Why hexadecimal is popular: The main advantage of hexadecimal numbers is the ease of conversion from hexadecimal to _____ and vice versa.

Introduction / Context:
Hexadecimal (base-16) and binary (base-2) are tightly related because 16 is a power of 2. This relationship allows clean grouping of bits into nibbles (4-bit chunks), making conversions direct and error-resistant compared to decimal conversions.

Given Data / Assumptions:

• A hex digit equals exactly 4 binary bits.
• We seek the system that offers the easiest two-way conversion with hex.
• Standard computing notation and grouping rules apply.

Concept / Approach:
Each hex digit maps to 0000–1111 in binary. Converting hex to binary is just replacing each hex digit by its 4-bit equivalent; converting binary to hex is grouping binary digits into sets of four (padding with leading zeros when needed) and translating each group to a hex digit. Decimal and BCD require arithmetic; ASCII/“ASCE” is a character encoding, not a numeric base.

Step-by-Step Solution:
Recognize that hex ↔ binary is a 1-to-1 mapping per nibble.Note that no division or multiplication is required; only table lookup or mental mapping is needed.Therefore, select “binary.”

Verification / Alternative check:
Example: hex 0x3A = binary 0011 1010. Reverse by regroupping bits into nibbles → 3 and A.

Why Other Options Are Wrong:
Decimal conversion involves arithmetic and is not as direct. “ASCE” (likely ASCII) is unrelated to numeric base conversion. BCD is a storage encoding of decimal digits, not a natural power-of-two base.

Common Pitfalls:
Forgetting to pad the leftmost binary group to 4 bits can cause digit misalignment.

Final Answer:
binary.