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IEEE Transactions on Applied Superconductivity

A new design approach for RSFQ logic circuits based on the binary decision diagram

Nobuyuki Yoshikawa, 博史 多胡, K. Yoneyama

Published Jun 1, 1999• 18 citations
Publisher

Abstract

We will propose a new design approach for single-flux-quantum (SFQ) logic circuits based on a binary decision diagram (BDD). The BDD is a way to represent a logical function by using a directed graph, which is composed of nodes having one input (root) and two outputs (branches). The node has binary states internally which can be controlled from outside, and it switches a messenger entering from the root into one of two branches depending on the internal state. It has been proven that any combinational logic can be represented by this basic element. We will show that the BDD is effectively implemented by an SFQ circuit, where the node is replaced with an SFQ D/sub 2/ flip-flop. Important features of the BDD SFQ logic circuit are simplicity of circuit structure, self-timed nature and high modularity. We have designed a BDD SFQ adder and showed that the junction count and latency are smaller than that of the conventional RSFQ adder.

DOI
10.1109/77.783700

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We will propose a new design approach for single-flux-quantum (SFQ) logic circuits based on a binary decision diagram (BDD). The BDD is a way to represent a logical function by using a directed graph, which is composed of nodes having one input (root) and two outputs (branches). The node has binary states internally which can be controlled from outside, and it switches a messenger entering from the root into one of two branches depending on the internal state. It has been proven that any combinational logic can be represented by this basic element. We will show that the BDD is effectively implemented by an SFQ circuit, where the node is replaced with an SFQ D/sub 2/ flip-flop. Important features of the BDD SFQ logic circuit are simplicity of circuit structure, self-timed nature and high modularity. We have designed a BDD SFQ adder and showed that the junction count and latency are smaller than that of the conventional RSFQ adder.
We have proposed a cell-based design approach for rapid single flux quantum (RSFQ) logic circuits. In our design approach, a binary decision diagram (BDD) is used for representation of logical functions in order to reduce the number of gates. We have made a standard cell library, which is composed of only five basic cells. We add one-junction Josephson transmission line (JTL) to the edge of the input and the output node of some basic cells, by which no deterioration of the DC bias margin is observed for the connection of each cell. In the layout level, the size and the position of the input/output node of each cell are equalized. The standard cell circuits were fabricated by NEC 2.5 kA/cm/sup 2/ and Hypres 1.0 kA/cm/sup 2/ Nb standard process and they were tested at low speed.
We are introducing a new subfamily of rapid single-flux-quantum (RSFQ) digital cells, based on a single B flip-flop template. The template can be considered as an SFQ flip-flop with up to 4 inputs and 6 outputs. Each input SFQ pulse can change the flip-flop's internal state. Each output presents (in the form of SFQ pulses a specific logic function of the initial state of the cell and input signals. Simple connection of various inputs and/or outputs, combined with shortening or opening of certain branches of the template allows one to implement a variety of RSFQ cells with wide margins. Of these various RSFQ cells, we have designed and successfully tested the T1 cell (asynchronous toggle flip-flop with synchronous destructive readout), single-bit full adder, and single-bit stage of an up-down counter. Experimentally measured margins for dc power supply voltage for these circuits were /spl plusmn/24%, /spl plusmn/24%, and /spl plusmn/17%, respectively.>
We have designed a high-speed SFQ bit-serial carry-save adder based on the binary decision diagram (BDD). A simple bit-serial carry-save adder based on the BDD we first designed has a carry-feedback loop. Its input data frequency is limited by the propagation delay in the feedback loop. In our second adder design, we have replaced one BDD gate with a nondestructive binary switch, by which we can eliminate the carry-feedback loop. We have designed the high-speed BDD SFQ bit-serial adder using the NEC 2.5 kA cm −2 Nb standard process and the CONNECT cell library. The circuit simulation indicates that the maximum operating frequency is 38 GHz and the dc bias margin at 10 GHz is ±23%. We have confirmed its correct operation in the on-chip high-speed test. The maximum operating frequency was found to be 23.8 GHz.
A novel method of design for controllers of pipelined microprocessors using single-flux-quantum (SFQ) logic has been proposed. The proposed design approach is based on one hot encoding and is very suitable for designing a finite state machine using SFQ logic circuits, where each internal state of the microprocessor is represented by a flip-flop. In this approach, decoding of the internal state can be performed instantaneously, in contrast to the case in the conventional method using a binary state register. Moreover, pipelining is effectively implemented without increasing the circuit size because no pipeline registers are required in the one hot encoding. By using this method, we have designed a controller for our new SFQ microprocessors, which employs pipelining. The number of Josephson junctions of the newly designed controller is 1067, while the previous version without pipelining contains 1721 Josephson junctions. These results indicate that the proposed design approach is very effective for pipelined SFQ microprocessors. We have implemented a new controller using the NEC 2.5 kA cm −2 Nb standard process and confirmed its correct operation experimentally.
Novel reconfigurable superconductive single flux quantum (SFQ) logic devices, the functions of which can be dynamically reconfigured by inputting control signals, have been investigated. The characteristics of single flux quantum circuits can be easily modulated by applying currents or magnetic fields because of the high sensitivity of superconductive circuits. We investigated several design approaches for the realization of dynamically reconfigurable SFQ logic devices. We employed direct current injection to the logic gate using a non-destructive read-out flip-flop. By changing the internal state of the non-destructive read-out flip-flop, the logic function can be dynamically reconfigured. We have designed and tested a dynamically reconfigurable Josephson transmission line (JTL)/delay flip-flop (DFF) circuit. The measured dc bias margin was 72.5-107.2%. Furthermore, we have demonstrated the operation of a variable bit-length shift register, composed of the dynamically reconfigurable JTL/DFF circuits. The investigated design approach can be applied to more sophisticated dynamically reconfigurable single flux quantum logic gates.
A methodology for designing single-flux-quantum (SFQ) flip-flops composed of both conventional (0-) and π -shifted Josephson junctions is investigated. We investigated the implementation of a storage loop, which can store flux quantum and is indispensable to express binary logic states in superconductor logic circuits. As all SFQ flip-flops have storage loops, the investigated design methodology can be applied to their design. We designed several SFQ flip-flops composed of 0- and π -shifted Josephson junctions using the investigated design methodology. The performances of the designed SFQ flip-flops were quantitatively evaluated by using an analog circuit simulator which we developed. We confirmed the correct operation of various SFQ flip-flops composed of 0- and π -shifted Josephson junctions with wide operating margins. Moreover, we observed that the investigated design methodology is suitable for SFQ flip-flops with complementary outputs because a storage loop composed of both 0- and π -shifted Josephson junctions has a symmetric structure and the complementary output function can be realized by using the storage loop. Our investigation indicates that the number of Josephson junctions and static power consumption of a non-destructive read-out flip-flop with complementary outputs (NDROC) can be reduced to less than half of those of the conventional NDROC, which has two storage loops composed of 0-Josephson junctions, to realize the complementary output function. The investigated design methodology is expected to be applied to not only SFQ circuits but also other superconducting logic circuits and novel reconfigurable logic devices using programmable 0- π Josephson junctions.