Digital electronics

Digital electronics is a fun field that studies digital signals and the devices that make or use them. Unlike analog electronics, which work with signals that 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 go 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 put together, they can show 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. Learning how these circuits work helps us make smarter and faster electronic devices.

History

The binary number system was refined by Gottfried Wilhelm Leibniz to connect arithmetic and logic. Digital logic started with George Boole in the 1800s, and Charles Sanders Peirce showed how electricity could do logic tasks. Early devices used vacuum tubes, but transistors changed everything.

Claude Shannon showed that electricity could handle logic, which started digital computers. The first electronic digital computer, the Z3, was built by Konrad Zuse in 1941. Transistors, invented in the late 1940s, were smaller and used less power than vacuum tubes. By the 1950s, computers used transistors. The integrated circuit in the late 1950s let many transistors fit on one chip, making modern digital devices possible. The wireless revolution in the 1990s gave us digital TV, mobile phones, and wireless Internet, thanks to advances in digital electronics.

Properties

Digital circuits are better than analog circuits because digital signals do not get worse from interference. For example, a sound can be sent as a series of 1s and 0s and then put back together perfectly, if the interference is not too strong.

In digital systems, you can make a signal more exact by using more 1s and 0s. This needs more digital parts, 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 with 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.

Integrated circuits are made by putting many transistors on a tiny silicon chip. They are a good 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 ways to make digital circuits simpler. This helps use fewer parts and can save money. There are special methods for this, such as binary decision diagrams, Boolean algebra, Karnaugh maps, the Quine–McCluskey algorithm, and computer programs called computer-aided design systems.

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

A digital circuit’s inputs and outputs can be shown in a truth table. A big circuit uses logic gates, each shown as a different shape. A small circuit uses electronic switches, usually transistors.

Most digital systems are split into two types: combinational and sequential systems. The output of a combinational system depends only on the current inputs. But a sequential system’s output may depend on past inputs too, making a sequence of steps. Simple drawings called state machines help with design and testing.

Sequential systems are divided into synchronous and asynchronous systems. Synchronous sequential systems change 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 build a synchronous sequential state machine is to split it into combinational logic and a group 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.

Many digital systems are data flow machines. They are often built using synchronous register transfer logic and written with special 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 built as a microprogram run by a microsequencer. A microprogram is like a player-piano roll. Each part of 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 holds 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 building the computer’s controls easier by using simpler logic machines.

Most computers work synchronously. But asynchronous computers have also been built. They use less power because they do not need a clock. They are used in some mobile-phone base-station controllers and may be more secure for some uses.

Computer architecture is a special engineering job that organizes the registers, logic, buses, and other parts of a computer for a specific purpose. Engineers work to save money, make things faster, and improve reliability. A common goal is to save power in devices like smartphones.

Digital circuits are built from analog parts. Design must make sure these parts do not affect the digital behavior. Digital systems must deal with noise, timing issues, and other problems.

Much of the work in building big logic machines is done automatically using electronic design automation (EDA). Simple descriptions of logic can be made better to use fewer logic gates or smaller tables. Common tools include the Espresso heuristic logic minimizer, the Quine–McCluskey algorithm, and binary decision diagrams. Other methods are also being tested.

EDA tools can take tables that describe state machines and make truth tables or function tables for the combinational logic. Real logic systems are often built in steps, put together using a tool flow controlled by a scripting language. Tool flows for big systems like microprocessors can have thousands of steps.

Parts of tool flows are tested by comparing simulated outputs with expected inputs. Once the input data is right, the design itself must be checked. Some tool flows check designs by looking for matching input data.

Tests called test vectors may be used in factories to test new logic. Tests are often made by automatic test pattern generation software, which looks at the logic structure and makes tests for possible problems.

Once a design exists and is checked, it must be made. Modern integrated circuits have very small parts, smaller than the wavelength of light used to expose photoresist. Software adds patterns to exposure masks to prevent problems and improve quality.

There are several reasons to test a logic circuit. When a circuit is first built, it must work right and meet timing rules. When many copies are made, each must be tested to make sure there are no manufacturing problems.

Big logic machines are often built from smaller parts. To save time, these smaller parts are tested separately using special test circuitry. One common way is boundary scan, which uses serial communication with outside test tools through shift registers called scan chains. After test data is in place, the design is tested, and results are checked against expected values.

In board testing, serial-to-parallel testing is done using the JTAG standard.

Cost

Because 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, using fewer chips saved money. Designers try to keep the number of parts low, which can sometimes make designs more complicated but still uses fewer parts, smaller boards, and less power.

Reliability

Another reason to use fewer parts is to lower the chance of manufacturing mistakes and make things more reliable. 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, extra logic can be added. This costs more and uses more power.

The reliability of a logic gate can be measured 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 going over current limits. The smallest useful 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 usually switches at 5 GHz, and some lab systems switch at more than 1 THz.

Logic families

Main article: Logic family

Digital design started with relay logic. This was slow and could break because of problems with its parts. Later, vacuum tubes were used. These were faster but could get too hot and stop working.

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

Transistor–transistor logic (TTL) was a big improvement. It worked faster and could handle more connections. Today, most digital circuits use CMOS logic. This 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 using very little space and power.

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. Recently, people have been trying to build computers that use light, called optical computing, to process information using special materials known as nonlinear optical elements.