Truth-table size of a BCD decoder A BCD (Binary-Coded Decimal) decoder accepts valid 4-bit BCD inputs for digits 0–9. How many rows (valid input cases) appear in its functional truth table for the decimal digits?

Introduction / Context:
BCD represents decimal digits using 4-bit codes 0000 through 1001. A BCD decoder activates a unique output for each valid digit (e.g., for seven-segment displays or one-of-ten lines). Counting the number of valid input rows in the truth table clarifies device behavior and helps when designing with invalid-code handling for 1010–1111.

Given Data / Assumptions:

• Valid BCD inputs: 0000–1001 (ten patterns).
• Invalid inputs: 1010–1111, typically ignored or treated as don’t-care by the decoder.
• Decoder maps each valid input to a specific output pattern/line.

Concept / Approach:

Count the valid BCD codes. There are ten decimal digits, hence ten valid code words and ten corresponding rows in the functional truth table that map directly to decimal outputs. Some datasheets show additional rows for invalid inputs, but the canonical “BCD decoder truth table for digits” has 10 main rows.

Step-by-Step Solution:

Verification / Alternative check:

Review 7447/7448 (BCD-to-seven-segment) documentation: ten entries illustrate segment patterns for digits 0–9; entries for 10–15 are either undefined or treated as blank/reset.

Why Other Options Are Wrong:

9 and 8 undercount the valid decimal symbols; 3 is unrelated.

Common Pitfalls:

Confusing a complete 4-bit truth table (16 rows including invalid codes) with the functional, digit-focused mapping (10 valid rows).

Final Answer:

10