Base Conversion — Binary to Hexadecimal Convert the binary number 1100101000110101 to its hexadecimal equivalent. Choose the correct hex representation.

Introduction / Context:
Hexadecimal is a compact way to represent binary values because 16 equals 2^4, allowing a direct 4-bit to 1-hex-digit mapping. This conversion skill is essential for reading memory dumps, opcodes, and register values.

Given Data / Assumptions:

• Binary: 1100101000110101.
• Group into nibbles of 4 bits from the right.
• Map each nibble to its hex digit.

Concept / Approach:
Pad on the left if necessary so the length is a multiple of 4, then translate each 4-bit group using the mapping 0000=0 through 1111=F.

Step-by-Step Solution:
1) Group: 1100 1010 0011 0101.2) Convert: 1100=C, 1010=A, 0011=3, 0101=5.3) Combine: CA35.4) Therefore, the hexadecimal result is CA35.

Verification / Alternative check:
Convert back: C=12=1100, A=10=1010, 3=0011, 5=0101. Concatenating reproduces the original binary, confirming correctness.

Why Other Options Are Wrong:

• 121035: Not a valid consistent hex mapping of the groups.
• 53AC1 and 530121: Wrong length and ordering relative to 16-bit grouping.

Common Pitfalls:
Failing to start grouping from the right, forgetting to pad leading bits, or reversing nibble order.

Final Answer:
CA35