BCD encoding — two-digit example Represent the decimal value 11 in BCD (Binary-Coded Decimal) using two 4-bit nibbles.

Introduction / Context:
BCD encodes each decimal digit independently into 4 bits. Thus, a multi-digit number is stored as a sequence of 4-bit nibbles, one per decimal digit. This preserves decimal digit boundaries, which simplifies display and certain arithmetic routines at the cost of storage efficiency versus pure binary.

Given Data / Assumptions:

• Target number: 11 in decimal (two digits: 1 and 1).
• Standard BCD mapping: 0→0000, 1→0001, …, 9→1001.
• No sign nibble or decimal point involved.

Concept / Approach:

Convert each decimal digit independently to a 4-bit code and then concatenate the codes in the same order (most significant digit first). For 11, both digits are 1, so both nibbles are identical.

Step-by-Step Solution:

Verification / Alternative check:

Reverse mapping: split 00010001 into 0001 and 0001 → digits 1 and 1 → 11 decimal. This confirms correct BCD representation.

Why Other Options Are Wrong:

00001011 is the pure binary of decimal 11 (1011) padded to 8 bits, not BCD.

00001100 equals binary 12 padded, not BCD for 11.

00010010 corresponds to digits 1 and 2 (i.e., 12 in BCD), not 11.

Common Pitfalls:

Confusing BCD with binary of the entire number, or reversing digit order. Always encode each decimal digit separately in BCD problems.

Final Answer:

00010001