BCD to binary using weighting factors — convert two BCD numbers Convert the following BCD groups to pure binary using weighting factors (8–4–2–1 per digit). Treat the first two nibbles as one BCD number and the last three nibbles as a second BCD number: 0101 0011 0010 0110 1000

Introduction / Context:
BCD (Binary-Coded Decimal) encodes each decimal digit separately using 4 bits (8–4–2–1 weights). To convert full multi-digit BCD numbers into pure binary, first decode each BCD digit to its decimal value, then convert the complete decimal number to binary. The “weighting factors” method emphasizes interpreting each nibble correctly before performing the base-10 to base-2 conversion.

Given Data / Assumptions:

• Nibbles: 0101 0011 represent one number; 0010 0110 1000 represent a second.
• BCD digits map via 8–4–2–1 weights.
• We output pure binary (base-2), not BCD.

Concept / Approach:
Step 1: Translate each 4-bit BCD nibble to its decimal digit. Step 2: Combine the digits into a decimal number. Step 3: Convert that decimal to binary using division-by-2 or place-value decomposition. We present each converted number separated by a space, matching the format of the options.

Step-by-Step Solution:

Verification / Alternative check:
Use repeated division by 2: 53 → 110101, 268 → 100001100. Cross-check with place-value sums to confirm correctness.

Why Other Options Are Wrong:

• (a) Simply echoes the original BCD groups, not pure binary.
• (b) Incorrect lengths and values; not the proper binary of 53 and 268.
• (d) Bit pattern errors; digits do not correspond to the correct powers-of-two sums.

Common Pitfalls:
Confusing BCD with pure binary and concatenating nibbles directly; always convert the decimal value represented by the BCD digits into base-2.

Final Answer:
110101 100001100