Convert the hexadecimal number 6B21 (base 16) to its exact binary (base 2) equivalent. Write the full 4-bit nibble for each hex digit.

Introduction / Context:Base conversion between hexadecimal and binary is routine in digital design and debugging. Each hex digit maps exactly to a 4-bit binary “nibble,” which makes the conversion quick and error-resistant when done systematically. We will convert 6B21 (hex) into binary by expanding each digit into 4 bits.

Given Data / Assumptions:

• Hex value: 6B21 (base 16).
• Hex-to-binary mapping uses 4 bits per hex digit.
• No leading nibbles are omitted; we keep all four nibbles.

Concept / Approach:Use the standard mapping: 0→0000, 1→0001, …, 9→1001, A→1010, B→1011, C→1100, D→1111, E→1110, F→1111. Expand each hex digit independently, then concatenate the nibbles in the same order to obtain the full binary string.

Step-by-Step Solution:6 (hex) → 0110.B (hex) → 1011.2 (hex) → 0010.1 (hex) → 0001.Concatenate: 0110 1011 0010 0001 → 0110101100100001.

Verification / Alternative check:Convert to decimal quickly: 6B21 (hex) = 616^3 + 1116^2 + 216 + 1 = 64096 + 11*256 + 32 + 1 = 24,576 + 2,816 + 33 = 27,425. Now check the binary value: 0110101100100001 (base 2) equals 27,425 decimal, confirming correctness.

Why Other Options Are Wrong:Each distractor differs in at least one nibble, often flipping a bit in the B or 2 positions, which changes the decimal value; only option A preserves the exact nibble mapping of 6, B, 2, 1.

Common Pitfalls:Dropping leading zeros in a nibble (e.g., writing 2 as 10 instead of 0010); reversing nibble order; confusing B (1011) with 13 (1101). Always write 4 bits per hex digit.

Final Answer:0110101100100001