3.1Fundamental Theory

The gateway to the Technology field is "Fundamental Theory." Internally, a computer represents all data using only 0s and 1s—binary—and understanding this is the foundation for grasping hardware and programming. This section also covers logical operations at the heart of conditional judgment, basic probability and statistics for spotting trends in data, and the ideas behind machine learning that power AI.

3.1.1Binary, base conversion, and logical operations

• Binary represents numbers using only 0 and 1. Decimal "5" is "101" in binary (4+0+1). Base conversion converts numbers between decimal, binary, and hexadecimal. Four binary digits correspond to exactly one hexadecimal digit, which is why hexadecimal is often used to represent internal computer data.
• Logical operations combine true (1) and false (0) values to produce a result. AND is true only when both inputs are true (logical product). OR is true when at least one input is true (logical sum). NOT inverts true/false. XOR is true only when exactly one input is true (exclusive OR; false when both are true or both are false).

3.1.2Sets, statistics, information units, character encoding, and AI basics

• A set is a collection of things. A Venn diagram visualizes relationships between sets (intersection, union, difference) using overlapping circles. "A and B" corresponds to the overlapping area; "A or B" corresponds to the combined area of both circles.
• Correlation measures the strength of the relationship between two sets of data (e.g., as one increases, the other tends to increase or decrease). Correlation does not necessarily imply causation. Regression fits an equation (such as a line) to data trends in order to make predictions. The normal distribution is a symmetric, bell-shaped distribution centered on the mean, commonly seen in natural phenomena and measurements.
• A bit is the smallest unit of information (a single 0 or 1). A byte groups 8 bits together (representing 256 possible values). Character encoding maps characters to bit patterns (e.g., ASCII, Unicode); opening the same file with the wrong character encoding causes garbled text (mojibake).
• Machine learning is a technique in which a computer learns rules and patterns from large amounts of data on its own (the core of AI). A neural network is a computational model inspired by the connections of neurons in the human brain, forming the basis for machine learning—especially deep learning.

Consider a company survey to see how these fundamental-theory elements connect. Drawing a Venn diagram of respondents who "know product A" and those who "purchased product A," the overlapping area represents people who both know and purchased it—corresponding to the AND condition (both true) in logical operations. Conversely, "know OR purchased" corresponds to the combined area of both circles, the OR condition. Internally, the survey system might store each answer as a single bit of binary (1 for "yes," 0 for "no"), and eight such answers together make up 1 byte. When saving free-text responses, the character encoding must be kept consistent so Japanese text displays correctly—mismatched encodings cause garbled text when opened in another system. When analyzing results, even if a correlation appears between "number of ad exposures" and "purchase rate," that alone does not prove "the ad caused the purchases" (a third factor, such as season, could be influencing both). To express the trend as an equation and forecast future purchase rates, you would use regression analysis, and when data like respondents' ages clusters symmetrically around the mean, it may be treated as approximating a normal distribution. In recent years, AI is increasingly used to auto-classify free-text survey answers—behind the scenes, this relies on machine learning that learns patterns from large volumes of text (including deep learning, which uses neural networks modeled on the human brain's neural connections).

3.1.3Section summary

• Binary is how computers represent numbers. AND = both true; OR = at least one true; XOR = exactly one true
• Venn diagrams visualize set relationships. Correlation is not causation. Regression predicts trends; the normal distribution is bell-shaped
• 1 byte = 8 bits. Mismatched character encoding causes garbled text. Machine learning and neural networks underlie AI