BCD to binary conversion — translate packed BCD 0001 0111 (i.e., decimal 17) into pure binary. Select the correct binary representation of decimal 17.

Introduction / Context:
Binary Coded Decimal (BCD) encodes each decimal digit into its own 4-bit nibble. Converting BCD to pure binary is a two-step process: first read the decimal digits from the BCD nibbles, then convert that decimal value to base-2. This skill is common in interfacing with displays, RTCs, and measurement devices that store values in BCD.

Given Data / Assumptions:

• BCD nibbles: 0001 and 0111.
• Interpretation: 0001 → 1, 0111 → 7.
• Therefore, the decimal value is 17.

Concept / Approach:
After decoding BCD into decimal, convert 17₁₀ into binary by expressing it as a sum of powers of two or by repeated division by 2. The goal is a minimal binary string with the most significant 1 at the 16’s place (2^4) for this number.

Step-by-Step Solution:

Verification / Alternative check:
Divide-by-2 method: 17/2=8 r1; 8/2=4 r0; 4/2=2 r0; 2/2=1 r0; 1/2=0 r1. Reading remainders upward gives 10001₂, confirming the result.

Why Other Options Are Wrong:

• 10101 = 21₁₀; 10010 = 18₁₀; 11000 = 24₁₀; 01111 = 15₁₀. None equals 17₁₀.

Common Pitfalls:

• Confusing BCD nibbles with a single binary value; BCD digits do not combine as base-2 place values.

Final Answer:
10001