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Multiplication of signed-digit numbers

Multiplication of signed-digit numbers

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A recently proposed technique for common-multiplicand multiplication of binary numbers is shown to be applicable to signed-digit numbers. The authors prove that multiplication of a single k-bit multiplicand by nk-bit multipliers can be performed using 0.306nk additions for canonically recoded signed-digit numbers, whereas the binary case requires 0.375nk additions.

Inspec keywords: computation theory; digital arithmetic

Other keywords: n k-bit multipliers; canonically recorded signed-digit numbers; single k-bit multiplicand; signed-digit number multiplication; common-multiplicand multiplication; binary number multiplication

Subjects: Other computer theory; Digital arithmetic methods

References

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      • Ö Eĝecioĝlu , Ç.K. Koç . Exponentiation using canonical recoding. Theoretical Computer Science
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      • S. Arno , F.S. Wheeler . Signed digit representations of minimal Hamming weight. IEEE Trans. , 8 , 1007 - 1010
    3. 3)
      • D.E. Knuth . (1981) The art of computer programming: Seminumerical algorithms. Vol. 2.
    4. 4)
      • S.M. Yen , C.S. Laih . Common-multiplicand multiplication and its applications to public keycryptography. Electron. Lett. , 17 , 1583 - 1584
    5. 5)
      • I. Koren . (1993) Computer arithmetic algorithms.
    6. 6)
      • R.L. Rivest , A. Shamir , L. Adleman . A method for obtaining digital signatures and public-key cryptosystems. Commun. ACM , 2 , 120 - 126
    7. 7)
      • G.W. Reitwiesner . Binary arithmetic. Advances in Computers , 231 - 308
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