Octal to Binary Conversion — Triplet Mapping Convert the octal number 104 (base 8) into its equivalent binary representation, showing how each octal digit expands into three binary bits.

Introduction / Context:
Octal to binary conversion is common in digital electronics because base 8 aligns neatly with base 2. Each octal digit corresponds to a fixed group of three binary bits. This question reinforces the quick mental mapping and the method of grouping or expanding digits without arithmetic longhand.

Given Data / Assumptions:

• Given value: 104 base 8.
• Each octal digit expands to a 3-bit binary group using 0→000 through 7→111.
• No sign or fractional point is present, and no leading group should be dropped except leading zeros that exist only as padding.

Concept / Approach:
Because 8 = 2^3, there is a one to one mapping between an octal digit and a 3-bit binary nibble of width three. Therefore convert each octal digit independently and concatenate the results from left to right to form the final binary string.

Step-by-Step Solution:
1) Write the mapping table snippet: 0→000, 1→001, 2→010, 3→011, 4→100, 5→101, 6→110, 7→111.2) Expand the most significant digit 1 as 001.3) Expand the middle digit 0 as 000.4) Expand the least significant digit 4 as 100.5) Concatenate groups: 001 000 100 → 001000100 base 2.

Verification / Alternative check:
Convert back to octal by grouping the binary result into triplets from the right: 001 000 100 gives 1 0 4 in base 8, confirming the round trip is correct.

Why Other Options Are Wrong:

• 1000000012: Represents 401 base 8 when re-grouped, not 104.
• 00101002: Corresponds to octal 122, not 104.
• 10000012: Mismatch of triplets that suggests 401 as well when regrouped.

Common Pitfalls:
Dropping leading zeros at the left of the most significant triplet, or attempting arithmetic conversion instead of direct triplet expansion, which is slower and error prone.

Final Answer:
0010001002