Digital electronics

Digital electronics is a fascinating field that studies digital signals and the devices that create or use them. Unlike analog electronics, which work with signals that can change smoothly, digital electronics uses signals that have only two states, like high voltage or low voltage. These signals can be mapped to binary numbers, which are the building blocks of all modern computing.

In digital electronics, electrical signals pass through special parts called logical gates, resistors, capacitors, amplifiers, and other electronic components. These parts help control how the signals behave and process information.

When many logic gates are combined together, they can represent more complex ideas and tasks. These groups of gates are often placed into tiny packages called integrated circuits, which are found in almost every piece of modern technology, from computers to smartphones. Understanding how these circuits work helps us create smarter and faster electronic devices.

History

The binary number system was refined by Gottfried Wilhelm Leibniz, who showed that it could join arithmetic and logic. Digital logic began with George Boole in the 1800s, and Charles Sanders Peirce described how electricity could perform logic tasks. Early devices used vacuum tubes, but later, transistors changed everything.

Claude Shannon proved that electricity could handle logic, laying the groundwork for digital computers. The first electronic digital computer, the Z3, was built by Konrad Zuse in 1941. Transistors, invented in the late 1940s, were smaller, better, and used less power than vacuum tubes. By the 1950s, computers used transistors instead of tubes. The invention of the integrated circuit in the late 1950s allowed many transistors to be placed on a single chip, making modern digital devices possible. The wireless revolution in the 1990s brought us digital TV, mobile phones, and wireless Internet, all thanks to advances in digital electronics.

Properties

Digital circuits have an advantage over analog circuits because digital signals can be sent without getting worse from interference. For example, a sound can be sent as a series of 1s and 0s and then put back together perfectly, as long as the interference isn’t too strong.

In digital systems, you can make a signal more exact by using more 1s and 0s. This needs more digital parts to work, but each part does the same job, making it easy to grow the system. Digital systems also let you store information without it getting worse over time, unlike analog systems. Even if there is some interference, the original information can often be recovered if you add extra copies of the data.

Construction

Digital circuits are built using small parts called logic gates. These gates help create different types of logic, like combinational logic and sequential logic. Each gate works by following rules of Boolean logic when it receives signals.

Another way to build digital circuits is by using lookup tables, often sold as programmable logic devices. These can do the same jobs as logic gates but can be changed easily without moving wires around. This makes it simpler to fix mistakes.

Integrated circuits are made by putting many transistors on a tiny silicon chip. They are a cost-effective way to create lots of connected logic gates. These chips are usually placed on a printed circuit board, which links all the parts together with copper paths.

Design

Engineers use many methods to make digital circuits simpler. This helps reduce the number of parts needed and can lower the cost. There are several well-known techniques for this, such as binary decision diagrams, Boolean algebra, Karnaugh maps, the Quine–McCluskey algorithm, and the heuristic computer method. These tasks are usually done using special computer programs called computer-aided design systems.

Embedded systems with microcontrollers and programmable logic controllers are often used to create digital logic for complex systems. These systems are usually programmed by software engineers or electricians, using ladder logic.

A digital circuit’s input-output relationship can be shown in a truth table. A high-level circuit uses logic gates, each shown as a different shape. A low-level representation uses electronic switches, usually transistors.

Most digital systems are split into combinational and sequential systems. The output of a combinational system depends only on the current inputs. However, a sequential system’s output may depend on past inputs as well as current inputs, creating a sequence of operations. Simplified representations called state machines help with design and testing.

Sequential systems are divided into synchronous and asynchronous systems. Synchronous sequential systems change state all at once when a clock signal changes. Asynchronous sequential systems change whenever inputs change. Synchronous systems use flip flops to store information.

Main article: synchronous logic

The usual way to create a synchronous sequential state machine is to split it into combinational logic and a set of flip flops called a state register. The state register shows the state as a binary number. The combinational logic decides the next state. On each clock cycle, the state register updates with new information from the combinational logic.

Many digital systems are data flow machines. They are often designed using synchronous register transfer logic and written with hardware description languages such as VHDL or Verilog.

In register transfer logic, binary numbers are stored in groups of flip flops called registers. A sequential state machine controls when each register gets new data. The outputs of each register are wires called a bus that carry the number to other calculations. Each calculation is a piece of combinational logic with its own output bus, which can connect to several registers. Sometimes a register has a multiplexer to choose data from different buses.

The most general-purpose register-transfer logic machine is a computer. It works like an automatic binary abacus. The control unit of a computer is usually designed as a microprogram run by a microsequencer. A microprogram is like a player-piano roll. Each entry in the microprogram tells the state of every bit that controls the computer. The sequencer counts, and the count points to the memory or logic that contains the microprogram. The bits from the microprogram control the arithmetic logic unit, memory, and other parts of the computer, including the microsequencer itself. This makes designing the computer’s controls easier by programming simpler logic machines.

