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Digital theory, logic, and two-state control
Published in Raymond F. Gardner, Introduction to Plant Automation and Controls, 2020
Boolean logic is named after George Boole, and uses two-state inputs and two-state outputs in a logic-gate decision-making process. The two states are often described as “true” or “false,” and are commonly represented as “1” or “0.” Conditional states are passed into logic gates where they are manipulated into a single true/false or 1/0 output. In Boolean logic, there are seven types of simple logic gates. The three primary gates are AND, OR, and NOT gates and are shown in Figure 4.1. The three primary gates form building blocks for creating the remaining four gates. The NOT gate is simply an inverter that toggles a single input to its opposite value as its output. Input/output maps and truth tables are two ways of showing every combination of input states and their resulting outputs, and they are useful for visualizing the output produced by logic functions. The input/output maps, truth tables, and Boolean representation symbols are shown in Figure 4.1 for the primary gates.
The Emergence of Temporal Order in a Chemical Laboratory
Published in Pier Luigi Gentili, Untangling Complex Systems, 2018
The repressilator is the biochemical counterpart of the ring oscillator in electronics. A ring oscillator is a device composed of an odd number of NOT gates. A scheme is shown in Figure 8.14. A NOT gate is a single input device that inverts the logic level of its input signal. In fact, it gives the output logic level 1 when the input is at the logic level 0, and the output logic level 0 when the input is at the logic level 1. In the ring oscillator, the output of the last inverter is fed back into the first. From Figure 8.14 it is evident that the last output of the chain is the logical NOT of the first input. This situation occurs whenever the chain contains an odd number of inverters. The final output of the ring oscillator is asserted a finite amount of time after the first input is asserted; the feedback of this last output to the input produces oscillations.
Digital Circuits
Published in Wai-Kai Chen, Analog and VLSI Circuits, 2018
John P. Uyemura, Robert C. Chang, Bing J. Sheu
The propagation delay tP for the gate is the average time required for a change in the input to be seen at the output. It is computed using the time intervals tPHL and tPLH shown in the diagram from () tP=(12)(tPHL+tPLH)
3D Double-Gate Junctionless Nanowire Transistor-Based Pass Transistor Logic Circuits for Digital Applications
Published in IETE Journal of Research, 2022
Achinta Baidya, Trupti R. Lenka, Srimanta Baishya
The main advantage of the pass transistor logic circuit is reduction in the number of transistors compared to conventional CMOS circuits. Pass transistor logic-based AND gate in Figure 6 uses only two n-JNTs. Transistor number decreases by 50% compared to CMOS configuration. Again Pass transistor logic circuits have an advantage of very low power dissipation as its operation depends only on the input signal voltages and no separate power supply is required. Two-input n-JNT PTL schematics for AND and OR gates, along with truth tables, are shown in Figures 6 and 7. These PTL circuits are prepared using only n-type JNTs. Keeping the gate voltages fixed, if we invert the inputs, PTL AND gate can work as an NAND gate and OR gate can work as an NOR gate. Thus, evaluating PTL AND and OR gate performance of JNT we can predict performance in NAND and NOR too.
A Novel Slice-Based High-Performance ALU Design Using Prospective Single Electron Transistor
Published in IETE Journal of Research, 2022
Rashmit Patel, Yash Agrawal, Rutu Parekh
The design of AL slice is shown in Figure 4. The AL slice is designed with SET-based inverter, NAND gate, NOR gate, and combination of these gates. The hardware design of the AL slice shows that it performs operation on two input signals, “A” and “B”. The AL slice performs desired operation based on the five input control signals, namely “sel_neg”, “sel_op1”, “sel_op2”, “shift_r”, and “force_carry1”. Table 1 describes each control signal value for specified instruction. The “carry_prev” and “Anext” are cascade inputs that are used to cascade multiple AL slices. Based on the values of input, control and cascade signals, the AL slice generates “carry” and “result” outputs. The “carry” and “carry_prev” are inverted polarity signals. Each AL slice comprises 74 SETs.
Delay and Energy Efficient Modular Hybrid Adder for Signal Processor Architectures
Published in IETE Journal of Research, 2022
It can be understood from Equation (19), that a reduction in critical path length may be achieved through a reduction in delay incurred by FSL of the final adder stage. For simplifying the representations in this section, it is assumed that . The carry cout of the penultimate adder stage has to ripple through an and-xor chain consisting of and gates and an xor gate for producing the most significant sum bit . As per the design of FSL in Figure 10, the sum generation in the final stage takes place sequentially. The LSB of the final adder stage is generated first with an xor gate delay. The sum bit is generated next with an and gate and xor gate delay and so on such that requires a delay equal to the sum of delays of (k − 1) and gates and an xor gate.