulas for some functions of prime numbers , 1962 .

[6]  M. Rem,et al.  Cost and performance of VLSI computing structures , 1979, IEEE Transactions on Electron Devices.

[7]  Richard Brent.  On the Addition of Binary Numbers , 1970, IEEE Transactions on Computers.

[8]  H. T. Kung,et al.  The chip complexity of binary arithmetic , 1980, STOC '80.

[9]  Harvey L. Garner,et al.  A Survey of Some Recent Contributions to Computer Arithmetic , 1976, IEEE Transactions on Computers.

[10]  Shmuel Winograd,et al.  On the Time Required to Perform Multiplication , 1967, JACM.

[11]  Richard P. Brent,et al.  Some Area-Time Tradeoffs for VLSI , 1982, SIAM J. Comput..

[12]  H. T. Kung,et al.  Systolic Arrays for (VLSI). , 1978 .

[13]  Shmuel Winograd,et al.  On the Time Required to Perform Addition , 1965, JACM.

[14]  Charles E. Leiserson,et al.  Area-Efficient Graph Layouts (for VLSI) , 1980, FOCS.

[15]  H. T. Kung,et al.  On the Area of Binary Tree Layouts , 1980, Inf. Process. Lett..

[16]  David L. Kuck,et al.  The Structure of Computers and Computations , 1978 .

[17]  John E. Savage,et al.  Area-Time Tradeoffs for Matrix Multiplication and Related Problems in VLSI Models , 1981, J. Comput. Syst. Sci..

[18]  D. H. Jacobsohn,et al.  A Suggestion for a Fast Multiplier , 1964, IEEE Trans. Electron. Comput..

[19]  Harold Abelson,et al.  Information transfer and area-time tradeoffs for VLSI multiplication , 1980, CACM.

[20]  Lynn Conway,et al.  Introduction to VLSI systems , 1978 .

[21]  L. B. Jackson,et al.  An approach to the implementation of digital filters , 1968 .

[22]  H. T. Kung,et al.  Corrigendum: `` The Area-Time Complexity of Binary Multiplication'' , 1982, JACM.