States in a BCD (decade) counter: How many unique states are present in a Binary-Coded Decimal (BCD) decade counter sequence?

Introduction / Context:BCD counters are used to represent decimal digits 0 through 9 using binary patterns. Understanding their number of states is essential for designing display drivers, timers, and digital instruments that need decimal outputs.

Given Data / Assumptions:

• BCD encodes decimal digits 0..9 with four-bit binary codes.
• After reaching 9, the counter resets to 0.
• Illegal codes (1010..1111) are skipped or corrected.

Concept / Approach:A BCD decade counter cycles through exactly ten valid states, corresponding to digits 0 to 9: 0000 to 1001. It then resets or recycles, giving a MOD-10 sequence. This behavior is different from a straight 4-bit binary counter, which would have 16 states (MOD-16).

Step-by-Step Solution:

Verification / Alternative check:Datasheets for BCD counters (e.g., decade counters) label them MOD-10 and show reset logic to skip the six unused codes.

Why Other Options Are Wrong:

Common Pitfalls:Assuming a 4-bit register always cycles through 16 states; forgetting that BCD purposely avoids 1010..1111.

Final Answer:10