Base conversion — convert the hexadecimal number to binary. Task: Convert C0B₁₆ into its binary equivalent (expand each hex digit into 4 bits).

Introduction / Context:Hexadecimal and binary interconvert cleanly because one hex digit equals a 4-bit group. Engineers convert hex to binary to inspect bitfields, flags, and masks precisely during low-level programming and hardware work.

Given Data / Assumptions:

• Hex number: C0B₁₆
• Digit values: C = 12, 0 = 0, B = 11
• No sign or fractional part; simple integer conversion

Concept / Approach:Replace each hex digit with its 4-bit binary nibble: C → 1100, 0 → 0000, B → 1011. Concatenate the nibbles in order to obtain the final binary string with no leading suppression beyond the natural nibbles.

Step-by-Step Solution:

Verification / Alternative check:Convert back to hex by regrouping: 1100 (C), 0000 (0), 1011 (B). The round-trip confirms correctness. As a decimal sense-check: C0B₁₆ = 1216^2 + 016 + 11 = 3072 + 11 = 3083; binary 110000001011₂ also equals 3083₁₀.

Why Other Options Are Wrong:

• 110000001001 / 110000001100 / 110100001011 / 111000001011: each has at least one nibble mismatched to the original hex digits.

Common Pitfalls:

• Mistyping B as 1010 (A) or 1101 (D).
• Dropping or adding zeros in the middle nibble for 0.

Final Answer:110000001011