Convert the binary number 1001001₂ to its hexadecimal (base 16) equivalent, showing grouping and place-value verification.

Introduction / Context:Binary–hexadecimal conversion is common because each hex digit maps exactly to 4 binary bits (a nibble). This makes grouping straightforward and error-resistant compared with decimal conversions.

Given Data / Assumptions:

• Binary input: 1001001₂.
• Target base: 16 (hexadecimal).
• No fractional bits.

Concept / Approach:Pad the binary string on the left, if necessary, so its length is a multiple of 4. Then translate each 4-bit group directly to one hex digit using the standard 0–F mapping.

Step-by-Step Solution:

Verification / Alternative check:Compute binary place values: 1*2^6 + 1*2^3 + 1*2^0 = 64 + 8 + 1 = 73. Converting 73 to hex gives 4*16 + 9 = 49₁₆, confirming the result.

Why Other Options Are Wrong:

• 40₁₆: equals 64 decimal; too small.
• 39₁₆: equals 57 decimal; incorrect.
• 42₁₆: equals 66 decimal; incorrect.
• None of the above: false because 49₁₆ is correct.

Common Pitfalls:Failing to pad on the left to a multiple of 4 bits or misreading the 1001₂ nibble as 8 instead of 9.

Final Answer:49₁₆