The computing elements and semiconductor chips that make up a computer

The computing elements and semiconductor chips that make up a computer

Digital processing, which is the basis of computers, is represented by two numbers “0” and “1” (binary digits). While a bit can represent only two states, “0” and “1,” a byte can represent 256 states (1 byte = 28=256).

Algebra (the study of solving equations using letters instead of numbers), which deals only with “0” and “1,” is called Boolean algebra. This Boolean algebra is a mathematical system invented by George Boole, and can be regarded as a logical mathematics that calculates logic with “1” as true and “0” as false.

In mathematics, the rule for determining a new number from two numbers is called a binomial operation. An example of this binomial operation is the four arithmetic operations on numbers (addition, multiplication, division, and subtraction). In Boolean algebra, the binary operations are ∨ (join) and ∧ (meet), and adding the unary operation ¬ (not), we obtain the exchange law (x∧y=y∧x, x∨y =y∨x), the join law ((x∧y)∧z=x∧(y∧z), (x∨y)∨z =x∨(y∨z)), the absorption law ((x∧y)∨x =x, (x∨y)∧x=x), the distribution law ((x∨y)∧z=(x∧z)∨(y∧z), (x∧y)∨z =(x∨z)∧(y∨z)), and the complement law (x∨¬x =1, x∧¬x=0). All operations and calculations can be expressed.

These axiomatic systems can be mathematically constructed by mathematical logic as described in “Making Logic, Part I: Notes on Beginning Logic” and “Formal Languages and Mathematical Logic“. For the mathematical basis of set theory, see “Fundamentals of Computer Mathematics” and “What is a set?

As mentioned above, all Boolean algebra (computations that can be performed on a computer) can be expressed as a combination of ∨ (join), ∧ (meet), and ¬ (not). This means that the basic elements to realize the computational function of a computer are only ∨ (join), ∧ (meet), and ¬ (not).

Among these, ∧ (meet) is also called AND in the world of logic, and can be expressed as a function using two switches in series as shown in the following figure. (The whole is turned on only when both switches A and B are turned on.)

The input-output relationship of this function is expressed as follows

In the world of logic, ∨ (join) is called logical OR, and its function is represented by switching in parallel, as shown in the following figure. (When either A or B is turned on, the whole is also turned on.)

The input-output relationship of this function is expressed as follows

Finally, ¬(˜not) is called NOT in the world of logic, and is manifested by the concept shown in the following figure.

The input-output relationship of this function is expressed as follows

From the above, it is clear that to construct the basic elements for computer computation, namely ∨ (join), ∧ (meet), and ¬ (not), it is sufficient to have an internal switch function. MOS transistors realize this switching, and a large number of MOS transistors are integrated into a semiconductor chip called an IC (Integrated Circuit) chip.

A semiconductor used in a semiconductor chip is literally a half-conductor (conducts electricity), and refers to a material with electrical resistance between conductors that conduct electricity (metals such as gold, silver, aluminum, and copper) and insulators that do not conduct electricity (glass, ceramics, and most plastics). Typical semiconductors include silicon (Si) and selenium (Se). In the periodic table, non-metallic materials are shown in light blue in the upper right part of the figure below.

However, simply having a resistance that is between that of a metal and that of an insulator does not make it a semiconductor. A semiconductor is one whose characteristics change, becoming an insulator or a conductor, depending on external electrical stimuli. Si and Se are semiconductors by themselves, while Ga and Cd become semiconductors when combined with other elements such as As.

Conductivity is achieved by the electrons (and electron holes, which are electron-deficient regions) of each atom. Electrons exist in a specific probability distribution around the nucleus, which can be calculated using statistical methods called statistical physics (the application of such methods to machine learning is a stochastic generative model such as Bayesian inference, as described in “About Stochastic Generative Models“). The following figure illustrates the distribution of s, p, and d orbitals learned in high school physics (chemistry), and each primitive electronic state is represented by a combination of these orbitals (e.g., sp3 state).

Si has electrons that are not strongly bound to these orbitals, which can move freely and exhibit “semiconductivity,” or by introducing tiny dopants (P, which has one more electron than Si (right neighbor on the periodic table), or B, which has one less electron (left neighbor on the periodic table)) into the Si structure, the electrons that can move inside are controlled. P and B).

MOS transistor (MOSFET) stands for Metal-Oxide-Semiconductor Field Effect Transistor and consists of

The basic operation is that there is an electron transfer area called the channel region in the center of the drain and source, and current flows from the gate electrode formed through an oxide film (insulating layer) on top of the channel region to achieve the switch function.

The principle of the computer is to use this switching function to construct the aforementioned ∨ (join), ∧ (meet), and ¬ (not) to realize all kinds of calculations. The latest CPUs are equipped with hundreds of millions of these transistors.

In the next article, we will discuss the semiconductor design process and semiconductor chips for AI applications.