Convert the binary number 101101₂ into its hexadecimal representation (showing the correct base-tagged form).

Introduction / Context:
Number base conversions are foundational in digital electronics and computer systems. Converting from binary to hexadecimal is particularly common because one hex digit corresponds exactly to a nibble (4 bits), simplifying interpretation of machine words, addresses, and opcodes. This question reinforces grouping and mapping rules.

Given Data / Assumptions:

• Binary input: 101101₂.
• Target base: hexadecimal (base 16).
• Standard digit mapping: 0000–1111 maps to 0–F.

Concept / Approach:

To convert binary to hex, group bits into 4-bit nibbles from the right. Pad the leftmost group with leading zeros if needed. Then map each nibble to its corresponding hex digit using the 0–F table. Finally, write the result with a base tag such as 16 to avoid ambiguity.

Step-by-Step Solution:

Verification / Alternative check:

Decimal cross check: 101101₂ = 132 + 016 + 18 + 14 + 02 + 11 = 45. Also, 2D16 = 2*16 + 13 = 45. The results are consistent.

Why Other Options Are Wrong:

3716 corresponds to 55 decimal, not 45. 2E16 equals 46 decimal. 2716 equals 39 decimal. 'None of the above' is wrong because 2D16 is correct.

Common Pitfalls:

Forgetting to pad the leftmost nibble, misreading D (13) as E (14), or grouping bits from the left instead of from the right.

Final Answer:

2D16