High-speed FPGA 10's complement adders-subtractors

This paper first presents a study on the classical BCD adders from which a carry-chain type adder is redesigned to fit within the Xilinx FPGA's platforms. Some new concepts are presented to compute the P and G functions for carry-chain optimization purposes. Several alternative designs are presented. Then, attention is given to FPGA implementations of add/subtract algorithms for 10's complement BCD numbers. Carry-chain type circuits have been designed on 4-input LUTs (Virtex-4, Spartan-3) and 6-input LUTs (Virtex-5) Xilinx FPGA platforms. All designs are presented with the corresponding time performance and area consumption figures. Results have been compared to straight implementations of a decimal ripple-carry adder and an FPGA 2's complement binary adder-subtractor using the dedicated carry logic, both carried out on the same platform. Better time delays have been registered for decimal numbers within the same range of operands.This work is supported by the Universities FASTA, Mar del Plata, Argentina, UNCPBA Tandil, Argentina, UAM ,Madrid, Spain, and URV, Tarragona, Spain; it has been partially granted by the CICYT of Spain under contract TEC2007- 68074-C02-02/MIC

Interconnection structure of injective counters composed entirely of JK flip-flops

Counters whose transition map is a permutation and whose constituting elements are JK flip-flops only are investigated in order to trace relationships between the interconnection structure and the state graph.Some equivalence relations over structure transformations are derived that reduce the number of relevant configurations. Numerical computations based on these structure properties show that no circular counter exists for n ⩽ 9