Efficient algorithm and fast hardware implementation for multiply-by-(1+2k)

Chin Long Wey, Ping Chang Jui, Muh Tian Shiue

Research output: Contribution to journalArticlepeer-review


A constant multiplier performs a multiplication of a datainput with a constant value. Constant multipliers are essential components in various types of arithmetic circuits, such as filters in digital signal processor (DSP) units, and they are prevalent in modern VLSI designs. This study presents an efficient algorithm and fast hardware implementation for performing multiply-by-(1+2k) operation with additions. No multiplications are needed. The value of (1+2k)N can be computed by adding N to its k-bit left-shifted value 2kN. The additions can be performed by the fulladder- based (FA-based) ripple carry adder (RCA) for simple architecture. This paper introduces the unit cells for additions (UCAs) to construct the UCA-based RCA which achieves 35% faster than the FA-based RCA in speed performance. Further, in order to improve the speed performance, a simple and modular hybrid adder is presented with the proposed UCA concept, where the carry lookahead adder (CLA) as a module and many of the CLA modules are serially connected in a fashion similar to the RCA. Results show that the hybrid adder significantly improves the speed performance.

Original languageEnglish
Pages (from-to)966-974
Number of pages9
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Issue number4
StatePublished - 1 Apr 2015


  • Booth algorithm
  • Carry-lookahead adder (CLA)
  • Constant multiplier
  • Hybrid adder (HyA)
  • Ripple carry adder (RCA)


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