Redundant Binary Multiplier Research Articles

Design and Analysis of Approximate Redundant Binary Multipliers

As technology scaling is reaching its limits, new approaches have been proposed for computional efficiency. Approximate computing is a promising technique for high performance and low power circuits as used in error-tolerant applications. Among approximate circuits, approximate arithmetic designs have attracted significant research interest. In this paper, the design of approximate redundant binary (RB) multipliers is studied. Two approximate Booth encoders and two RB 4:2 compressors based on RB (full and half) adders are proposed for the RB multipliers. The approximate design of the RB-Normal Binary (NB) converter in the RB multiplier is also studied by considering the error characteristics of both the approximate Booth encoders and the RB compressors. Both approximate and exact regular partial product arrays are used in the approximate RB multipliers to meet different accuracy requirements. Error analysis and hardware simulation results are provided. The proposed approximate RB multipliers are compared with previous approximate Booth multipliers; the results show that the approximate RB multipliers are better than approximate NB Booth multipliers especially when the word size is large. Case studies of error-resilient applications are also presented to show the validity of the proposed designs.

Modified Partial Product Generator for Redundant Binary Multiplier with High Modularity and Carry-Free Addition

Modified Partial Product Generator for Redundant Binary Multiplier with High Modularity and Carry-Free Addition

A Modified Partial Product Generator for Redundant Binary Multipliers

Due to its high modularity and carry-free addition, a redundant binary (RB) representation can be used when designing high performance multipliers. The conventional RB multiplier requires an additional RB partial product (RBPP) row, because an error-correcting word (ECW) is generated by both the radix-4 Modified Booth encoding (MBE) and the RB encoding. This incurs in an additional RBPP accumulation stage for the MBE multiplier. In this paper, a new RB modified partial product generator (RBMPPG) is proposed; it removes the extra ECW and hence, it saves one RBPP accumulation stage. Therefore, the proposed RBMPPG generates fewer partial product rows than a conventional RB MBE multiplier. Simulation results show that the proposed RBMPPG based designs significantly improve the area and power consumption when the word length of each operand in the multiplier is at least 32 bits; these reductions over previous NB multiplier designs incur in a modest delay increase (approximately 5 percent). The power-delay product can be reduced by up to 59 percent using the proposed RB multipliers when compared with existing RB multipliers.

A New Redundant Binary Booth Encoding for Fast $2^{n}$-Bit Multiplier Design

The use of redundant binary (RB) arithmetic in the design of high-speed digital multipliers is beneficial due to its high modularity and carry-free addition. To reduce the number of partial products, a high-radix-modified Booth encoding algorithm is desired. However, its use is hampered by the complexity of generating the hard multiples and the overheads resulting from negative multiples and normal binary (NB) to RB number conversion. This paper proposes a new RB Booth encoding scheme to circumvent these problems. The idea is to polarize two adjacent Booth encoded digits to directly form an RB partial product to avoid the hard multiple of high-radix Booth encoding without incurring any correction vector. The proposed method leads to lower encoding and decoding complexity than the recently proposed RB Booth encoder. Synthesis results using Artisan TSMC 0.18-mum standard-cell library show that the RB multipliers designed with our proposed Booth encoding algorithm exhibit on average 14% higher speed and 17% less energy-delay product than the existing multiplication algorithms for a gamut of power-of-two word lengths from 8 to 64 b.

An 80-MOPS-peak high-speed and low-power-consumption 16-b digital signal processor

This paper describes a 16-b fixed point digital signal processor (DSP), especially its multiply-accumulate (MAC) unit, memories, and instruction set. By adopting a redundant binary multiplier and a variable pipeline structure, this DSP's MAC unit, compared to a conventional MAC unit, consumes about 15% less power and operates 24% faster. Furthermore, its double-speed MAC mechanism can realize twice the performance of a single MAC operation while consuming only 69% more power. By being able to more finely control which portions of memory are activated, the data ROM and data RAM's precharge current was reduced to about 1/8 of the conventional ROM and RAMs. We redesigned the instruction set and reduced its width from 32 b to 24 b based on the analysis of data generated by simulating an application program on our previous DSP. The reduction in instruction width made our on-chip instruction memory size 33% smaller than the previous one. This chip is fabricated with a 0.5-/spl mu/m double-metal-layer CMOS process and achieves 80-MOPS-peak double speed multiply-accumulate performance.

High-performance VLSI multiplier with a new redundant binary coding

This paper describes the design of a 16×16 redundant binary multiplier for signed 2's complement numbers. The multiplier uses a new coding scheme for representing radix-2 signed digits. The coding results in a factor of two reduction in the number of summands used with respect to the modified Booth algorithm. The design has a small number of modular cells and regular routing, making it suitable for automatic synthesis of larger data-width multipliers. In addition, the row-based redundant binary adder tree is an ideal structure for high-throughput applications.