BCD encoding check — map each decimal digit to 4 bits Which BCD bit pattern represents the decimal value 342 using 3-digit packed groups?

Introduction / Context:
Binary-Coded Decimal (BCD) represents each decimal digit with its own 4-bit binary nibble. For multi-digit numbers, we concatenate nibbles for each digit in order. Here we encode 342 into BCD, ensuring the digit-by-digit mapping is correct and preserving leading zeros only as needed for alignment.

Given Data / Assumptions:

• Decimal input: 342 (three digits).
• BCD uses 4 bits per digit: 0→0000, 1→0001, …, 9→1001.
• No sign or decimal point is included.

Concept / Approach:

Translate 3 → 0011, 4 → 0100, 2 → 0010, then concatenate nibbles in the same order to produce the packed BCD string. Optional leading zeros on the very left may be omitted, so some answer choices shorten the leftmost group.

Step-by-Step Solution:

Verification / Alternative check:

Check each 4-bit chunk in the chosen answer: 0011 (3), 0100 (4), 0010 (2). Any deviation indicates a wrong digit mapping.

Why Other Options Are Wrong:

11010001001000 mis-maps the middle or last digit nibble ordering.

011010010000010 includes misplaced ones and zeros and an extra bit count.

110100001101010 shows an extra nibble and incorrect digit substitution.

Common Pitfalls:

Confusing BCD with pure binary of the entire number (which would be different), reversing digit order, or using invalid nibble values above 1001. Always map each decimal digit separately to a legal 4-bit nibble.

Final Answer:

11010000101000