Magnitude vs. representation: “When converting a decimal number to hexadecimal, the hex result will be a larger number than the original decimal.” Decide whether this claim makes sense in number-system conversions.

Introduction / Context:
Conversions among bases (decimal, binary, hexadecimal) preserve numeric value. What changes is the representation—the symbols and their positions. The statement claims the hexadecimal result will be “larger,” which confuses value with how many digits or which symbols appear in a given base.

Given Data / Assumptions:

• Decimal is base-10, hex is base-16.
• “Larger number” is interpreted as larger numeric value, not “more characters” or “visually higher symbols like A–F.”
• Standard positional weights apply: base^position.

Concept / Approach:
Base conversion is an isomorphism on natural numbers: value stays identical. For example, decimal 255 equals hex FF and binary 11111111; all three denote the same quantity. Digit count and glyph choices differ, but the magnitude does not change because we are only re-expressing the same value in a different radix.

Step-by-Step Solution:

Verification / Alternative check:
Try another: decimal 12 = hex C. Although “C” looks like a single symbol, its value remains 12. Similarly, decimal 4096 = hex 1000; both represent the same magnitude with different digit counts due to base choice.

Why Other Options Are Wrong:

• Correct: Would falsely imply value inflation through conversion.
• Only true above 255 / BCD / endianness: These factors do not alter mathematical equality across bases.

Common Pitfalls:
Equating string length or alphabetic ordering with numeric magnitude; assuming that “letters” in hex imply larger value than digits; confusing byte order (endianness) with base conversion (they are unrelated concepts).

Final Answer:
Incorrect