Hex-to-binary mapping cardinality: Each single hexadecimal digit directly maps to how many binary digits (bits)?

Introduction / Context:
Engineers prefer hexadecimal because it compresses binary data while preserving exact structure. Understanding the fixed correspondence between hex digits and binary bits is essential for fast conversions and for reading machine-level representations.

Given Data / Assumptions:

• Base-16 uses symbols 0–9 and A–F.
• We are mapping a single hex digit to binary.
• No sign or arithmetic; pure notation mapping.

Concept / Approach:
Because 16 = 2^4, every hex digit encodes exactly 4 binary bits (a nibble). This one-to-one mapping enables simple grouping: one hex digit ↔ one nibble. Consequently, two hex digits map to a byte (8 bits), and so on.

Step-by-Step Solution:
Note 16 = 2^4.Therefore, each hex digit spans the range 0–15, which is exactly the range of a 4-bit binary field (0000–1111).Hence, 1 hex digit ↔ 4 binary digits.

Verification / Alternative check:
Convert a sample digit: A₁₆ = 10₁₀ = 1010₂ (4 bits); F₁₆ = 15₁₀ = 1111₂ (also 4 bits). Examples confirm the fixed 4-bit width per digit.

Why Other Options Are Wrong:
eight would correspond to two hex digits (a byte).
12 and six have no standard base relationship for a single hex digit.

Common Pitfalls:
Confusing byte-level groupings (8 bits) with per-digit mappings; assuming leading zeros can be dropped within a nibble (they must be kept to preserve 4-bit width).

Final Answer:
four