BCD Counter: Carry Out for Cascade
Digital clocks, multimeters, and frequency counters rely on cascaded decimal stages to represent human-readable numbers. The carry-out signal of a Binary-Coded Decimal (BCD) counter acts as the enable for the next highest digit in the cascade.
A standard 4-bit binary counter overflows at 15, but a BCD counter wraps around after 9. The combinational carry-out logic must assert CO HIGH only when the counter state Q[3:0] reaches 9 (binary 1001). Assume the input state is a valid BCD digit (0 through 9). States 10 through 15 will never occur.
| Q3 | Q2 | Q1 | Q0 | CO | |------|------|------|------|------| | 0 | 0 | 0 | 0 | 0 | | 0 | 0 | 0 | 1 | 0 | | 0 | 0 | 1 | 0 | 0 | | 0 | 0 | 1 | 1 | 0 | | 0 | 1 | 0 | 0 | 0 | | 0 | 1 | 0 | 1 | 0 | | 0 | 1 | 1 | 0 | 0 | | 0 | 1 | 1 | 1 | 0 | | 1 | 0 | 0 | 0 | 0 | | 1 | 0 | 0 | 1 | 1 |
Constraints
- Use only combinational logic.
- Derive the output
COdirectly from the state bitsQ3,Q2,Q1, andQ0.
Topics
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