Binary to hexadecimal by nibble grouping Convert the binary number 111111110010 (base 2) to hexadecimal (base 16).

Introduction / Context:Hexadecimal maps cleanly onto binary because every 4 binary bits (a nibble) correspond to one hex digit. Grouping the binary string into nibbles from right to left enables fast, error-resistant conversion. We will apply that rule here and verify the result by mapping each nibble to its hex equivalent.

Given Data / Assumptions:

• Binary input: 111111110010.
• Left padding with zeros is allowed to complete the leftmost nibble.
• Use standard hex digits 0–9 and A–F.

Concept / Approach:

Partition the bits into 4-bit groups from right to left, then translate each group using the table 0000→0 … 1111→F. Keep the order of nibbles the same (most significant nibble on the left).

Step-by-Step Solution:

Verification / Alternative check:

Convert the last nibble 0010 back to confirm → 2. The leading two nibbles 1111→F and 1111→F are standard and unambiguous. Reassembling returns to the original bit pattern.

Why Other Options Are Wrong:

EE216 would require nibbles 1110 1110, not present here.

2FE16 implies nibble order 0010 1111 1110, which is incorrect ordering.

FD216 requires 1111 1101 0010; the middle nibble would be 1101 (D), not 1111 (F), so it does not match.

Common Pitfalls:

Grouping from the left instead of the right, forgetting to pad the most significant nibble, or accidentally reordering nibbles. Always move right-to-left in binary when forming hex nibbles.

Final Answer:

FF216