Nibble grouping practice — convert a 16-bit binary value to hex: Translate the binary value 0010 1111 0111 1110 into its hexadecimal representation.

Introduction / Context:Hexadecimal is a compact way to express binary values. Every hex digit corresponds to a 4-bit nibble, making conversion between binary and hex a straightforward grouping exercise. This is essential when reading datasheets or debugging at the register level.

Given Data / Assumptions:

• Binary input: 0010111101111110.
• We will group from the left as 4-bit nibbles.
• No sign; pure bit-pattern conversion.

Concept / Approach:Partition the 16-bit binary into four nibbles. Convert each nibble independently to a hex digit and concatenate the digits in order. Leading zeros in the most significant nibble are preserved when a fixed width is implied (16 bits here).

Step-by-Step Solution:Group: 0010 1111 0111 1110.0010 → 2.1111 → F.0111 → 7.1110 → E.Combine → 2F7E16.

Verification / Alternative check:Decimal spot-check: Convert 2F7E16 back to binary nibbles 0010 1111 0111 1110; the round-trip confirms correctness.

Why Other Options Are Wrong:77F216, 4EEE16, and 2F7716 each mismatch at least one nibble compared to the given binary, so their hex digits do not map to the provided bit pattern.

Common Pitfalls:Accidentally regrouping bits from the right without maintaining the original fixed width; misreading 1110 (E) and 1111 (F).

Final Answer:2F7E16