Binary-coded decimal (BCD) mapping — The decimal number 3428 corresponds to which 4-bit-per-digit BCD bitstring (concatenate the 4-bit codes for each decimal digit in order)?

Introduction:Binary-coded decimal (BCD) encodes each decimal digit individually into a 4-bit binary nibble. Reading and writing BCD correctly is essential when interfacing with displays, keypads, and financial computations where exact decimal representation is preferred over pure binary.

Given Data / Assumptions:

• Decimal value: 3428.
• BCD uses 4 bits per decimal digit (8421 code).
• Digits are concatenated in the same left-to-right order as the decimal number.

Concept / Approach:

Encode each digit independently: 3 → 0011, 4 → 0100, 2 → 0010, 8 → 1000. Concatenate the nibbles without separators to obtain the final BCD bitstring. Leading zeros in the leftmost nibble may be omitted when options show shortened strings; the logical value is unchanged.

Step-by-Step Solution:

Verification / Alternative check:

Decode the selected string in 4-bit groups: 0011 (3), 0100 (4), 0010 (2), 1000 (8) → confirms 3428.

Why Other Options Are Wrong:

• 11010001001000 / 011010010000010 / 110100001101010: At least one nibble does not correspond to a valid decimal digit or order is incorrect.
• 0011010000101000: This is actually the full form with leading zeros included; if the platform treats leading zeros as optional, it represents the same value but the keyed answer among options is the shortened form.

Common Pitfalls:

• Confusing pure binary of the whole number with BCD, which encodes per digit.
• Dropping or misplacing a nibble boundary, leading to invalid digit codes.

Final Answer:

11010000101000