A digital computer internally represents and processes all data using which fundamental number system?

Introduction / Context:
Digital computers are built from electronic circuits that have two stable states, typically represented by low and high voltage levels. Because of this physical reality, computers naturally work with a number system that has two symbols rather than ten. Although humans usually think in decimal numbers, the machine itself uses a different representation. This question asks which fundamental number system a digital computer uses internally for all data processing.

Given Data / Assumptions:
- The topic is a general digital computer, such as a PC, laptop, or server.
- We are concerned with internal representation of data, not with how numbers may be displayed to users.
- The options mention binary, octal, decimal, and hexadecimal systems.
- We assume standard electronic digital circuitry based on two stable states.

Concept / Approach:
Digital circuits use transistors and logic gates that operate in two states, often described as off and on. These states map directly to a number system with two digits, 0 and 1. This system is the binary number system, also called base 2. All types of data, including numbers, characters, images, and sound, are encoded as sequences of binary digits. Octal and hexadecimal systems are sometimes used as shorthand representations for groups of binary digits, because they are more compact and easier for humans to read. However, these are just convenient notations. Inside the hardware, operations are performed on binary values, not octal or hexadecimal directly, and certainly not pure decimal representations.

Step-by-Step Solution:
Step 1: Recall that a bit is the smallest unit of information in a computer, and it can take the value 0 or 1. Step 2: Recognise that sequences of bits form binary numbers, which are base 2 representations of values. Step 3: Understand that all higher level data structures and formats are ultimately built from these binary sequences. Step 4: Consider octal and hexadecimal. Both of these systems group binary digits into sets of three or four, providing shorter human readable forms without changing the underlying base 2 nature of the data. Step 5: Note that decimal numbers are commonly used in user interfaces, calculators, and printed outputs, but they are converted to binary for actual processing inside the machine. Step 6: Therefore conclude that the correct answer is the binary (base 2) number system.

Verification / Alternative check:
Computer architecture textbooks and digital logic courses start by introducing binary numbers and logic gates. They show how addition, subtraction, and other operations can be performed directly on binary values using circuits such as adders and multiplexers. They also demonstrate how binary codes represent characters and other data types. In contrast, decimal, octal, and hexadecimal numbers are explained as alternate notations built on top of binary. This consistent teaching across many sources confirms that the fundamental system for internal computation is the binary number system.

Why Other Options Are Wrong:
Octal (base 8) number system: Used occasionally as a shorthand for binary but not as the internal working base of digital circuits.
Decimal (base 10) number system only: Used in user interfaces and printed output, but inside the machine all data is converted to binary before processing.
Hexadecimal (base 16) number system only: Similar to octal, hexadecimal is a convenient way for programmers to write large binary values, but the hardware still operates on binary digits.

Common Pitfalls:
Some students confuse the notation they see in programming or assembly language with the actual internal representation. For example, they may see addresses written in hexadecimal and assume the system works directly in base 16. Others may think that because humans enter decimal numbers from the keyboard, the computer must also store them this way. To avoid this confusion, remember that binary is the universal foundation, and all other bases are interpreted or converted to binary before use by the processor.

Final Answer:
A digital computer internally represents and processes data using the Binary (base 2) number system.