Digital computers represent and encode all internal data and programs using which number system?

Introduction / Context:
This question covers one of the most fundamental ideas in computer science. Although humans usually think in decimal numbers, digital computers represent data in a different form. Understanding the basic number system that computers use internally is important for topics such as data representation, storage size and low level programming.

Given Data / Assumptions:

• The focus is on digital computers.
• The question asks which system they use to encode data and programs.
• Options include semiconductor, decimal, binary, RAM and hexadecimal only.
• We assume standard digital electronics, where hardware is based on two voltage levels.

Concept / Approach:
Digital computers are built from electronic circuits that can distinguish between two stable states, often represented as high and low voltage. These two states are naturally modelled using the binary number system, which has only two digits, zero and one. Each binary digit is called a bit. While hexadecimal is used as a convenient shorthand for groups of bits, the actual hardware operates in binary. Decimal is used mainly for human interfaces, not internal encoding.

Step-by-Step Solution:
Step 1: Recall that digital devices use two states to represent information, such as on or off, high or low voltage. Step 2: The number system that matches two states is the binary system, which uses only digits zero and one. Step 3: Inside the computer, all data, including numbers, text and program instructions, is ultimately represented as sequences of bits. Step 4: Decimal uses ten digits and is efficient for human use but not for two state electronic circuits. Step 5: Hexadecimal is useful for human reading of binary values but is derived directly from binary patterns and is not the fundamental representation in hardware. Step 6: Semiconductor refers to the material used to build electronic components and is not a number system. Step 7: RAM is a type of memory, not a number system, so it cannot be the answer to this question. Step 8: Therefore, the correct answer is that digital computers use the binary number system to encode data and programs.

Verification / Alternative check:
Introductory computer science books always explain that computers use binary numbers internally. Examples show how decimal numbers such as ten are converted into binary representations such as one zero one zero. The text also describes how characters are encoded using binary codes such as ASCII or Unicode. At every level, the underlying representation is binary, even when hexadecimal or decimal notations are used for convenience by programmers.

Why Other Options Are Wrong:
The semiconductor option refers to hardware materials like silicon and is not a numeric encoding system. Decimal is used in user interfaces but is not practical for two state circuits internally. Random access memory is a hardware component and again not a number system. Hexadecimal is a base sixteen system used mainly as a shorter way to write binary values, not as the fundamental representation in hardware logic.

Common Pitfalls:
Some learners think that because programmers sometimes write values in hexadecimal, the computer uses hexadecimal internally. In reality, hexadecimal is a convenient way for humans to view binary data. The hardware logic still processes all data as binary patterns. Keeping this distinction clear will help you answer many basic digital logic and computer architecture questions correctly.

Final Answer:
Digital computers encode data and programs internally using the binary number system.