Niranjan Kulkarni

Identification of Threshold Functions and Synthesis of Threshold Networks

This paper presents a new and efficient heuristic procedure for determining whether or not a given Boolean function is a threshold function, when the Boolean function is given in the form of a decision diagram. The decision diagram based method is significantly different from earlier methods that are based on solving linear inequalities in Boolean variables that derived from truth tables. This methods success depends on the ordering of the variables in the binary decision diagram (BDD). An alternative data structure, and one that is more compact than a BDD, called a max literal factor tree (MLFT) is introduced. An MLFT is a particular type of factoring tree and was found to be more efficient than a BDD for identifying threshold functions. The threshold identification procedure is applied to the MCNC benchmark circuits to synthesize threshold gate networks.

Design of a robust, high performance standard cell threshold logic family for DSM technology

This paper presents the threshold logic latch (TLL), which provides a high performance, low power alternative to traditional CMOS logic networks. TLL is highly robust, even in deep sub-micron technology nodes. Experimental results obtained from simulation of a commercial 65 nm low power process demonstrate a static noise margin up to an order of magnitude greater than those of existing implementations of threshold logic. Examples of automated synthesis of pipelined multipliers using a combination of standard CMOS and a small number of TLL gates are shown through simulation to improve both area and total power by a factor of up to 1.5 and reduce leakage power by a factor of up to 2.3.

Minimizing area and power of sequential CMOS circuits using threshold decomposition

This paper describes the design of a standard cell library of differential mode threshold gates, referred to as a Threshold Logic Latch or TLL, and new threshold function identification and decomposition methods to map a conventional logic network consisting of logic gates and flipflops, into a hybrid network that consists of both TLLs and conventional logic gates. After logic synthesis and physical design (placement and routing) using a commercial 65nm LP (low power) library, and commercial design tools, the hybrid circuits are shown to have up to 35% less dynamic power, about 50% less leakage power and around 37% less area when compared to the corresponding conventional design operated at the same (peak) frequency.

Spintronic Threshold Logic Array (STLA) - A compact, low leakage, non-volatile gate array architecture

Abstract This paper describes a novel, first of its kind architecture for a threshold logic gate using conventional MOSFETs and an STT-MTJ (Spin Transfer Torque-Magnetic Tunneling Junction) device. The resulting cell, called STL which is extremely compact can be programmed to realize a large number of threshold functions, many of which would require a multilevel network of conventional CMOS logic gates. Next, we describe a novel array architecture consisting of STL cells onto which complex logic networks can be mapped. The resulting array, called STLA has several advantages not available with conventional logic. This type of logic (1) is non-volatile, (2) is structurally regular and operates like DRAM, (3) is fully observable and controllable, (4) has zero standby power. These advantages are demonstrated and compared by implementing a 16-bit carry look-ahead adder and a 32-bit Wallace tree multiplier in STLA and FPGA.

Digital IP protection using threshold voltage control

This paper proposes a method to completely hide the functionality of a digital standard cell. This is accomplished by a differential threshold logic gate (TLG). A TLG with n inputs implements a subset of Boolean functions of n variables that are linear threshold functions. The output of such a gate is one if and only if an integer weighted linear arithmetic sum of the inputs equals or exceeds a given integer threshold. We present a novel architecture of a TLG that not only allows a single TLG to implement a large number of complex logic functions, which would require multiple levels of logic when implemented using conventional logic primitives, but also allows the selection of that subset of functions by assignment of the transistor threshold voltages to the input transistors. To obfuscate the functionality of the TLG, weights of some inputs are set to zero by setting their device threshold to be a high Vt. The threshold voltage of the remaining transistors is set to low Vt to increase their transconductance. The number of low Vt transistors whose gates are driven by a given input xi determines the weight of that input. The function of a TLG is not determined by the cell itself but rather the signals that are connected to its inputs. This makes it possible to hide the support set of the function by essentially removing some variable from the support set of the function. This is done by selective assignment of high and low Vt to the input transistors. We describe how a standard cell library of TLGs can be mixed with conventional standard cells to realize complex logic circuits, whose function can never be discovered by reverse engineering. A 32-bit Wallace tree multiplier and a 28-bit 4-tap filter were synthesized on an ST 65nm process, placed and routed, then simulated including extracted parastics with and without obfuscation. By obfuscating the cells the delay was shown to increase by approximately 5% at the cell level. Both obfuscated designs had much lower area (25%) lower area and much lower dynamic power (30%) than their nonobfuscated CMOS counterparts, operating at the same frequency.

