Implement a Full Adder Using a 3:8 Decoder and OR Gates
Read-only memory and look-up tables often implement multiple Boolean functions simultaneously by decoding all possible input combinations once. The full adder provides a canonical example of this architecture: a single decoder generates all minterms, which are then selectively combined to produce both the sum and carry outputs.
The circuit must implement a standard 1-bit full adder with inputs A, B, and Cin. The outputs Sum and Cout must be generated by combining the appropriate minterm outputs from a single shared 3-to-8 decoder.
| A | B | Cin | Cout | Sum | |-----|-----|-------|--------|-------| | 0 | 0 | 0 | 0 | 0 | | 0 | 0 | 1 | 0 | 1 | | 0 | 1 | 0 | 0 | 1 | | 0 | 1 | 1 | 1 | 0 | | 1 | 0 | 0 | 0 | 1 | | 1 | 0 | 1 | 1 | 0 | | 1 | 1 | 0 | 1 | 0 | | 1 | 1 | 1 | 1 | 1 |
Constraints
- Use exactly one 3:8 decoder for the entire circuit.
- Use only OR gates for the remaining logic.
- Do not use any other logic gates or arithmetic components.
- Purely combinational logic only.
Topics
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