Cross-base identity check — decimal 15 across binary, hex, and BCD: Validate the compound statement: “15₁₀ = 1111₂ = F₁₆ = 0001 0101 (BCD).”

Introduction / Context:
Verifying the same numeric value in different bases reinforces fluency with conversions used in digital systems. Here we check binary, hexadecimal, and Binary-Coded Decimal (BCD) representations for the decimal number 15.

Given Data / Assumptions:

• Decimal value: 15.
• Binary representation: base-2 positional system.
• Hex representation: base-16 using symbols 0–9 and A–F.
• BCD: 4-bit codes for each decimal digit.

Concept / Approach:
Convert 15₁₀ to binary by successive division-by-2: 15 → 1111₂. In hex, 1111₂ corresponds to F₁₆. For BCD, represent each decimal digit separately: “1” → 0001 and “5” → 0101, concatenated as 0001 0101.

Step-by-Step Solution:
Binary: 15 = 8 + 4 + 2 + 1 → 1111₂.Hex: group binary by 4 bits → 1111₂ = F₁₆.BCD: digit 1 → 0001; digit 5 → 0101 → 0001 0101.All three forms are consistent with 15₁₀.

Verification / Alternative check:
Reverse conversions: F₁₆ → 15₁₀; BCD 0001 0101 → digits 1 and 5 → 15₁₀.

Why Other Options Are Wrong:
Claiming BCD cannot represent 15 is false; BCD represents each decimal digit, not the entire value in binary.

Common Pitfalls:
Confusing BCD with binary of the whole number; forgetting that grouping by nibbles (4 bits) maps neatly between binary and hex.

Final Answer:
Correct