Mixed-base conversion practice: Convert the octal number 143₈ to its hexadecimal (base 16) equivalent.

Introduction / Context:
Octal and hexadecimal are compact ways to represent binary values. Converting between them is efficient via an intermediate binary mapping because 8 = 2^3 and 16 = 2^4, so digit boundaries align to groups of 3 or 4 bits respectively.

Given Data / Assumptions:

• Given: 143 in base 8.
• Find: equivalent in base 16.
• No change in value; only representation differs.

Concept / Approach:
Two straightforward methods: (1) convert 143₈ → binary by expanding each octal digit to 3 bits, then regroup into 4-bit nibbles to form hexadecimal; or (2) convert octal → decimal, then decimal → hexadecimal. Both lead to the same result when done correctly.

Step-by-Step Solution:
Decimal route: 143₈ = 18^2 + 48 + 3 = 64 + 32 + 3 = 99₁₀.Convert 99₁₀ to hex: 99 / 16 = 6 remainder 3 → 0x63.Therefore, 143₈ = 63₁₆.

Verification / Alternative check:
Binary route: 1→001, 4→100, 3→011; concatenate 001100011₂; group from right into 4-bit nibbles: 0110 0011 → 6 3 → 0x63. Same result confirms correctness.

Why Other Options Are Wrong:
6016, 5016, and 5716 correspond to different decimal values. Only 6316 matches 99₁₀ exactly.

Common Pitfalls:
Mis-grouping bits when switching between 3-bit and 4-bit boundaries; dropping leading zeros that help correct nibble grouping.

Final Answer:
6316