Binary to hexadecimal grouping — write compact hex form Express the binary number 11101011000111010 in hexadecimal notation.

Introduction / Context:
Binary-to-hex conversion is efficient because hexadecimal digits map neatly to groups of 4 bits (nibbles). Converting by grouping avoids long division and reduces error risk. We will pad on the left as needed to form complete 4-bit groups, then translate each nibble to a hex digit.

Given Data / Assumptions:

• Binary input: 11101011000111010.
• We want a hexadecimal output (base 16).
• Left padding with zeros is allowed for a complete nibble.

Concept / Approach:

Partition the binary string into 4-bit nibbles from right to left. Map each nibble to hex using 0000→0 … 1111→F. If the leftmost group has fewer than 4 bits, pad with leading zeros to a full nibble.

Step-by-Step Solution:

Verification / Alternative check:

Convert back a digit or two: D = 1101 and A = 1010 appear at the ends of the grouped string; re-grouping reproduces the original bits, confirming consistency.

Why Other Options Are Wrong:

DD63A16 duplicates the first nibble (1→D), producing too many bits.

1D33A16 replaces the middle nibble 6 with 3, altering the bit pattern.

1D63116 substitutes the last nibble A with 1, changing 1010 to 0001.

Common Pitfalls:

Grouping left-to-right instead of right-to-left, forgetting to pad the most significant nibble, or mistranslating a nibble (especially 10–15 which map to A–F). Always check the count of bits equals 4 times the number of hex digits.

Final Answer:

1D63A16