# Digital Integrated Circuits Arithmetic Circuits...

In the previous chapter, we discussed about the basic applications of op-amp. Note that they come under the linear operations of an op-amp. In this chapter, let us discuss about arithmetic circuits, which are also linear applications of op-amp.

## Digital Integrated Circuits Arithmetic Circuits...

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The electronic circuits, which perform arithmetic operations are called as arithmetic circuits. Using op-amps, you can build basic arithmetic circuits such as an adder and a subtractor. In this chapter, you will learn about each of them in detail.

A microprocessor is a computer processor where the data processing logic and control is included on a single integrated circuit (IC), or a small number of ICs. The microprocessor contains the arithmetic, logic, and control circuitry required to perform the functions of a computer's central processing unit (CPU). The IC is capable of interpreting and executing program instructions and performing arithmetic operations.[1] The microprocessor is a multipurpose, clock-driven, register-based, digital integrated circuit that accepts binary data as input, processes it according to instructions stored in its memory, and provides results (also in binary form) as output. Microprocessors contain both combinational logic and sequential digital logic, and operate on numbers and symbols represented in the binary number system.

Before microprocessors, small computers had been built using racks of circuit boards with many medium- and small-scale integrated circuits, typically of TTL type. Microprocessors combined this into one or a few large-scale ICs. While there is disagreement over who deserves credit for the invention of the microprocessor, the first commercially available microprocessor was the Intel 4004, designed by Federico Faggin and introduced in 1971.[2]

As integrated circuit technology advanced, it was feasible to manufacture more and more complex processors on a single chip. The size of data objects became larger; allowing more transistors on a chip allowed word sizes to increase from 4- and 8-bit words up to today's 64-bit words. Additional features were added to the processor architecture; more on-chip registers sped up programs, and complex instructions could be used to make more compact programs. Floating-point arithmetic, for example, was often not available on 8-bit microprocessors, but had to be carried out in software. Integration of the floating-point unit, first as a separate integrated circuit and then as part of the same microprocessor chip, sped up floating-point calculations.

Occasionally, physical limitations of integrated circuits made such practices as a bit slice approach necessary. Instead of processing all of a long word on one integrated circuit, multiple circuits in parallel processed subsets of each word. While this required extra logic to handle, for example, carry and overflow within each slice, the result was a system that could handle, for example, 32-bit words using integrated circuits with a capacity for only four bits each.

Microprocessors can be selected for differing applications based on their word size, which is a measure of their complexity. Longer word sizes allow each clock cycle of a processor to carry out more computation, but correspond to physically larger integrated circuit dies with higher standby and operating power consumption.[3] 4-, 8- or 12-bit processors are widely integrated into microcontrollers operating embedded systems. Where a system is expected to handle larger volumes of data or require a more flexible user interface, 16-, 32- or 64-bit processors are used. An 8- or 16-bit processor may be selected over a 32-bit processor for system on a chip or microcontroller applications that require extremely low-power electronics, or are part of a mixed-signal integrated circuit with noise-sensitive on-chip analog electronics such as high-resolution analog to digital converters, or both.Some people say that running 32-bit arithmetic on an 8-bit chip could end up using more power, as the chip must execute software with multiple instructions.[4]However, others say that modern 8-bit chips are always more power-efficient than 32-bit chips when running equivalent software routines.[5]

The advent of low-cost computers on integrated circuits has transformed modern society. General-purpose microprocessors in personal computers are used for computation, text editing, multimedia display, and communication over the Internet. Many more microprocessors are part of embedded systems, providing digital control over myriad objects from appliances to automobiles to cellular phones and industrial process control. Microprocessors perform binary operations based on boolean logic, named after George Boole. The ability to operate computer systems using Boolean Logic was first proven in a 1938 thesis by master's student Claude Shannon, who later went on to become a professor. Shannon is considered "The Father of Information Theory".

