Hexadecimal to decimal conversion Convert the hexadecimal number 731₁₆ to its decimal (base 10) value.

Introduction / Context:
Hexadecimal (base 16) is compact for representing binary values because each hex digit corresponds to exactly four binary bits. Converting hex to decimal uses the same positional method as any base conversion: multiply each digit by its power of 16 and sum the results.

Given Data / Assumptions:

• Hex number: 731₁₆ (digits 7, 3, 1).
• Powers of 16: 16^0 = 1, 16^1 = 16, 16^2 = 256.
• Digit values: 7 = 7, 3 = 3, 1 = 1 (A–F would map to 10–15).

Concept / Approach:
Apply positional notation: value = d216^2 + d116^1 + d016^0. This yields an exact integer result for any hex numeral.

Step-by-Step Solution:

Verification / Alternative check:
Convert to binary nibbles first: 7→0111, 3→0011, 1→0001 → 0111 0011 0001₂, then evaluate as binary to decimal to confirm 1841.

Why Other Options Are Wrong:

• 216.4: Decimal conversion of an integer in hex must be an integer; fractional result is invalid.
• 985: Equals 0x3D9 decimal, not 0x731.
• 3D9: This is a hex string, not a decimal value; 0x3D9 = 985.

Common Pitfalls:
Reversing the order of remainders, confusing hex digits with decimal digits, or miscomputing 16^2.

Final Answer:
1841