BCD to 7-Segment Decoder
Digital clocks, multimeters, and legacy instrumentation rely on translating binary-coded decimal values into human-readable numeric displays. The 7-segment decoder acts as the bridge between internal machine state and physical light-emitting diodes.
The circuit accepts a 4-bit binary input A, B, C, D (where A is the most significant bit) representing digits 0 through 9. It drives seven independent outputs corresponding to segments a through g. Input values 10 through 15 will never occur in a valid BCD system and act as don't-care conditions.
| A | B | C | D | a | b | c | d | e | f | g | |-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----| | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 |
Constraints
- Implement the logic using only combinational gates.
- Optimize each segment's logic independently by treating inputs 10 through 15 as don't-care conditions.
- Minimize the total gate count for each output.
Topics
Solve this problem
Place the gates, wire them up and watch the signals settle. Every submission runs on the same simulation engine that grades it.
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