Redundant Binary Adder Research Articles

Improved Redundant Binary Adder Realization in FPGA

This paper presents the design of improved redundant binary adder (IRBA) by utilizing positive–negative encoding rules in FPGA platform. The proposed design deals with inverted encoding of negative binary (IEN) and positive binary number to get addition result using readily available standard hardware module. The Verilog hardware description language is used as design entry for synthesis of the proposed architecture in Xilinx ISE Desisn Suite 14.4 software. This structure is realized on Vertex-4 xc4vfx12-12sf363 FPGA device. The proposed IRBA is found to be time efficient in comparison with the performance parameters such as propagation delay and area over previous reported architecture.

An efficient redundant binary adder with revised computational rules

Redundant binary representation (RBR) offers a carry-free addition of two redundant binary (RB) numbers. The computational rules of the conventional RB adder (CRBA) generate intermediate sum and carry vectors in RBR, leads to area overhead and pre-hardware elements for reverse conversion (RC). We have considered that the intermixing of inverted encoding of negabits (IEN) representation and conventional binary bits or posibits can be realized using standard hardware blocks. This paper provides a new computational rule for RB adder generating the intermediate sum and intermediate carry in posibit and IEN representations replacing the redundant digits. Thus, the proposed RB adder provides a single stage RB adder omitting the requirement of intermediate RB digits. For circuit synthesis of the proposed designs, we have considered Encounter® RTL Compiler and Xilinx Synthesis Technology in ASIC and FPGA platforms respectively. The comparative study of proposed NRBA offers improved design parameters as compared to CRBA.

Efficient Conversion Technique from Redundant Binary to NonRedundant Binary Representation

Redundant Binary (RB) to Two’s Complement (TC) converter offers nonredundant representation. However, the sign bit of TC representation has to be handled using nonstandard hardware blocks. The concept of Inverted encoding of negative weighted bits (IEN) eliminates the need of sign extension and offers design only using predefined hardware blocks. NonRedundant Binary (NRB) representation refers to both conventional and IEN representations. The NRB representation is also useful considering problem related to shifting in Carry Save (CS) representation of a RB number. In this paper, we have proposed two new conversion circuits for RB to NRB representation. The proposed circuits of the RB to NRB converter are coded in Verilog Hardware Description language (HDL) and synthesized using the Encounter(R) RTL Compiler RC13.10 v13.10-s006_1 of Cadence tool considering ASIC platform. Considering 64 bits’ operand, the delay power product performances of proposed one-bit and two-bit computations offer improvement of almost 29.9% and 47%, respectively as compared to Carry-Look-Ahead (CLA). The proposed one-bit converter is also applied in the final stage of the Modified Redundant Binary Adder (MRBA). The 32-bit MRBA offers a delay improvement of 7.87% replacing conventional converter with proposed one-bit converter in same FPGA 4vfx12sf363-12 device.

Memristor based N-bits redundant binary adder

This paper introduces a memristor based N-bits redundant binary adder architecture for canonic signed digit code CSDC as a step towards memristor based multilevel ALU. New possible solutions for multi-level logic designs can be established by utilizing the memristor dynamics as a basis in the circuit realization. The proposed memristor-based redundant binary adder circuit tries to achieve the theoretical advantages of the redundant binary system, and to eliminate the carry (borrow) propagation using signed digit representation. The advantage of carry elimination in the addition process is that it makes the speed independent of the operands length which speeds up all arithmetic operations. One memristor is sufficient for both the addition process and for storing the final result as a memory cell. The adder operation has been validated via different cases for 1-bit and 3-bits addition using HP memristor model and PSPICE simulation results.

A fast final adder for a 54-bit parallel multiplier for DSP application

A novel redundant binary-to-natural binary converter circuit is proposed which is used in the final addition stage of parallel multipliers. Use of this circuit in the final adder stage proves to be 17% faster than carry-look-ahead implementation. We used this algorithm in such a way that no redundant binary adder is required in compressing partial product rows. Only the natural 4:2 compressor circuits are used.