Following the development of MOS integrated circuit chips in the early 1960s, MOS chips reached higher transistor density and lower manufacturing costs than bipolar integrated circuits by 1964. MOS chips further increased in complexity at a rate predicted by Moore's law, leading to large-scale integration (LSI) with hundreds of transistors on a single MOS chip by the late 1960s. The application of MOS LSI chips to computing was the basis for the first microprocessors, as engineers began recognizing that a complete computer processor could be contained on several MOS LSI chips.[6] Designers in the late 1960s were striving to integrate the central processing unit (CPU) functions of a computer onto a handful of MOS LSI chips, called microprocessor unit (MPU) chipsets.

As applied t digital integrated circuits, the MDs transistor is studied in depth-from its fabrication to its electrical characteristics. Combinational, sequential, and dynamic logic circuits are considered. While the focus of the course is on CMOS technology, bipolar, nMOS, and BiCMOS circuits are introduced as well. SPICE is used as both an analysis and design tool. Semiconductor memory circuits are also discussed.

Vast arrays of arithmetic circuits have powered NVIDIA GPUs to achieve unprecedented acceleration for AI, high-performance computing, and computer graphics. Thus, improving the design of these arithmetic circuits would be critical in improving the performance and efficiency of GPUs.

In PrefixRL, we focus on a popular class of arithmetic circuits called (parallel) prefix circuits. Various important circuits in the GPU such as adders, incrementors, and encoders are prefix circuits that can be defined at a higher level as prefix graphs.

We pose arithmetic circuit design as a reinforcement learning (RL) task, where we train an agent to optimize the area and delay properties of arithmetic circuits. For prefix circuits, we design an environment where the RL agent can add or remove a node from the prefix graph, after which the following steps happen:

To the best of our knowledge, this is the first method using a deep reinforcement learning agent to design arithmetic circuits. We hope that this method can be a blueprint for applying AI to real-world circuit design problems: constructing action spaces, state representations, RL agent models, optimizing for multiple competing objectives, and overcoming slow reward computation processes such as physical synthesis.

Electrical Engineering 141: Introduction to Digital Integrated Circuits (Fall 2010, UC Berkeley). Instructor: Professor Elad Alon. This course is an introduction to digital integrated circuits. The material will cover CMOS devices and manufacturing technology along with CMOS inverters and gates. Other topics include propagation delay, noise margins, power dissipation, and regenerative logic circuits. This course will look at various design styles and architectures as well as the issues that designers must face, such as technology scaling and the impact of interconnect. Examples presented in class include arithmetic circuits, semiconductor memories, and other novel circuits.

Four-terminal FinFETs were extensively studied and analyzed in [4, 7]. The front and back gates of the four-terminal FinFET (4T FinFET) can be connected in various configurations. One of these configurations is to short both gates (SG FinFET). Alternatively, a 4T FinFET can be considered as two parallel transistors, and the two gates can be driven independently as shown in Figure 1. One gate which is normally called the back gate influences the vertical field of the other transistor in the channel area, hence altering its threshold voltage. Also, it impacts the diffusion current in the subthreshold regime of operation, hence controlling the leakage current. In addition, the two parallel transistors in the 4T FinFET can be tied together to improve drivability or to form a single transistor with its gates driven independently. This will be beneficial in reducing area and power dissipation in digital circuits [6]. For the device shown in Figure 1, the effective channel length and width are equal to and , respectively. The device parameters used in this paper are listed in Table 1.

Back gate biasing technique is more beneficial for NFinFETs due to their dominance in the total leakage current in FinFET based digital circuits. On the other hand, the back gate of PFinFETs is more beneficial to use in SG configuration to achieve high driving capability and performance since the PFinFETs have lower subthreshold leakage current than their N counterparts.

In this paper, four-terminal FinFETs have been extensively analyzed with the goal of reducing subthreshold leakage current. We applied both back gate biasing and asymmetric work functions, which are two effective methods to achieve ultra-low subthreshold leakage current level in FinFETs. We have used these powerful techniques to design optimized circuits for arithmetic components, namely, a full adder and compressor circuits in different configurations. Our simulation results show that by applying asymmetric work functions, the subthreshold leakage current can be reduced significantly with low delay penalty and we can also avoid the use of additional power supply. However, one must also consider that asymmetric circuits are more costly to fabricate since careful adjustment of the doping profiles is required for both sides of the same FinFET. 041b061a72