Most computers are synchronous. However, asynchronous computers have also been built. They do not have speed advantages because modern computers already run at the speed of their slowest part, usually memory. They use less power because they do not need a clock network. An unexpected benefit is that asynchronous computers do not create strong radio noise. They are used in some mobile-phone base-station controllers and may be more secure for certain applications.

Computer architecture is a specialized engineering activity that arranges the registers, logic, buses, and other parts of a computer for a specific purpose. Architects work to reduce cost, increase speed, and improve reliability. A common goal is to reduce power use in battery-powered devices like smartphones.

Digital circuits are made from analog parts. Design must ensure that the analog nature of these parts does not interfere with the digital behavior. Digital systems must handle noise, timing issues, and other factors.

Much of the work in designing large logic machines is done automatically using electronic design automation (EDA). Simple descriptions of logic can be optimized to use fewer logic gates or smaller tables. Common tools include the Espresso heuristic logic minimizer, the Quine–McCluskey algorithm, and binary decision diagrams. Genetic algorithms and annealing optimizations are also being tested.

EDA tools can take state tables that describe state machines and create truth tables or function tables for the combinational logic. Often, real logic systems are built in stages, combined using a tool flow controlled by a scripting language. Tool flows for large systems like microprocessors can be thousands of commands long.

Parts of tool flows are tested by comparing simulated outputs with expected inputs. Once the input data is correct, the design itself must be checked. Some tool flows verify designs by scanning them to match input data.

Functional verification data, called test vectors, may be used in factories to test new logic. Production tests are often created by automatic test pattern generation software, which examines the logic structure and creates tests for possible faults.

Once a design exists and is verified, it must be processed to be made. Modern integrated circuits have very small features, smaller than the wavelength of light used to expose photoresist. Software designed for manufacturability adds patterns to exposure masks to prevent open-circuits and improve contrast.

There are several reasons to test a logic circuit. When a circuit is first developed, it must meet functional and timing requirements. When multiple copies are made, each must be tested to ensure no manufacturing flaws.

Large logic machines are often built from smaller parts. To save time, these smaller parts are tested separately using special test circuitry. One common method is boundary scan, which uses serial communication with external test equipment through shift registers called scan chains. After test data is in place, the design is tested, and results are compared to expected values.

In board testing, serial-to-parallel testing is formalized as the JTAG standard.

Cost

Since digital systems use many logic gates, their cost depends on the cost of a single gate. In the 1930s, digital logic was built from telephone relays because they were cheap and reliable.

The first integrated circuits were made to save weight and control spacecraft guidance systems. Early integrated circuit logic gates cost nearly US$50. Mass-produced gates on integrated circuits became the cheapest way to build digital logic.

With integrated circuits, reducing the number of chips saved costs. Designers aim to keep the component count low, which can sometimes lead to more complicated designs but still reduces the number of parts, board size, and power use.

Reliability

Another reason to reduce the number of parts is to lower the chance of manufacturing defects and increase reliability. More parts mean more chances for failure.

The failure of a single logic gate can make a digital machine stop working. Where extra reliability is needed, redundant logic can be added. Redundancy costs more and uses more power.

The reliability of a logic gate can be described by its mean time between failure (MTBF). Digital machines became useful when the MTBF for a switch was more than a few hundred hours. Modern transistorized integrated circuit logic gates have MTBFs greater than 82 billion hours. This high reliability is needed because integrated circuits have so many logic gates.

Fan-out

Fan-out describes how many logic inputs can be controlled by one logic output without exceeding current limits. The minimum practical fan-out is about five. Modern logic gates using CMOS transistors have higher fan-outs.

Speed

Switching speed is how long it takes a logic output to change from true to false or vice versa. Faster logic can do more operations in less time. Modern digital logic routinely switches at 5 GHz, and some lab systems switch at more than 1 THz.

Logic families

Main article: Logic family

Digital design began with relay logic, which was slow and sometimes broke because of mechanical problems. Later, vacuum tubes were used. These were fast but could get too hot and sometimes stopped working.

The first semiconductor logic family was resistor–transistor logic. It was much better than tubes, used less power, and didn’t get as hot, but it still had some limits. Diode–transistor logic improved things a bit more.

Transistor–transistor logic (TTL) was a big step forward. It worked faster and could handle more connections. Today, most digital circuits use CMOS logic, which is fast, fits a lot in a small space, and doesn’t use much power. This type is used in many modern computers, like the IBM System z.

Recent developments

In 2009, scientists found that special parts called memristors can store information and work with very little space and power, using common methods for making tiny chips.

They also discovered that superconductivity helped create a new kind of circuit called rapid single flux quantum (RSFQ), which uses special links called Josephson junctions instead of regular parts. Recently, people have been trying to build computers that use light, called optical computing, to process information using special light-bending materials known as nonlinear optical elements.