Redundant binary partial product generators for compact accumulation in Booth multipliers

The use of signed-digit number systems in arithmetic circuits has the advantage of constant time addition. When signed-digit number systems are used in binary, they are referred as redundant binary. Here, we present a new encoding technique for generating redundant binary partial products for a multiplier, without using any additional hardware. We express each normal binary partial product in one's complement form, with an extra bit denoting the sign bit. The proposed redundant binary partial product generator (RBPPG) achieves the highest reduction in the number of partial products (75%) for a radix-4 multiplier. The carry-free nature of redundant binary adders is exploited to add the extra bits with the partial products, without using any extra adder stages. The new partial product generation (PPG) technique is shown to improve the speed of multipliers, with the least number of adder stages, irrespective of the multiplier size.

A Systematic Approach for Designing Redundant Arithmetic Adders Based on Counter Tree Diagrams

This paper introduces a systematic approach to designing high-performance parallel adders based on Counter Tree Diagrams (CTDs). By using CTDs, we can describe addition algorithms at various levels of abstraction. A high-level CTD represents a network of coarse-grained components associated with word-level operands, whereas a low-level CTD represents a network of primitive components that can be directly mapped onto physical devices. The level of abstraction in circuit representation can be changed by decomposition of CTDs. We can derive possible variations of adder structures by decomposing a high-level CTD into low-level CTDs in a formal manner. In this paper, we focus on an application of CTDs to the design of redundant arithmetic adders with limited carry propagation. For any redundant number representation, we can obtain the optimal adder structure by trying every possible CTD decomposition and CTD-variable encoding. The potential of the proposed approach is demonstrated through an experimental synthesis of Redundant-Binary (RB) adders with CMOS standard cell libraries. We can successfully obtain RB adders that achieve an about 30-40% improvement in terms of power-delay product compared with conventional designs.

SRT Division Based on Redundant Signed Number

SRT division schemes are presented based on a redundant number operand format aiming high speed operation. The proposed SRT division method based on a redundant binary adder (RBA) and one based on a recoded binary signed digit adder (RBSDA) show a 33% and 50% speed improvement, respectively. The time complexity of the proposed division based on redundant number is O(n); importantly, the redundant number based design is easy to implement due to its structural regularity.

Design of a multiple‐operand redundant binary adder

AbstractThis paper describes a novel multiple‐operand redundant binary adder. The novel multiple‐operand addition algorithm can eliminate the carry propagation chain by dividing the input operands into an even place part and an odd place part, and adding them. The multiple‐operand adder with this algorithm can add six operands in parallel, and is faster than the ordinary tree‐structured method. A hardware model for the proposed adder implemented by the bidirectional current‐mode MOSFET circuit technology is described. Simulations have been made with HSPICE in order to verify the function of the proposed circuit. © 2002 Wiley Periodicals, Inc. Syst Comp Jpn, 33(10): 1–9, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/scj.10182

1桁2ビット/3ビット混合型高性能冗長2進加算器とその乗算器への応用

1桁2ビット/3ビット混合型高性能冗長2進加算器とその乗算器への応用

Multiple-valued signed digit adder using negative differential resistance devices

