BCD to Binary — Convert 0001 0010 0110 (BCD) to Pure Binary A BCD code of 0001 0010 0110 represents the decimal digits 1, 2, and 6. Convert this BCD value to its equivalent pure binary representation.

Introduction / Context:
Binary Coded Decimal (BCD) encodes each decimal digit separately using 4 bits. To obtain a pure binary number, first interpret the BCD as a standard decimal value, then convert that decimal to base-2. This question strengthens fluency with both codings.

Given Data / Assumptions:

• BCD digits: 0001 0010 0110.
• Digit mapping: 0001 = 1, 0010 = 2, 0110 = 6.
• Therefore the decimal value is 126.

Concept / Approach:
Step 1: Decode BCD to decimal by reading each 4-bit group as a digit. Step 2: Convert the resulting decimal number to binary using place values or division by 2. For 126, determine the combination of powers of two that sums to 126.

Step-by-Step Solution:
Decode BCD: 0001 0010 0110 → 1 2 6 → decimal 126.Find nearest powers of two: 64, 32, 16, 8, 4, 2, 1.Express 126 = 64 + 32 + 16 + 8 + 4 + 2.Write ones for used powers and zeros otherwise: 1111110 (bit weights 64 32 16 8 4 2 1).

Verification / Alternative check:
Convert 1111110 back to decimal: 64 + 32 + 16 + 8 + 4 + 2 = 126, matching the original decimal value obtained from BCD.

Why Other Options Are Wrong:

• 1111101: Equals 125 decimal.
• 1111000: Equals 120 decimal.
• 1111111: Equals 127 decimal.

Common Pitfalls:
Treating the entire 12-bit BCD as one binary number directly, or misreading a 4-bit BCD group like 0110 as decimal 6 but then re-encoding incorrectly.

Final Answer:
1111110