Binary-to-hexadecimal conversion technique: When converting a binary value to hexadecimal, is it valid to pad the left side (most significant side) with leading zeros to form complete groups of 4 bits before translating each group to a hex digit?

Introduction / Context: Hexadecimal is a compact way to express binary numbers by grouping bits in sets of four, since 16 = 2^4. This question tests whether you may add leading zeros on the most significant side of a binary number to complete 4-bit groups prior to conversion to hexadecimal digits.

Given Data / Assumptions:

• A binary number may not have a length that is a multiple of 4.
• Leading zeros do not change the value of an unsigned number.
• Hex conversion maps each 4-bit nibble to one hex digit (0–F).

Concept / Approach: Adding zeros to the left (toward the MSB) simply increases the bit width without altering numeric value. Grouping bits into 4-bit nibbles aligns perfectly with hexadecimal, enabling a one-to-one mapping from each nibble to a hex character. This is standard practice in debugging, memory dumps, and digital design documentation.

Step-by-Step Solution:

Verification / Alternative check: Convert back from the hex digits to binary and verify that dropping any leading zeros restores the original bit pattern; the numeric value remains unchanged.

Why Other Options Are Wrong: Signedness does not affect leading zeros for magnitude; requiring MSB = 1 is unnecessary; octal uses 3-bit groups, not 4-bit groups.

Common Pitfalls: Mistaking leading zeros for sign extension (that applies to two’s complement when extending sign with 1s for negative numbers); confusing octal grouping (3 bits) with hex grouping (4 bits).

Final Answer: Correct