Integration of threshold logic gates with RRAM devices for energy efficient and robust operation

Differential mode threshold-logic gates can be programmed to compute complex logic functions within a single cell, resulting in significant reduction in area and power. However the circuit yield reduces if they are operated at low voltages. This paper describes a novel integration of RRAM with such threshold-logic gates to achieve robust, low voltage (0.6V for 65nm technology) and energy efficient computation of threshold-logic functions. Below 0.6V, we observed that the performance(and thereby, energy delay product) of conventional CMOS circuits degrades substantially compared to the proposed threshold-logic circuits. The improvement in performance and energy of the new circuit architecture are demonstrated while considering process variations in both the MOSFET and RRAM devices. For each threshold function implementable by threshold-logic gate, comparison of energy, delay and energy delay product with equivalent CMOS implementation is given. The advantages in area, energy and delay of threshold logic implementations over conventional CMOS logic gates is demonstrated by two commonly used functional components.

Spintronic threshold logic array (STLA) - a compact, low leakage, non-volatile gate array architecture

This paper describes a novel, first of its kind architecture for a threshold logic gate using conventional MOSFETs and an STT-MTJ (Spin Torque Transfer-Magnetic Tunnelling Junction) device. The resulting cell, called STL which is extremely compact can be programmed to realize a large number of threshold functions, many of which would require a multilevel network of conventional CMOS logic gates. Next, we describe a novel array architecture consisting of STL cells onto which complex logic networks can be mapped. The resulting array, called STLA has several advantages not available with conventional logic. This type of logic (1) is non-volatile, (2) is structurally regular and operates like DRAM, (3) is fully observable and controllable, (4) has zero standby power. These advantages are demonstrated by implementing a 16-bit carry look-ahead adder and compared with two optimized conventional FPGA implementations (Carry Look Ahead Adder and Ripple Carry Adder). The STLA has 12X lower transistor count (compared to CLA-FPGA) and 10X reduction (compared to RCA-FPGA) with comparable energy which will continue to reduce as the STT-MTJ device technology matures.

A Clock Skewing Strategy to Reduce Power and Area of ASIC Circuits

A new method for reducing power and area of standard cell ASICs is described. The method is based on deliberately introducing clock skew without the use of extra buffers in the clock network. This is done by having some flipflops, called sources, generate clock signals for other flipflops, called targets. The method involves two key features: (1) the design of new differential flipflop, referred to as KVFF, that is functionally identical to a master-slave edge-triggered D flipflop, but in addition, produces an completion signal that is a skewed version of its input clock, which is used to clock other flipflops; and (2) an efficient algorithm that identifies the sources and targets involved in the new clocking scheme, with the objective of reducing area and power. These are reduced because deliberate skew introduces extra slack on the logic cones that feed the target flipflops, which is exploited by synthesis tools to reduce area and power. In addition, the overhead of conventional methods of introducing skew, e.g. buffers, is eliminated. Using commercial tools, significant improvements in power and area are shown on placed and routed netlists of several circuits.

Fast and robust differential flipflops and their extension to multi-input threshold gates

In this paper, we describe two single input threshold gate (TLG) designs, which are functionally equivalent to differential flipflops. We present a detailed comparison of TLGs with two well established D-flipflop designs. The comparisons are done in both 65nm and 28nm commercial processes. We compare total delay, which is defined as the sum of setup delay and clock to output delay. We also show a comparison of tolerance against noise and process variation between the different designs. The two proposed designs are found to be as robust as an existing D-flipflop from both commercial standard cell libraries. Meanwhile, they are 33% and 25% faster in 65nm post-layout and 25% and 22% faster in 28nm post-layout compared to a commercial D-flipflop. The energy delay product of two proposed designs is 46% and 25% smaller in the 28nm process post layout simulation. Single input threshold gates can also be extended to multi-input threshold gates. We compare the total delay, power and leakage of a three-input threshold gate as well as a seven-input threshold gate with those of the equivalent (Complementary Metal Oxide Semiconductor) CMOS counterpart, which shows 52% 48% improvement in 65nm and 35% speed improvement in the 28nm process.

Dynamic and leakage power reduction of ASICs using configurable threshold logic gates

This article demonstrates an unconventional approach to computing logic functions for use in ASICs, and a fully automated approach to technology mapping for standard cell ASICs using the new cells. The approach results in a significant reduction in power, leakage, area and wire-length, without sacrificing performance of the design. At the heart of this approach is a configurable threshold logic gate. Using a standard cell library of such gates, a new technology mapping algorithm is applied to automatically transform a given netlist into one with an optimal mixture of conventional logic gates and threshold gates. The mapping algorithm is based on logic decomposition of Boolean functions into specific threshold functions. This approach was used to fabricate a 32-bit signed 2-stage Wallace-Tree multiplier in a 65-nm LP technology. Simulation and chip measurement results of the multiplier show a 33% improvement in dynamic power at 30% switching activity, 24% lower core area, 45% lower wire-length and 50% lower leakage without any performance degradation, compared to a functionally equivalent, conventional standard cell implementation. Similar results are shown for a FIR filter, a 32-bit MIPS, a 128-bit AES encryption circuit and a floating-point multiplier.