Decimal-to-BCD encoder inputs How many separate input lines must a decimal-to-BCD encoder provide to uniquely encode decimal digits 0 through 9?

Introduction / Context:
An encoder maps many input lines into a smaller set of output bits. A decimal-to-BCD encoder accepts one-of-ten decimal inputs (0–9) and outputs a 4-bit binary-coded-decimal representation. Understanding the number of input lines clarifies pin counts and truth-table sizing for practical IC selection and schematic design.

Given Data / Assumptions:

• Digits 0–9 must be represented.
• Only one decimal input is active at a time (one-hot input model).
• Outputs are 4 BCD lines representing 0000–1001.

Concept / Approach:

For N distinct symbols in a one-hot input scheme, the encoder needs N inputs. Decimal digits are ten symbols, so 10 input lines are required, each mapped to a unique 4-bit BCD output.

Step-by-Step Solution:

Verification / Alternative check:

Examine common encoder ICs or truth tables (e.g., 10-to-4 encoders): there are 10 input pins, often with enable/priority features.

Why Other Options Are Wrong:

4 and 8 are fewer than the number of symbols; 16 would imply hexadecimal.

Common Pitfalls:

Confusing encoder inputs with decoder outputs; a decoder would have 10 outputs for BCD-to-decimal.

Final Answer:

10