The paper describes a signed digit full adder (SDFA) circuit consisting of resonant tunneling diodes (RTDs) and metal oxide semiconductor field effect transistors (MOSFETs). The design is primarily based on a multiple valued logic literal circuit that utilizes the folded back I-V (or negative differential resistance, NDR) characteristics of RTDs to compactly implement its gated transfer function. MOS transistors are configured in current mode logic, where addition of two or more digits is achieved by superimposing the signals of individual wires being physically connected at the summing nodes. The proposed SDFA design uses redundant arithmetic representation and therefore, the circuit can perform addition of two arbitrary size binary numbers in constant time without the need for either carry propagation or carry look-ahead. The SDFA cell design has been verified through simulation by an augmented SPICE simulator that includes new homotopy based convergence routines to tackle the nonlinear device characteristics of quantum devices. From the simulation result, the SDFA cell has been found to perform addition operation in 3.5 nanoseconds, which is somewhat superior to other multivalued redundant arithmetic circuits reported in the literature. The SDFA cell requires only 13 MOS transistors and one RTD, as opposed to the state of the art CMOS redundant binary adder requiring 56 transistors, and to the conventional multivalued current mode adder consisting of 34 MOS transistors. In order to verify the simulation result, a prototype SDFA cell has been fabricated using MOSIS 2-micron CMOS process and GaAs based RTDs connected externally to the MOSFET circuit.

An 8.8-ns 54×54-bit multiplier with high speed redundant binary architecture

A high speed redundant binary (RB) architecture, which is optimized for the fast CMOS parallel multiplier, is developed. This architecture enables one to convert a pair of partial products in normal binary (NB) form to one RE number with no additional circuit. We improved the RB adder (RBA) circuit so that it can make a fast addition of the RB partial products. We also simplified the converter circuit that converts the final RE number into the corresponding NE number. The carry propagation path of the converter circuit is carried out with only multiplexer circuits. A 54/spl times/54-bit multiplier is designed with this architecture. It is fabricated by 0.5 /spl mu/m CMOS with triple level metal technology. The active area size is 3.0/spl times/3.08 mm/sup 2/ and the number of transistors is 78,800. This is the smallest number for all 54/spl times/54-bit multipliers ever reported. Under the condition of 3.3 V supply voltage, the chip achieves 8.8 ns multiplication time. The power dissipation of 540 mW is estimated for the operating frequency of 100 MHz. These are, so far, the fastest speed and the lowest power for 54/spl times/54-bit multipliers with 0.5-/spl mu/m CMOS.

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.

A high-speed multiplier using a redundant binary adder tree

A 16-bit /spl times/ 16-bit multiplier for 2 two's-complement binary numbers based on a new algorithm is described. This multiplier has been fabricated on an LSI chip using a standard n-E/D MOS process technology with a 2.7-/spl mu/m design rule. This multiplier is characterized by use of a binary tree of redundant binary adders. In the new algorithm, n-bit multiplication is performed in a time proportional to log/SUB 2/ n and the physical design of the multiplier is constructed of a regular cellular array. This new algorithm has been proposed by N. Takagi et al. (1982, 1983). The 16-bit/spl times/16-bit multiplier chip size is 5.8 /spl times/ 6.3 mm/SUP 2/ using the new layout for a binary adder tree. The chip contains about 10600 transistors, and the longest logic path includes 46 gates. The multiplication time was measured as 120 ns. It is estimated that a 32-bit /spl times/ 32-bit multiplication time is about 140 ns.

High-Speed VLSI Multiplication Algorithm with a Redundant Binary Addition Tree

A high-speed VLSI multiplication algorithm internally using redundant binary representation is proposed. In n bit binary integer multiplication, n partial products are first generated and then added up pairwise by means of a binary tree of redundant binary adders. Since parallel addition of two n-digit redundant binary numbers can be performed in a constant time independent of n without carry propagation, n bit multiplication can be performed in a time proportional to log2 n. The computation time is almost the same as that by a multiplier with a Wallace tree, in which three partial products will be converted into two, in contrast to our two-to-one conversion, and is much shorter than that by an array multiplier for longer operands. The number of computation elements of an n bit multiplier based on the algorithm is proportional to n2. It is almost the same as those of conventional ones. Furthermore, since the multiplier has a regular cellular array structure similar to an array multiplier, it is suitable for VLSI implementation. Thus, the multiplier is excellent in both computation speed and regularity in layout. It can be implemented on a VLSI chip with an area proportional to n2 log2 n. The algorithm can be directly applied to both unsigned and 2's complement binary integer multiplication.